Autonomous Restructuring of Asteroids into Rotating Space Stations

February 2023 Asteroid Restructuring 1
Autonomous Restructuring of Asteroids into Rotating Space Stations
David W. Jensen, Ph.D.
Technical Fellow, Retired
Rockwell Collins
Cedar Rapids, IA 52302
david.jensen@alumni.iastate.edu
Abstract
Asteroid restructuring uses robotics, self replication, and mechanical automatons to autonomously restructure an asteroid into
a large rotating space station. The restructuring process makes structures from asteroid oxide materials; uses productive self-
replication to make replicators, helpers, and products; and creates a multiple floor station to support a large population.
In an example simulation, it takes 12 years to autonomously restructure a large asteroid into the space station. This is accom-
plished with a single rocket launch. The single payload contains a base station, 4 robots (spiders), and a modest set of supplies.
Our simulation creates 3000 spiders and over 23,500 other pieces of equipment. Only the base station and spiders (replicators)
have advanced microprocessors and algorithms. These represent 21st century technologies created and transported from
Earth. The equipment and tools are built using in-situ materials and represent 18th or 19th century technologies. The equipment
and tools (helpers) have simple mechanical programs to perform repetitive tasks. The resulting example station would be a
rotating framework almost 5 kilometers in diameter. Once completed, it could support a population of over 700,000 people.
Many researchers identify the high launch costs, the harsh space environment, and the lack of gravity as the key obstacles
hindering the development of space stations. The single probe addresses the high launch cost. The autonomous construction
eliminates the harsh space environment for construction crews. The completed rotating station provides radiation protection
and centripetal gravity for the first work crews and colonists.
Keywords: Space station, asteroid, autonomous, automaton,
productive replicator, anhydrous glass
1 Asteroid Restructuring - Introduction
Many researchers identify the high launch costs, the harsh
space environment, and the lack of gravity as key obstacles
hindering the development of space stations. Two of these
obstacles produce detrimental effects on human workers (ra-
diation and low gravity). In this paper we overview an ap-
proach to use robotics, self replication, and mechanical au-
tomatons to autonomously restructure an asteroid into a mul-
tiple-floor rotating space station. Researchers have designed
space station for over fifty years. In the restructuring process,
we use robotics to completely automate the building process.
Other than a modest seed package of materials, we use only
the bulk material of an asteroid to build our station. We show
in Figure 1-1 a rendering of an envisioned station with its
remaining asteroid and a moon.
Individuals familiar with previous space exploration and
habitat construction studies [Johnson and Holbrow 1977]
[Globus et al. 2007] [Metzger et al. 2012] often have precon-
ceived notions of how this restructuring effort will work. Ta-
ble 1-1 contains bullet summaries to help define the restruc-
turing process. One column outlines what the restructuring
process “produces” and the other column outlines what the
restructuring process “does not produce.”
Our goal is to land on an asteroid and restructure it to become
the enclosed framework of a space station with a wealth of
inventoried supplies. Using a modest seed package of mate-
rials and tools, robotic workers use the asteroid material to
create copies of themselves, tools, vehicles, and automata.
Credit: Self produced with Blender using Background Milky Way:
ESO/Serge Brunier [Brunier 2009] [CC BY-4.0]; Doug Ellison model [El-
lison 2018] [CC BY-4.0] modified/rescaled to appropriate Atira and
Moon dimensions
Figure 1-1 – Large Rotating Space Station

The initial probe and seed package are built with state-of-the-
art 21st
century technology. The materials, tools, vehicles,
and automata produced on the asteroid will be more like 18th
and 19th
century technology. The seed package includes sev-
eral thousand 21st
century circuit board modules to replicate
spiders; however, the spider framework, legs, connectors,
and covers will ultimately be built with in-situ asteroid ma-
terial and 19th
century processes.
An initial set of four spiders use these modules and processes
to construct thousands of robots and mechanical automata.
With thousands of spiders and tens of thousands of mechan-
ical automata, our simulations show that a large asteroid
could be completely restructured into a usable space station
framework in about twelve years. Within a decade, some
parts of the space station would be ready for habitation. The
rotating space station provides Earth-like gravity. A thick
shell with regolith fill provides radiation protection. The
mining and manufacturing process also produces excess
metal and frozen volatiles. The spiders use sensors (e.g., test-
ing jigs, optical, and base station) to measure and identify
metals and volatiles. The identified products are categorized
and stored in the station. This inventory information will be
relayed to Earth and support the planning of future manned
missions. The first manned mission will arrive at the rotating
space station and be able to use these excess materials to en-
hance the framework with air, energy, heating, cooling, and
light. The restructuring process overcomes the detrimental
effects of space on human workers and the high cost of
launching building material.
Asteroid restructuring mandates understanding technology
details on space stations, asteroids, and robotics. We provide
a section on each of these topics. Although somewhat
lengthy, these sections are simply overviews and exclude
much available detail. We first present a section on asteroids.
This provides the background and information required to
select an asteroid for the restructuring mission. We next pre-
sent a section on space stations. This provides the back-
ground and information on the type of space station to create
from the asteroid. The third section covers robotics. This pro-
vides the background and information describing the process
to convert the asteroid into the space station. We include a
fourth section to discuss system and construction concepts.
These concepts include technology aspects from all three
subject areas. The paper ends with a section covering future
thoughts. This section includes final thoughts on station ge-
ometry, shuttle traffic, early colonist activities, asteroid
moons, and future projects for restructuring. This section
ends with our conclusions for asteroid restructuring.
2 Asteroid Restructuring – Asteroids
The purpose of this section is to review asteroid characteris-
tics and select one for the restructuring process. We organize
this section with subsections on background, analysis, re-
sults, and a summary.
2.1 Asteroids – Background
The goal of the restructuring process is to convert an asteroid
to an enclosed space habitat framework. We offer in this
background section an overview on asteroids. We introduce
examples of asteroids, spectral classification, asteroid min-
ing, and surface characteristics. We also overview asteroid
resources and applications from those resources.
2.1.1 Asteroid – Background Credit
Asteroids exist throughout the solar system and vary in com-
position, shape, size, and surface features. These various at-
tributes help define the restructuring process and the asteroid
selection. For our background on asteroids, we present key
asteroid characteristics and research. In our later analysis and
results sections, we present the selection process using those
characteristics.
• Researchers use multiple approaches to determine aster-
oid types and materials. We use approaches and results
developed by [Kesson 1975] [Ross 2001] [Mazanek et al.
2014] [Angelo 2014] and [Metzger 2015]. We use data
from meteorites, asteroid spectral data, and lunar sample
analysis to define our asteroid metrics.
• Terrestrial, lunar, and asteroid mining processes have
been studied by many researchers. We use mining and
beneficiation of lunar ores from [Williams et al. 1979],
mining concepts from [Vandenbos 2006], and lunar
Table 1-1 – Restructuring Process Definition
What Restructuring Produces: What Restructuring Does Not Produce:
• Space station framework construction
• Multiple story/floor habitat design supporting large populations
with abundant living space
• Earth like gravity and radiation protection
• Relatively low cost – low risk – automata intensive
• Inventoried valuable materials – metals & volatiles
• Single launch seed probe – completely autonomous – minimal
human interaction
• No personnel support in space - minimal ground support required
once launched
• Historic 18th and 19th century tools, technologies, and materials
• Processing with thousands of small systems
• Near 100% closure coverage using in-situ materials and initial seed
• Advances using 21st century robotics and artificial intelligence
• Finishing touches on space station
• Efficient small living quarters geared for short transportation
distances
• Earth like air and temperature environment
• High cost – high risk – human labor intensive
• Mining business
• Multiple launches – semi-autonomous – human in the loop
• Launches of personnel, human base stations in space, extensive
ground support
• Advanced 20th and 21st century tools, technologies, and materials
• Processing with a large monolithic system
• Requirement for continuous flow of support material and multiple
launches
• Requirements for an Apollo or Artemis class program

resource processing from [Kayser 2011], and solar fur-
nace concepts from [Sanders and Larson 2012].
• Missions to orbit and survey asteroids are occurring more
frequently. We use concepts and parameters from various
space missions and literature [Maynard and Sevier 1966]
[Doody 2011] [Bradley et al. 2012] and [Fritz and
Turkoglu 2017] to plan our mission to a selected asteroid.
• Most asteroid mining studies focus on retrieving and pro-
cessing metals and/or volatiles. A good example study is
[Mazanek et al. 2014]. We use the asteroid oxides as
building materials and that changes the focus and mate-
rial priorities. We plan to use these oxides as rods or tiles
for our construction structures. It appears that these ox-
ides could be formed into anhydrous glass.
• Anhydrous glass has been found to have remarkably high
tensile strength [Bell and Hines 2012]. The asteroid vac-
uum environment will work well to create the anhydrous
glass. We use concepts and results from [Blacic 1985],
[Carsley, Blacic, and Pletka 1992], [Bell and Hines 2012]
and [Soilleux 2019]. Rapidly cooling the glass will in-
crease its strength [Yale 2013]. We envision that thin
plies of anhydrous glass would be stacked, pressed, and
sintered into high strength laminates.
• The asteroid restructuring process will produce excess
metal and frozen volatiles. We do not discard these prod-
ucts; instead, they are categorized and stored in the sta-
tion. This inventory will support future manned missions.
2.1.2 Asteroid Examples
There are over 150 million asteroids larger than 100 meters
diameter in our solar system. We want an asteroid with
enough material to build a large space habitat. There are al-
most one thousand asteroids over 1 kilometer in diameter
that are considered Near-Earth Objects (NEOs). Twenty-one
known NEOs are over four kilometers in diameter. Each has
enough material to construct a space station that could house
a million people. We show in Figure 2-1 a set of asteroids
ranging in radius from 256 meters to 2580 meters. We select
this set of asteroids to evaluate a range of sizes. Šteins is the
largest in that set and Bennu is the smallest.
Size is not the only important criteria. The location is im-
portant too. Ideally, we want the asteroid (and station) close
to Earth to better support tourism and trade. We want it to be
relatively close to the sun to provide solar power for manu-
facturing and energy. A station close to the orbit of Earth
would reduce round-trip travel time. Apollo and Aten class
asteroids cross the Earth’s orbit. Amor asteroids always stay
outside Earth’s orbit and Atira asteroids stay inside Earth’s
orbit. Šteins is in the inner edge of the asteroid belt. The other
asteroids of our set reside inside the orbit of Mars.
The asteroids shown in Figure 2-1 have had significant anal-
ysis and observation. The European Space Agency (ESA)
OSIRIS mission photographed 2867 Šteins in 2008. Atira is
a Near-Earth Object that has been radar imaged by the
Arecibo Observatory [Rivera-Valentin et al. 2017]. The as-
teroid Moshup is a Near-Earth Object that has been radar im-
aged by the Goldstone Observatory. The JAXA Hayabusa2
mission explored the asteroid Ryugu. The NASA OSIRIS-
REx mission explored the asteroid Bennu.
We include in Figure 2-1 known metrics from the JPL Small-
Body Database. The metrics for Šteins came from [Deller
2017]. A few metrics came from various Wikipedia pages.
Finally, we have computed our own estimates for missing
metrics. These metrics are important for the analyses and
simulations of this effort.
Besides the asteroids of Figure 2-1, we also considered 433
Eros, 25143 Itokawa, 65803 Didymos, 3753 Cruithne, and
the comet 67P/Churyumov-Gerasimenko. All these bodies
have had significant studies. They provide excellent exam-
ples of features that our restructuring process will need to
take into consideration. Space missions have explored some
of these asteroids. Others have been surveyed with Earth
based radar or space-based telescopes. Most have been spec-
trum-analyzed to provide insights on their surface materials.
We illustrate ten of these bodies in Figure 2-2. The bubble
chart organizes the bodies along their distance from the Sun
(semi-major axis) on the x-axis. It organizes them along their
diameters on the y-axis. The bubble size also represents their
diameters. The chart also includes coloring of the bubbles
Name 101955 Bennu 162173 Ryugu 66391 Moshup 163693 Atira 2867 Šteins
Diameter (km)
Volume (m3)
Mass (kg)
Material (m3)
Density (g/cm3)
Orbit (AU)
0.482
6.15e7
7.33e10
1.54e7
1.19
1.13
0.896
3.4e8
4.5e11
8.50e7
1.32
1.19
1.53x1.50x1.35
1.62e9
2.49e12
4.05e8
1.54
0.64
5.2x4.8×2.3
21.9e9
4.11e13
5.48e9
1.87
0.74
6.8×5.7×4.4
76.0 e9
1.98e14
19.8e9
1.9
2.36
Bennu: Credit: NASA/Goddard/University of Arizona; [NASA Image Public Domain]. Ryugu: Credit: JAXA, University of Tokyo & collaborators; [CC BY-NC-ND 4.0]. Moshup: Credit:
ESA; [ESA Standard License] Modified: Cropped Image. Atira: Credit: Self Produced with Blender using Doug Ellison model; [Ellison 2018] [CC BY-4.0] Modified: scaled to match
Atira dimensions. Šteins: Credit: Data from ESA 2008 OSIRIS Team, processing by T. Stryk [Stryk 2008]; [CC BY-SA 2.0].
Figure 2-1 – Asteroid Preview – Key Characteristics – Documented and Estimated Values

based on the asteroid’s spectral type. The asteroids covered
five different spectral types and we include a U-Type as the
undefined type of comet 67P. Comets are not typically given
a type and have an icy composition. The shapes of six of the
asteroids were ellipsoid, diamond, or somewhat spherical.
Three of the bodies were irregular or peanut shaped with two
major lobes. Three of the asteroids had moons.
This short review covered a broad set of asteroids. Their di-
ameters ranged from 350 meters to 16.8 kilometers. Their or-
bits ranged from 0.65 AU to 3.46 AU. There are dozens of
other asteroids with similar levels of detail. There are thou-
sands of asteroids with minimal physical and orbit infor-
mation. This wealth of information will guide the selection
of an asteroid for our restructuring effort.
2.1.3 Asteroid Spectral Classification
We need the composition of a target asteroid for our restruc-
turing effort. The structure of the asteroid will help determine
the mining and construction. The composition will help de-
termine the building material and construction approaches.
Significant research has been done to identify asteroid types.
Historically, observations of asteroids have been limited to
ground-based telescopic sensing of the visible, near infrared,
and radio spectrums. The surface of different asteroids re-
flect light uniquely. Scientists have used this reflected light
to understand the asteroid surface chemical composition. Re-
cently, ground-based spectral readings have been augmented
with satellite and space probe sensor measurements. Space
probes have visited several asteroids and obtained close
measurements. In the last decade, samples from a comet and
two asteroids have been returned to Earth. Spectral analysis
provides the foundation for current asteroid classification
schemes.
Because most meteorites come from asteroids, their taxono-
mies have relevance to understanding the composition of as-
teroids. Just like meteorites, the asteroids are classified into
three main groups. They are often classified as C-Type (Car-
bonaceous), S-Type (Stony or Siliceous), and M-Type
(Metal); see Figure 2-3a. More than 75% of asteroids are type
C carbonaceous, which now includes similar types B and D.
C-Type asteroids are more common in the asteroid belt and
D-Type asteroids become more common in the outer solar
system. Less than 17% of the asteroids are type S siliceous
and this now includes similar types R, V, and O. The S-Type
are more common in the inner solar system and inner asteroid
belt. The other 8% of asteroids are metallic type M, which
also includes similar types P, X, and E.
We provide in Figure 2-3b three major asteroid types. We
show the estimated composition for the asteroids computed
from three sources [Ross 2001] [Angelo 2014] [Mazanek et
al. 2014]. For most of the restructuring analysis, we use an
S-Type asteroid. A C-Type has similar percentage of materi-
als. In both cases, they are composed of over 80% oxides.
The S-Type asteroids have more free metal. The C-Type as-
teroids have more volatiles and water. The M-Type is quite
different in composition. The costs to extract and refine met-
als is higher than simply melting bulk oxide material. As
such, we want either an S-Type or C-Type and this affects
our final selection. Based on the sample from the JPL data-
base, almost 90% of the asteroids will be acceptable for our
restructuring effort.
A key take-away from Figure 2-3 is that most asteroids are
C-Type or S-Type, and those asteroids are comprised
Credit: Self produced using data from JPL Small Body Database Search
Engine; [JPL SBD Search Engine] [Public Domain]
Figure 2-2 – Asteroids Reviewed
a) Main Types of Asteroids
b) Materials in Asteroids
Credit: Self produced using data computed from [Ross 2001] [Angelo
2014] [Mazanek et al. 2014] [Facts]
Figure 2-3 – Main Groups of Asteroids
Other/Metallic (Iron and
nickel in X-type, E-type, M-
type asteroids)
8%
Siliceous (Stony and
metal oxides in S-type,
R-type, V-type, and O-
type asteroids)
17%
Carbonaceous (Organics and
water in C-type, B-type, and
D-type asteroids)
75%

primarily of oxides. The S-Type asteroid material is moder-
ately friable and more easily crushed than M-Type asteroid
metal materials. The C-Type asteroid material is weakly fri-
able and the easiest to crush for processing. For this study we
use the oxides as our building material. The stony asteroids
(S-Type) are dominated by silicates and are good candidates
for processing into our construction elements.
We note two other types of NEAs that are valuable from a
resource standpoint are designated as D-Type and P-Type.
Few of these types exist as NEAs because they likely origi-
nate from the outer main belt or beyond. These are believed
to be composed of organic-rich silicates, carbon, and anhy-
drous silicates, possibly with water ice in their interiors [Ma-
zanek et al. 2014]. Mining these in the future will be im-
portant but not for our immediate restructuring goals.
2.1.4 Asteroid Mining
Asteroid mining has been seriously considered for less than
50 years [O’Leary et al. 1979]. The major steps of terrestrial
mining are relevant to asteroid mining. The terrestrial mining
process can be organized with six major steps: prospecting,
excavating, processing, extracting, fabricating, and storing.
The restructuring process uses all these steps.
We provide one high-level view of the restructuring regolith
processing in Figure 2-4. This view focuses on the excava-
tion, processing, and extraction. We do not include many de-
tails in this summary. From the initial regolith, three groups
of resources are produced: free metal, volatiles, and oxides.
Many products can be created using these three resources.
A rubble pile asteroid will have loose surface material to in-
itially process. Small robotic systems will first bring regolith
dust, grains, and pebbles to the base station. Small pebbles
could be further fragmented with an impact crusher. Crush-
ers should reduce the fragments to grains and separate aggre-
gates of ice, silicates, and metals. Jaw crushers will reduce
cobbles and the product will be sized with screens. Larger
fragments will be crushed again. Mechanical systems will
use jack hammer chisels to reduce larger boulders. Monoliths
and slabs may require tunneling and blasting.
Magnetic beneficiation should extract most of the free ferro-
magnetic metal grains (iron, nickel, and cobalt) from the sil-
icate and carbonaceous grains. With additional complexity
and higher strength magnetic fields, we could extract the par-
amagnetic metals too (platinum, titanium, zirconium, and
magnesium). These metals will be separated, inventoried,
and stored. Some of the iron-nickel grains will be used for
3D printing of metal parts.
Mirror systems and Fresnel lenses will focus sunlight to pro-
cess the material. Low temperature solar heating will release
much of the free volatiles from the regolith grains. A typical
melt temperature of 1200°C is often referenced for oxides.
There will be volatiles chemically bound to the minerals that
will be released in this process. Cyclones can be used to sep-
arate the volatile gas from dust carried with the gas [O’Leary
et al. 1979]. Staged cooling and condensing of the volatiles
will separate the gasses for inventory and storage. Carefully
lowering the temperature will condense gasses in an order
like water (100°C), hydrogen sulfide (-60°C), carbon-diox-
ide (-78°C), methane (-161°C), oxygen (-183°C), carbon
monoxide (-191°C), nitrogen (-196°C), hydrogen (-253°C),
and helium (-269°C).
A solar furnace will be used to melt the regolith grains to cast
ceramic tiles and to produce anhydrous glass tiles. Initially
the tile production from the molten regolith will be in the
base station system. Casting is one option and could use a
handful of molds brought on the restructuring mission. New
molds can be produced using the asteroid resources. Instead
of molds, we prefer the concept of continuous casting of the
regolith. Anhydrous oxide strips will be rapidly cooled and
used to produce strong laminate plies. Those laminate plies
will be stacked as they cool and sintered under pressure. The
laminate will be nearly as strong as the individual plies and
provide the structural strength required in our construction.
2.1.5 Asteroids Surface Characteristics
Classifying the various surface features will be important for
programming the autonomous exploration, mining, and pro-
cessing of the asteroids. Surface features to consider include
craters, plains, terraces, cliffs, sink holes, boulders, and equa-
torial ridges. Each of these surface variations have a unique
impact on mining and navigation.
2.1.6 Asteroids Resources and Applications
Our effort is not the first to consider how to use asteroid ma-
terial. We include Table 2-1 to review a set of resources and
potential applications for our asteroid material. This was
adapted from a seminar entitled Construction with Regolith
[Mueller 2017]. The focus of this seminar was on processing
regolith from the moon. The seminar did briefly consider
Mars and asteroids. Most of these regolith resources are also
available from asteroids. The applications include products
Figure 2-4 – Restructuring processing of regolith

for initial mining, early construction, and occupied space
habitats. Their inclusion of oxide asteroid resources and the
structural beam applications are consistent with our goals.
2.2 Asteroids – Analysis
In the previous subsection, we introduced asteroid back-
ground research and identified a set of 10 potential asteroids
for our restructuring effort. In the following subsections we
build on that background in order to select a candidate aster-
oid for restructuring. We cover the topics of asteroid materi-
als, construction materials, material production, and mission
cost. We also cover a technique to compute a return on in-
vestment (ROI) for a restructuring mission. These topics pro-
vide the criteria to select the asteroid.
2.2.1 Asteroid Materials
Our restructuring effort uses the bulk oxide material from an
asteroid to create the habitat framework. Most asteroid min-
ing efforts focus only on valuable metals or water. These val-
uable products represent a small percentage of the asteroid.
These mining efforts typically consider the bulk oxides to be
waste. We advocate using the bulk oxides to create rods and
tiles. Suddenly 80% to 90% of the asteroid is valuable. We
use those rods and panels to build trusses, siding, and panels.
Some leftover materials like volatiles and metals will be
identified, inventoried, and stored for future use. Other bulk
materials not suitable for construction can be used for fill.
We include Table 2-2 to illustrate how our asteroid restruc-
turing process has the opposite priorities compared to typical
asteroid mining approach. We use details from [Mazanek et
al. 2014] as a typical asteroid mining approach. The table
provides the high, medium, and low product priorities for the
two approaches. We show the expected products and the pro-
cesses used to obtain those products. The table shows the ex-
pected percentage of the products and the relative costs asso-
ciated with obtaining those products. For our restructuring
process, we consider an S-Type asteroid for the material
composition percentages. A C-Type asteroid has similar per-
centages. The table results show the traditional and restruc-
turing approaches have almost opposite product priorities.
2.2.2 Construction Material
Glass can be used for structural applications (bricks, slabs,
beams, windows) [Haskin 1992]. Glass oxides can easily be
cast into structural elements for construction. Feasible ele-
ments include beams, columns, slabs, shells, blocks, and cyl-
inders. End products such as floors, sinks, pipes, and electri-
cal insulators can also be fabricated from these materials. Ca-
bles can also be made from high strength glass fiber [Ruess,
Schaenzlin, and Benaroya 2006].
We plan that the primary product produced in our restructur-
ing process will be rods and tiles for constructing trusses and
panels. The vision is to melt the silicate resource and form
the rods and tiles. The S-Type asteroid has about 85% oxide
material. An example breakdown of these oxides on an S-
Type asteroid would include SiO2 at almost 40%, MgO at
25%, and FeO at 10%. In the Construction with Regolith re-
port [Mueller 2017], they considered building with basalt.
Basalt is an igneous rock comprised of minerals such as py-
roxene and olivine. Compositionally this is like the oxides on
the S-Type asteroid. They used a Hawaiian basalt with Si2O
at 50%, MgO at 7.2%, Fe2O3 at 12%, and Al2O3 13.5%
[Mueller 2017]. They compared the sintered basalt rocks to
concrete. They found basalt rock density is similar to con-
crete and the compressive strength is better. Table 2-3 con-
tains metrics for several basalt products. For reference, we
also include values for concrete, conventional glass, and for
anhydrous glass.
Glasses and ceramics generally work well under compres-
sive loads but not well under tension stress. It may be possi-
ble to reinforce glass structures with asteroidal nickel-iron
steel and enhance them to withstand a wide range of both
tension and compression. This complexity may not be nec-
essary with the additional tensile strength produced with the
anhydrous, vacuum-produced glass [Blacic 1985] [Prado and
Fraser 2018]. Glass produced in the absence of hydrogen or
water has significantly better mechanical properties [Prado
and Fraser 2018]. It may be possible to substitute this glass
for structural metals [Blacic 1985] [Carsley, Blacic, and
Pletka 1992] [Soilleux 2019]. This glass is called anhydrous
glass. On Earth, water and hydrolysis weakens the strength
of the silicate bonds by about an order of magnitude [Blacic
1985]. Production on the asteroid will be in a hard vacuum
and water is extremely limited. Quickly cooling this glass
could further increase the tensile strength [Yale 2013]. Re-
searchers believe it may be possible to substitute this anhy-
drous glass for structural metals in a variety of space engi-
neering applications [Blacic 1985]. They note that this glass
would be competitive or superior to metals [Carsley, Blacic,
and Pletka 1992]. A study in 2012 found that anhydrous glass
could attain a tensile strength of 13,800 MPa [Bell and Hines
2012]. A 2019 report claims a bending strength of over 100
Table 2-1 – Asteroid Resources and Applications
Some asteroid resources and their uses
• Oxygen: propellant, life support
• Iron, aluminum, titanium: structural elements
• Magnesium: less strong structural elements
• Oxides: sintered blocks, concrete, glass
• Water: Ice blocks, molded ice
Potential applications
• Structural beams, rods, plates, cables
• Cast shapes (e.g., anchors, fasteners, bricks, and rods)
• Solar cells, wires for power generation and distribution
• Pipes and storage vessels for fuel, water, and other fluids
• Roads, foundations, shielding
• Spray coatings or linings for buildings
• Powdered metals for rocket fuels, insulation
• Fabrication in large quantities can be a difficult engineering
problem in terms of materials handling and heat dissipation
Credit: Self produced using data and concepts from [Mueller 2017]
[NASA Report Public Domain]

MPa for the anhydrous glass [Soilleux 2019]. We intend to
use properly designed trusses to exploit the high tensile
strength and compensate for the weaker bending strength.
For our space station structure, we assume anhydrous glass
could be used to produce high strength rods and tiles. We
plan to use the anhydrous glass as structural beams and skin
panels, regolith as fill, and basalt fibers as cables.
2.2.3 Construction Material Production
The researcher Schoroers states “A glass can have com-
pletely different properties depending on the rate at which
you cool it. If you cool it fast, it is very ductile, and if you
cool it slow it¹s very brittle” [Yale 2013]. It appears that tem-
perature control will be key, and quickly cooling the glass
will be necessary. Obviously, thin plies of anhydrous glass
can be cooled more rapidly than thick slabs. Stacking and
pressure sintering those thin plies of anhydrous glass could
produce high strength laminates for our tiles and beams. The
laminate should maintain the tensile strength of the individ-
ual anhydrous glass plies.
Continuous strip casting would be ideal to produce sheets of
basalt to use as panels. Terrestrial continuous casting sys-
tems continuously melt feedstock, extrude that molten stock,
and form a sheet of cooling material [Tosaka 2008]. The mol-
ten substance travels downward, solidifies, and increases in
length. Molten material is fed into the tundish mold at the
same rate as the solidifying casting exits the system. Gravity
is required to flow molten regolith and form panels. The low
gravity and vacuum of the asteroid will mandate modifica-
tions to the terrestrial continuous casting process. Rotating a
continuous casting system could generate some gravity to
cause the molten material to flow. The typical size and
weight of this system may make a rotating version impracti-
cal. Operating on the outer rim structure would be possible
once it begins to rotate. It may be possible to rotate smaller
versions of the continuous casting system. We have begun an
alternative smaller design to produce the laminated anhy-
drous glass tiles. The smaller design will produce smaller
tiles at a slower rate; however, building the smaller design
will take much less time and material. A multitude of small
units could outperform the single monolithic unit.
In continuous casting, using augers or pressure plates to
move the material is another option. The vacuum helps pre-
vent contamination of the molten material in the tundish. Un-
fortunately, the vacuum reduces the cooling speed of the ma-
terial with low-rate radiative cooling. We envision using
large rollers to provide faster cooling with their larger sur-
face area and direct contact with the anhydrous plies. Similar
rollers would provide the pressure to sinter the plies into a
laminate. Anhydrous oxide strips will be stacked and sin-
tered with pressure assistance as they rapidly cool.
2.2.4 Mission Cost
Delta-v is a measure used to quantify the cost to transfer from
one orbit to another. It often represents the velocity change
needed to achieve a new trajectory. Delta-v is typically meas-
ured in meters per second or kilometers per second. Mission
designers use delta-v as the measure of the energy needed to
carry out a space mission. We use delta-v as part of the se-
lection criterion for picking an asteroid for restructuring. Our
focus for this effort is to reach and restructure a near-Earth
asteroid. The orbits of near-Earth asteroids can bring them
within about 0.5 astronomical units of the Earth. It turns out
Table 2-2 – Material Importance in Asteroid Mining and Restructuring
Priorities
Typical Asteroid Mining [Mazanek et al. 2014] Asteroid Restructuring
Products Process Products Process
Top Priority Regolith – Oxygen from oxides.
Extract platinum group metals
Available Oxides: 75%
Valuable metals: 10%
Refine the regolith to extract the
oxygen and metal products
Extracting oxygen cost: High
Extracting metals cost: Medium
Bulk Material – Oxides
such as Olivines and
Pyroxenes.
Available Oxides: 85%
Melt and form into rods, tiles, and
sheets
Processing bulk material cost: Low
Secondary Water and other volatiles
Available Volatiles: 15%
Refine the regolith to extract wa-
ter and volatile products
Refining costs: Low
Water and other vola-
tiles: Total: 4%; Water
0.13%
Identify materials with product and
store for later processing
Refining costs: Low
Lowest Pri-
ority
Bulk material for shielding and
construction
Available material: 50%
Excess from the refining process
Refining costs: Low
Free metal and platinum
group metals
Free metals: 11%
Identify materials with product and
store for later processing
Identification and storage cost: Low
Credit: Self produced using data and concepts from [Mazanek et al. 2014] [NASA Report Public Domain]
Table 2-3 – Basalt Product Comparison
Metric
Terrestrial
concrete
Basalt rock
Sintered basalt
regolith
Conventional
glass
Anhydrous glass
Density
Compressive strength
Tensile strength
2500 - 2900 kg/m3
~20 - 40 MPa
2 – 5 MPa
2630 +/- 140 kg/m3
~144 - 292 MPa
11.2 – 17.8 MPa
2650 to 2900 kg/m3
206 MPa
7.29 MPa
2500 kg/m3
1000 MPa
45 MPa
2700 kg/m3
1000 MPa
3,000 – 13,800 MPa
Basalt rocks can be 4-7 X stronger in compression than normal terrestrial concrete [Mueller 2017]. Sintered basalt regolith can be 5X stronger in compression than normal
terrestrial concrete [Mueller 2017]. Anhydrous glass can typically provide 3 GPa [Blacic 1985] or ideally up to 13.8 GPa [Bell and Hines 2012].
Credit: Self produced using data and concepts from NASA [Mueller 2017] [NASA Report Public Domain] [Bell and Hines 2012] [Blacic 1985] [Facts]

that many of these asteroids require less fuel and lower delta-
v than required to reach the Moon or Mars.
There will be multiple trajectory paths to reach our asteroid.
Some use 2 impulses, others use 3 impulses or more. Low
energy trajectories and slingshots offer additional means to
reach an asteroid. For missions from Earth, asteroids in orbits
with a semimajor axis less than 2.5 AU and inclination less
than 10 degrees tend to minimize delta-v. Numerous studies
exist showing how to optimize the trajectory to an asteroid.
An earlier example is an asteroid retrieval mission [Bender
et al. 1979]. We advocate using slingshots or low energy
paths. Those methods seem important to reach asteroids on
inner Earth orbits and with potentially higher inclination.
2.2.5 Return on Investment
Planetary Resources owns the Asterank website and database
containing ranked asteroids for mining [Webster 2020].
Asterank estimates the costs and values of mining asteroids.
Value estimates are based on the mass of a given asteroid and
its spectral type. Accessibility estimates are based primarily
on delta-v. Profit and Return on Investment (ROI) calcula-
tions are a combination of accessibility and value.
We adapted the Asterank approach to evaluate asteroids for
our restructuring. We assign a cost metric of the mission to
reach an asteroid using delta-v (dV). The values come from
the JPL Small-Body Mission-Design Tool [JPL SB Mission
Design Tool] and we use the Low Thrust value and the min-
imum Total Delta-v. For comparison purposes, the values
provide a first estimate of the travel cost to the asteroids.
We assign a value metric to the asteroid. The diameter of the
asteroid provides a value measure of the available asteroid
material. We also experimented with using the asteroid vol-
ume as the value metric. The asteroid type and material com-
position would have a significant effect on the value of the
material. We are using only the oxide material from S-type
(or C-type) asteroids. Instead of using the asteroid composi-
tion, using the diameter (or volume) is reasonable as the
value metric because of the large percentage of oxide mate-
rial in those types of asteroids.
We use the mission delta-v and asteroid diameter to compute
a return-on-investment (ROI). We used this ROI in the selec-
tion process of an asteroid for our restructuring process.
2.3 Asteroids – Results
We presented in previous subsections our asteroid back-
ground and analysis approach. In this asteroid subsection, we
offer results from applying that analysis approach. The ap-
proach criteria helps to winnow the selection to a single as-
teroid. We present our selection process and the final se-
lected asteroid. We also include details on that asteroid and
the expected material to be harvested.
2.3.1 Asteroid Selection
There are many millions of asteroids in our solar system that
could be considered for restructuring. There are estimates of
over 3 million asteroids in the inner solar system to the
Jupiter orbit. We show in Figure 2-5 the selection process we
used to select an asteroid. This is like the approach used to
select the asteroid Bennu for the OSIRIS-REx mission [Enos
2020]. The JPL Small Body Database lists 22,122 asteroids
as members of the Aten, Apollo, Amor, and Atira asteroid
classes as of February 2020. This represents only a fraction
of the estimated 200,000 sizeable asteroids in those classes.
We restricted the asteroids by limiting the inclination and or-
bits to be more Earth like. This would help reduce mission
costs and improve future access for colonization and trade.
We used an inclination less than 26 degrees, an eccentricity
less than 0.4, a perihelion greater than 0.4 AU, an aphelion
less than 2.2 AU, and a semimajor axis less than 1.5 AU. We
used the following JPL SBD search constraints: asteroids and
orbital class (IEO or ATE or APO or AMO) and i < 26 (deg)
and e < 0.4 and Q < 2.2 (au) and q > 0.4 (au) and a < 1.5 (au).
This reduced our choices to 5,570 asteroids.
We then restricted the asteroids using size and rotation
speeds. We first eliminated small asteroids with an absolute
magnitude parameter less than 20. We used the following
JPL SBD search constraints: H < 20 and rot_per > 3 (h). This
reduced our choices to 228 asteroids. Some of those asteroids
did not have diameters in the database. We used the absolute
Selection Process for Atira Asteroid
• Asteroids: 1,000,000s
• NEO: 22,122 asteroids; orbital classes (IEO or ATE or APO or AMO)
• Orbit Cost: 5570 with i < 26 (deg) and e < 0.4 and Q < 2.2 (au) and q
> 0.4 (au) and a < 1.5 (au)
• Diameter: 288 with H<20 (size)
• Diameter: 87 with size 0.45 to 5 km
• ROI: Best 6 for delta-v mission cost and asteroid value
• Final: Atira
Credit: Self produced; Image Concept: Heather Enos, [Enos 2020],
NASA/Goddard Space Flight Center, [NASA Report Public Domain];
Atira Image from Doug Ellison model [Ellison 2018], [CC BY-4.0] modi-
fied/rescaled to asteroid dimensions
Figure 2-5 – Overview of Asteroid Selection Criteria

magnitude and albedo to computed diameters and selected
only those in the range of 0.45 kilometers to 5.0 kilometers.
This left 87 asteroids.
We use our simple estimate of the return on investment
(ROI) for each of the candidate asteroids. That ROI is the
ratio of the travel cost over the asteroid value. The delta-v
provides a travel cost measure. The diameter provides the as-
teroid value measure. For the largest asteroids, the delta-v
costs ranged from 4.6 to 16.7 meters per second. With the
delta-v constraint, we found 55 asteroids being identified as
potential candidates. The spectral type of many of the aster-
oids have not been determined. Sixteen of the 55 asteroids
have spectral types of C or S (or similar). Both spectral types
are expected in this region of the solar system. Figure 2-6
shows the ROI for each of the candidate asteroids. We show
a line graph for all the asteroids and include the column bars
for well-defined asteroids (i.e., spectral type available).
We separate the best six return-on-investment (ROI) aster-
oids from Figure 2-6. Those six asteroids are shown in Table
2-4 with their mission delta-v cost and their diameter value.
From those 6 asteroids, the best ROI was for the asteroid
163693 Atira.
2.3.2 Harvested Material
The Atira asteroid is an S-Type asteroid. We assume it is
comprised of free metal (11.1%), volatiles (4.0%), and ox-
ides (84.9%). We have computed its volume using a mesh
grid (2.19e10 cubic meters) and as an ellipsoid (3.01e10 cu-
bic meters). We computed its mass of 41 trillion kilograms
using the orbit period of its moon. We derived that the aster-
oid has a porosity of 48.3% and assume there is a 24.4% loss
when processing the oxide. Table 2-5 contains these pro-
cessing values and metrics. As a preview, the table also
includes the amount of material required to build the exam-
ple Atira space station with a major radius of 2116 meters
and elliptical minor axes of 334 and 1003 meters. We found
that we can extract enough building material for the station
by harvesting 269 meters of regolith from the surface of the
asteroid. The Atira asteroid has a mean radius of 1928 me-
ters; harvesting only the top 14% of the asteroid is conserva-
tive. This volume of harvested material represents 30% of
the total volume of the Atira asteroid.
2.4 Asteroids – Summary
The purpose of this section was to review asteroid character-
istics and select one for the restructuring process. We have
looked for one that has enough material to construct a large
station. We want an asteroid between 1 kilometer and 5 kil-
ometers for this effort. We also want the asteroids to be in
the Goldilocks zone near the Sun – not too hot and not too
cold. A location near the Earth orbit will also reduce the mis-
sion costs. Our selection process has considered a return-on-
investment metric using the mission cost and the available
asteroid material. From our decision criteria, we selected the
asteroid Atira.
3 Asteroid Restructuring – Space Stations
Asteroid restructuring mandates understanding space sta-
tions, asteroids, and robotics. The previous section covered
the subject of asteroids. In this section we delve into the his-
toric and foundational concepts and supporting technologies
for space stations. The purpose of this section is to under-
stand the type of space station to be built from a selected as-
teroid. We again organize this section with subsections to
cover background, analysis, results, and a summary.
Credit: Self produced using JPL Small Body Database Search Engine Results: 87
matching objects (Top 30 Largest Diameters); Constraints: asteroids and orbital
class (IEO or ATE or APO or AMO) and H < 20 and rot_per > 3 (h) and i < 26 (deg)
and e < 0.4 and Q < 2.2 (au) and q > 0.4 (au) and a < 1.5 (au); Data: [JPL SBD
Search Engine] [Public Domain] and [JPL SBD Small Body Lookup] [Facts]
Figure 2-6 – Return on Investment for Candidates
Table 2-4 – Best Return on Investment Asteroids
Credit: Self produced using [JPL SBD Search Engine] [Public Domain]
Table 2-5 – Asteroid Material Summary
Material Metric Volume (m3 millions)
Atira Mesh Model 21,900
Harvested 269 meters deep 6,572
Packed 51.7% 3,397
Loss 24.4% 829
Regolith Processed 2,569
Building 84.9% 2,181
Metals 11.1% 285
Volatiles 4.0% 103
Station Calculated 2,181

3.1 Space Stations – Background
We offer in this background section a brief overview on
space station designs. We introduce key concepts on the
space stations geometries, the rotation produced artificial
gravity, and the effects of gravity on humans.
3.1.1 Space Stations – Background Credit
Space stations have been researched and designed for over
150 years. Thousands of books and journal articles have been
written about the design and construction of space stations
and provide a foundation for our restructuring study.
We present a series of key technology areas and some of the
associated researchers. In our later analysis and results sub-
sections, we present some extensions to these space station
technology areas. We also provide more details in later sub-
sections on some extensions that may be innovative.
• Station Geometry: NASA Studies [Johnson and
Holbrow 1977] [O’Neill et al. 1979] and Globus [Globus
1991] [Globus et al. 2007] present a solid foundation for
station geometries. We review and extend this foundation
to include large, rotating, multiple floors, and balanced
space stations.
• Rotational Imbalance: Rotational stability is a con-
straint on space station designs [Brown 2002] and im-
poses new limits on their geometry sizes [Globus et al.
2007]. We apply this constraint to four rotating space sta-
tion geometries.
• Gravity Ranges: Rotating the stations to provide centrip-
etal gravity has long been a part of space station designs
[Oberth 1923]. We review and consider the gravity
ranges with multiple floors on the human physiology
[Hall 1999] [Globus and Hall 2017].
• Runways: Most rotating station designs use the central
hub to support shuttle arrivals, servicing, and departures.
This single central hub can become a bottleneck for pas-
sengers and trade. We evaluate landing on runways built
on the exterior of the rotating station.
• Lighting: The O’Neill cylinder [O’Neill 1976] [Johnson
and Holbrow 1977] windowed half of its exterior to pro-
vide light. More recent station studies eliminate those
windows and use internal lighting [Globus 1991]. Solar
panel materials, light efficiencies, and prices have stead-
ily improved since the 1970s. Power requirements for
light generation have dropped by 4x using LEDs. Using
narrow spectrum light generation further drops the power
requirement by 7.5x [Wheeler 2017] [Soilleux and Gunn
2018]. We have also seen improved light transmission
concepts through light pipes, fiber, chevrons, and light
shelves [Johnson and Holbrow 1977] [Savard 2012]
[Janhunen 2018].
• Space Allocations: The 1977 NASA Report [Johnson
and Holbrow 1977] detailed the allocation of space sta-
tion floor space to purposes such as open space, support
infrastructure, agriculture, industry, and residence. We
have enhanced these values to more modern allocations.
• Agriculture: NASA Studies [Johnson and Holbrow
1977] [Bock, Lambrou, and Simon 1979] and more re-
cently [Fu et al. 2016] [Soilleux and Gunn 2018] [Stanley
2018] have evaluated the use of agriculture and plants to
create a closed system environment. We review their
findings and include recent advancements. Floor space
requirements for agriculture in space stations have been
dropping steadily since the 1970s. We have found details
on recent advancements in hydroponics, aeroponics, and
new biological approaches [Kersch 2015] [Cornall 2021].
Those recent advancements offer even more reduction to
the agriculture space requirements.
• Structural Material: O’Neill [O’Neill 1974] and
McKendree [McKendree 1995] present concepts on the
maximum structural radius of rotating stations. We sum-
marize and extend these structural values with new mate-
rials. A material of interest for our station is anhydrous
glass [Blacic 1985] [Carsley, Blacic, and Pletka 1992]
[Bell and Hines 2012] [Soilleux 2019].
• Equipment: Most terrestrial mining and construction
equipment will not work in the low gravity and vacuum
asteroid environment. Design modifications have been
researched [Eisele 2001] [Schrunk et al. 2008]. Our re-
structuring equipment will need many of these modifica-
tions.
3.1.2 Space Station Geometries
There are four common space station geometries: Sphere,
Dumbbell, Torus, and Cylinder [Johnson and Holbrow
1977]. We include four artworks to help visualize these sta-
tions in Figure 3-1. These shapes have symmetry to support
spinning and the production of centripetal gravity. They also
have hollow regions to hold atmosphere. These space station
geometries have been documented for over 150 years. We
review those four geometries in the following paragraphs.
Dumbbell: The dumbbell is typically the smallest geome-
tries considered for space habitats. The dumbbell consists of
two small modules connected with a tether or trusses; see
Figure 3-2a. The modules rotate around a common axis and
produce an artificial gravity inside the module. The length of
the tether and the rotation speed determines the artificial
gravity. The centripetal gravity is equal to the rotation radius
times the angular rotation speed squared. To prevent motion
sickness, most dumbbell designs use a tether that is several
100 meters in length [Mordanicus 2014]. Long tethers can
provide Earth-like gravity with fairly slow rotation rates. The
tether structure connects each pair of modules and would
need to withstand the centripetal force of rotation [García et
al. 2016]. With dumbbells, the rotation radius and speed are
independent from the size of the two dumbbell modules. This
provides the advantage of a small module shape requiring
less material and atmosphere than many of the other shapes
[Mordanicus 2014]. The drawings in Figure 3-2a illustrate
single dumbbells and a composite shape with multiple dumb-
bells [Johnson and Holbrow 1977]. The basic dumbbell
shape provides a building block for composite shape stations.
The composite structure is advantageous in that early

pioneers could live in the simplest configuration as addi-
tional dumbbells are constructed and attached [Mordanicus
2014].
Sphere: A space colony could reside inside a sphere or ball
shaped structure. Spherical space stations have been pro-
posed since the 1880s. Examples include Konstantin Tsiol-
kovsky’s spherical spaceship in 1883 [Tsiolkovsky 1883], a
Dyson Sphere in 1960 [Dyson 1960], and Gerard O’Neill’s
Island Two in 1976 [O’Neill 1976]. O’Neill wrote that
“spherical geometries for space colonies ranked highest in
simplicity, ruggedness, economy, and safety among Earth-
like colony designs” [O’Neill 1976]. Spheres have a strong
structure because stresses are evenly distributed over the en-
tire surface. For a given wall thickness, a spherical vessel has
twice the strength of a cylindrical vessel. Thinner walls are
considered valuable because thickness directly affects mate-
rial weight and launch costs.
We show the basic spherical shape in Figure 3-2b. The
sphere would rotate to produce Earth-like gravity at the outer
shell equator. Gravity would decrease as one moves toward
the rotation poles. A rotating sphere design has the risk of
being imbalanced. We also include an oblate ellipsoid shape
in Figure 3-2b. Unlike the sphere, the oblate ellipsoid geom-
etry would be rotationally balanced. The ellipsoid minor axis
length should be less than 0.8165 times the major axis length
to passively balance the rotating ellipsoid station.
Cylinder: Another geometry for a space colony is a cylin-
drical structure. Cylinder space stations have been consid-
ered since the 1920s and have ranged from 30 meters to sev-
eral kilometers in radius. The radius and rotation speed are
typically chosen to provide one Earth-like gravity (1g) at the
outer shell. A rotation speed of less than 2 revolutions per
minute (rpm) is usually acceptable to avoid motion sickness
and disorientation. A radius of 224 meters revolving at 2 rpm
produces 1g at the outer shell.
We show basic cylindrical shapes in Figure 3-2c. The cylin-
der includes end caps that could be flat, hemispherical, or
other shapes. We show the hemispherical and flat end caps
in Figure 3-2c. Longer cylinder lengths produce more habit-
able square footage and support higher population. Multiple
reports from the 1970s used lengths that were 10 times the
radius. O’Neill and his students connected two counter-
rotating cylinders to eliminate gyroscopic effects and preces-
sion [O’Neill 1976]; see Figure 3-1. This design arrangement
would properly point the station at the sun during the sta-
tion’s circumsolar orbit. Recently, authors have imposed a
limit on the cylinder length to passively control the imbal-
ance of the rotating structure. Globus and his group found the
cylinder length should be less than 1.3 time the radius [Glo-
bus et al. 2007]. This design produces a station looking more
like a hatbox; see Figure 3-2c. Longer length cylinders would
require some active balance technology to prevent the risk of
possibly tumbling.
Torus: Another geometry for a space colony is a torus or
wheel structure. Torus structures have been described by re-
searchers and science fiction writers since the early days of
space science [Noordung 1929]. The torus sizes in our his-
toric review range from 50 meters to 30,000 meters in radius.
The station is typically rotated at a speed to provide one
Earth-like gravity at the outer rim. We show torus examples
in Figure 3-2d. The torus can have a cross-section of a circle,
ellipse, or extended cylinder. Alternatively, the torus shape
can be composite with many smaller spheres or nodes. Early
researchers envisioned connecting 22 emptied rocket stages
end-to-end to produce a 160-foot-radius, rotating, wheel-
shaped space station [Koelle and Williams 1959].
The torus has an advantage that the tube structure size is in-
dependent of the center rotation radius. The habitable region
of the torus can be located far from the center of rotation. A
larger rotation radius provides lower rotation rates to gener-
ate Earth-like gravity. Lower rotation rates reduce stresses
and the required material tensile strength. Independent of the
rotation radius, the radius of the habitable region can be made
larger or smaller based on available construction material.
3.1.3 Artificial Gravity
As a part of our space station background, we review
artificial gravity. Even in the 1920s, researchers were
rotating space stations to provide centripetal gravity
[Tsiolkovsky 1920] [Oberth 1923] [Noordung 1929]. We
review in this subsection the forces in a rotating station that
produce the artficial gravity. We cover the issue of rotation
causing disturbances in the inner ear, which leads to motion
sickness and disorientation. We cover microgravity health
problems to end this review of artificial gravity.
NASA Dumbbell Station Interior Spherical Space Station Cylinder Space Station Torus Space Station
Image Credit: NASA, Marshall Space
Flight Center, 1 January 1970; [NASA
Image Public Domain]
Image Credit: NASA, ARC, Artist: Rick
Guidice: 1976-04-01; [NASA Image Pub-
lic Domain]
Image Credit: NASA, Artist: Rick Guidice:
27 May 1975; [NASA Image Public Do-
main]
Credit: NASA Ames Research Center.
Artist: Rick Guidice; [NASA Image Pub-
lic Domain]
Figure 3-1 – Space Station Geometries – Artwork from 1970s

Forces in Rotating Station: We review the three forces felt
in the rotating station: centripetal (inward), centrifugal
(outward), and Coriolis (movement) forces. The word
centripetal means center-seeking. It is from the Latin word
centrum meaning center and petere meaning to seek.
Similarly, the word centrifugal means center-fleeing. It is
from the Latin word centrum meaning center and fugere
meaning to flee. The Coriolis force is named after Gaspard-
Gustave de Coriolis. Almost 200 years ago, he defined these
forces in a rotating frame of reference [Coriolis 1835].
Only the centripetal force is a “real” force. The centripetal
force is always directed radially towards the center of
rotation. The Coriolis and centrifugal forces are typically
called fictious, inertial, or supplementary forces. When
Newton's laws are transformed to a rotating frame of
reference, the inertial forces appear [Hand and Finch 1998].
The equation of motion for a rotating body takes the form:
𝑭
⏟
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡
𝐹𝑜𝑟𝑐𝑒𝑠
= 𝑚𝒂
⏟
𝑀𝑜𝑡𝑖𝑜𝑛
𝐹𝑜𝑟𝑐𝑒
+ 𝑚
𝑑𝝎
𝑑𝑡
× 𝒓
⏟
𝐸𝑢𝑙𝑒𝑟
+ 2𝑚𝝎 × 𝒗
⏟
𝐶𝑜𝑟𝑖𝑜𝑙𝑖𝑠
+ 𝑚𝝎 × (𝝎 × 𝒓)
⏟
𝐶𝑒𝑛𝑡𝑟𝑖𝑓𝑢𝑔𝑎𝑙
.
In that equation, F is the sum of the forces acting on the
object in the rotating frame, m is the mass of the object, and
ω is the angular velocity. Multiple parameters describe the
object relative to the rotating frame: a is the acceleration, r is
the position, and v is the velocity. In the rotating frame, the
inertial or fictitious forces act as additional forces and
contribute to the object acceleration. The Euler force only
applies with changing angular velocity, ω. In a rotating space
station, the rotation speed is constant and the term dω/dt is
zero. The Coriolis force is function of the object velocity.
The centrifugal force is a function of the object position, r
(distance from the center of rotation). Multiple sources are
available to provide details on these forces [Hall 1991]
[Hand and Finch 1998] [Lucas 2019].
Large Station Example: We offer one example to illustrate
the effect of large stations on the artificial gravity. We show
in Figure 3-3a a ladder oriented with the rotation of the
station. This diagram shows the Coriolis and centrifugal
accelerations. The individual is ascending the ladder at a
constant velocity, vr. Centripetal force maintains the person’s
position in the rotating system and pulls towards the rotation
center. The apparent centrifugal force is equal and opposite
to the centripetal force and pulls the individual downward to
the base of the ladder. The Coriolis force pulls the ascending
individual in the spinward direction. When ascending, the
climber leans antispinward to counteract the Coriolis force.
When descending, the climber leans spinward to resist the
opposite direction Coriolis force [Queijo et al. 1988]. The
angle of the lean would be the arctangent of the ratio of Acor
over Acent and simplifies to atan(2vr/vt).
We also include a chart showing the lean angle as a function
of the station radius; see Figure 3-3b. The x-axis of the chart
is logarithmic and shows the radius of the station. The
stations are rotating to produce a 1g centripetal gravity at the
outer rim. The y-axis is also logarithmic and shows the lean
angle. The chart includes lean angles for three velocity ladder
climbers. The data of the chart shows that the lean angle
increases with climber velocity and with smaller station radii
(faster rotation). Fast climbers would ascend a ladder at 0.5
meters per second. We show a building code limit of 0.5
degree lean in the chart. This is below the terrestrial building
code limits for cross slopes, parking stalls, and stairway
treads [ICC 2009] [ADA 2010]. Slower climbers on most
rotating stations would experience less than 0.5 degree lean
on the ladder from the Coriolis force. Another study defined
lean angles less than 1.8 degrees would be neglible in a
rotating environment [O’Neill and Driggers 1976]. The
results in this chart shows the lean angle will be barely
noticeable on our large rotating stations.
SPHERICAL NODES
PROLATE ELLIPSOID NODES
COMPOSITE STRUCTURE
a) Dumbbell Space Station Geometries
SPHERE OBLATE ELLIPSOID
b) Spherical Space Station Geometries
TALL CYLINDER
CYLINDER
FLAT END CAPS
c) Cylindrical Space Station Geometries
TORUS ELLIPTICAL
TORUS
BEADED TORUS
d) Torus Space Station Geometries
Images Credit: Self Produced using Images and Concepts from [John-
son and Holbrow 1977][NASA Report Public Domain]
Figure 3-2 – Space Station Geometries

In addition to this ladder climbing example, we have further
explored these forces and their effects. We considered
scenarios with objects in motion and people in motion in
larger stations. Objects in motion scenarios included dropped
objects, thrown objects, hopping objects, free fall, high speed
vehicles, and fire arms. The people in motion scenarios
include walking, climbing ladders, stairs, ramps and paths,
and elevators. Evaluation parameters include drop
displacement, extra weight, lean, and elevator velocity. Our
exploration has reviewed and consolodated multiple studies
[Hall 1991] [Hand and Finch 1998] and [Lucas 2019]. We
extend their results to larger stations and to new scenarios.
The combination of forces creates anomalous movements of
the objects and people. Striving to attain Earth-like gravity
with moving objects or people requires reducing the Coriolis
force. Our exploration leads us to agree with Hall who
ultimately finds “that it is impossible to design away the
gravitational distortions inherent in rotating environments.
They can be kept arbitrarily small only by keeping the radius
sufficiently large.” [Hall 1993].
Human Rotation Tolerance: In a rotating space station,
centripetal gravity replaces the normal Earth gravity. If the
rotation rate is too fast (radius too small), a Coriolis effect
will cause disturbances in the inner ear and lead to motion
sickness and disorientation. Rotation rates below 2 revolu-
tions per minute (rpm) are acceptable to most people [Globus
and Hall 2017]. This is a threshold revolution speed used by
many researchers.
Theodore Hall provides a thorough review and analysis of
five historic guidelines [Hall 1997]. He composites the five
studies into one “comfort chart.” He identifies a comfort
zone in a station radius and rotation rate chart. He notes that
the boundaries of these charts can be influenced by tasks and
other environment criteria [Hall 1997].
Hall uses five boundaries [Hall 1997] [Hall 2006] to limit the
consolidated comfort area and produces a pentagon shaped
comfort zone. The pentagon is bounded by gravity values,
head-to-foot acceleration gradient, rotation rate, and
tangential velocity. Recently Al Globus and Theodore Hall
used this comfort chart in their paper on rotation tolerance
[Globus and Hall 2017]. It may be comfortable (and fun) to
be in zero or low-gravity zones for a short time; however,
long term there are serious health problems from
microgravity. It is more appropriate to call these tolerance
charts rather than comfort charts. We are looking for long-
term living tolerance limits, not comfort zones.
We use five boundary points in our tolerance chart; see Fig-
ure 3-4. The chart shows the station radius on the y-axis from
100 to 25,600 meters on a logarithmic scale. The x-axis
shows the rotation in revolutions per minute. We label the
same five boundary points to form a pentagon like Hall. The
maximum gravity tolerance we show in Figure 3-4 is 1.2g
and the minimum gravity is 0.8g. In most of our designs and
analysis, we conservatively limit the habitable region of the
rotating space station between 0.95g and 1.05g. Results from
future experiments aboard the International Space Station
such as [JAXA MHU 2019] may refine these boundary
ranges. We limit the spin tolerance to 2 rpm to prevent mo-
tion sickness. Like Globus and Hall, we include a limit using
a large ratio of Coriolis to centripetal force (Acor/Acent
=25% at velocity=5 meters per second). For our large sta-
tions, the Coriolis distortion and the motion sickness limits
have minimal effect on our tolerance zone. Unlike Hall, we
limit the top boundary points (① and ⑤) to a maximum
hoop stress radius. In a later section, we define a maximum
rotation radius of 10 kilometer considering material
strengths. The stresses of the top boundary points are
determined from this maximum. This stress radius is a
structural limit and not a human tolerance measure; however,
exceeding a structural limit could have a significant impact
on the health of the inhabitants.
We update the definitions of the pentagon boundary points:
• Top Boundary (points ⑤ and ①): Maximum hoop
strength. Near-Earth-like normal gravity.
• Angle Right Boundary (points ① and ②): High gravity
limit with increasing Coriolis effects.
a) Lean Angle Climbing Ladder
b) Lean Angle Function of Radius
Figure 3-3 – Climbing Ladder Oriented with Rotation
0.01
0.1
1
10
100 1000 10000
Ladder
Lean
Angle
(degrees)
Station Radius (meters)
Lean Angle While Acending Ladder
(Station rotating to produce 1g)
v=0.25 m/s
v=0.50 m/s
v=1.00 m/s
Neglible Angle
Building Code Limit

• Bottom Right Boundary (points ② and ③): Motion
sickness limit from maximum high angular velocity.
• Bottom Left Angle Boundary (points ③ and ④):
Distortion from high Coriolis to centripetal forces.
• Top Left Angle Boundary (points ④ and ⑤): Low
gravity limit with decreasing Colriolis effects.
We highlight 1 rpm in Figure 3-4 as a maximum rotation ve-
locity when using an attached shield [Johnson and Holbrow
1977]. This implies a minimum rotation radius of almost 900
meters. Newer materials appear strong enough to permit at-
tached shields at higher speeds and we allow a maximum ro-
tation speed of 2 rpm in our tolerance chart. We strive to keep
the rotation speed lower than 1 rpm in our designs.
Microgravity Health Problems: Today it is known that mi-
crogravity can negatively affect human health. One of the
more common effects is called the Space Adaptation Syn-
drome and includes nausea, vomiting, anorexia, headache,
malaise, drowsiness, lethargy, pallor, and sweating [Hall
1997]. Longer term issues have been found such as cardio-
vascular changes, muscle damage, bone damage, and possi-
ble genetic changes.
We know that the human body has no problem with Earth
gravity; we know that it has a plethora of problems with zero
gravity. What is not known is if the human body can tolerate
long-term gravity between 0g and 1g [NASA 2004]. Studies
are planned to investigate these partial gravities. Lower grav-
ities are of interest because of planned long missions and col-
onies on the Moon and on Mars. We include in Figure 3-4
the Mars gravity of 0.38g and the moon gravity of 0.17g for
reference. Those gravities are outside the tolerance zone.
There is debate on whether those gravities could prevent the
low-gravity physical problems. Boyle [Boyle 2020] writes
that, despite more gravity than microgravity, the “long-du-
ration visitors will still experience some of low gravity’s del-
eterious effects.”
We hope to avoid those deleterious effects by maintaining a
near-Earth gravity range in the habitable areas of the large
rotating space stations. For most of our restructuring analysis
we limit the artificial gravity range in the station between
0.8g to 1.2g. We strive to limit the primary long-term
residential areas to a gravity range between 0.95g to 1.05g.
Artificial Gravity Summary: Centripetal gravity addresses
microgravity health issues but introduces anomalous effects
on moving objects and people. Multiple papers provide our
foundation for artificial gravity [Johnson and Holbrow 1977]
[Hall 1997] [Hall 2006] and [Globus and Hall 2017]. In our
research, we have reviewed and extended their results to
larger stations. The large stations envisioned with the re-
structuring process minimize these anomalous effects.
3.2 Space Stations – Analysis
We extend the space station findings introduced in the previ-
ous background section. We cover the broad topics of station
characteristics, rotational stability, and station gravity
ranges. We review rotational stability and gravity ranges for
the four geometries. We cover the geometry adaptations to
support these topics. We investigate the required station
mass for the design.
3.2.1 Station Characteristics
As a part of our space station analysis, the following para-
graphs contain more details on the station geometries, station
size, structure stress, population, multiple floors, station
mass, and floor allocation usage of our envisioned space sta-
tion. Large station sizes and using almost half of the station
volume as multiple floors are important details and consid-
ered in all the following subsections.
Station Geometries: The literature contains four types of
space station geometries: spheres, torus, dumbbells, and cyl-
inders. From the 1900s to today, the preferred space station
geometry has varied from the torus, to spheres, and to cylin-
ders. In our studies, we have found there are many ways to
evaluate and select a station geometry. For maximum vol-
ume, the sphere geometry was superior [O’Neill 1976]. To
minimize the mass for a given population, the cylinder ge-
ometry was superior [O’Neill 1976] [Globus et al. 2007]. To
minimize mass for a given rotation radius, the torus geometry
was superior [Johnson and Holbrow 1977] [Misra 2010].
These assessments and selections were typically based on
thin space station shells. In our asteroid restructuring, we use
thick shells to provide structural integrity, radiation protec-
tion, and safety from debris collisions. These historic assess-
ments were also typically based on a single projected floor.
We design our station with many floors to support greater
populations. We also explored slightly different geometries
than earlier studies. We use ellipsoids instead of spheres;
short cylinders instead of long cylinders; elliptical cross-
Credit: Self Produced using [Hall 1993] concepts [Facts]
Figure 3-4 – Tolerance Zones in Rotating Space Station

section toruses instead of circular cross-section toruses; and
avoid composite dumbbell structures.
Station Sizes: Historically, space station designs have
ranged from tiny cans to huge habitats. With the near unlim-
ited resources of a large asteroid, one wonders how large to
make the space station. There are multiple ways to structur-
ally analyze this problem [O’Neill 1974] [McKendree 1995].
Using their approaches, we replicate their set of maximum
radius values in Table 3-1. We extend their estimates with
additional materials. The exterior station shell could be over
20 kilometers in radius by using melted asteroid material
(basalt rods). We include anhydrous glass data [Blacic 1985]
[Carsley, Blacic, and Pletka 1992] [Bell and Hines 2012].
The tensile strength of anhydrous glass suggests a station of
over 40 km could be feasible.
O’Neill’s envisioned rotating cylinders with a radius of 16
kilometers. We see that this does not require esoteric materi-
als such as graphene or nanotechnology. A recent paper
[Soilleux 2019] uses anhydrous glass as a shell material. The
paper does not review maximum radii for tensile strengths;
however, it does introduce bending strength. We realistically
do not expect perfect results from our restructuring (some-
what primitive) manufacturing techniques. We include a
filled shell structure using anhydrous trusses and processed
regolith fill in our estimates. The structure does have lower
tensile strength; however, the low density increases the sta-
tion radius to over 20 kilometer in Table 3-1. We conserva-
tively intend to aim for a much smaller radius closer to 3 or
4 kilometers.
Station Stress: We provide a brief review of the stresses pro-
duced in the rotating space station. Stresses are produced
from air pressure and from centripetal forces. We compare
these stresses in Figure 3-5 for a rotating cylinder. The loga-
rithmic x-axis shows the rotation radius from 100 meters to
10,000 meters. The logarithmic y-axis shows the stress
ranging from 1 kilopascal to 1 gigapascals. The cylinder shell
is 20 meters thick. The shell rotates at a speed to produce one
Earth gravity on the outer rotation radius. The shell centrip-
etal hoop stress, σc, is the largest and is equal to gρR where
g is the centripetal gravity, ρ is the material density, and R is
the rotation radius. In this design, the circumferential air
pressure, σa, is the next largest and is equal to P R/t where P
is the internal air pressure, t is the shell thickness, and R is
the rotation radius. We use the furnishing stress values from
the 1977 NASA study [Johnson and Holbrow 1977]. The ra-
dial centripetal force and the radial air pressure force are both
minimal in the overall stresses in the cylinder; see Figure 3-5.
We assume a truss-like structure made of anhydrous glass
filled with crushed regolith. The tensile strength of this struc-
ture is defined as 1500 MPa and the density is set to 1720
kilograms per cubic meter.
We present in Figure 3-6 the working stress for various ma-
terials. The working stress is the sum of the stresses intro-
duced in Figure 3-5 and includes the stresses from the air
pressure, the centripetal forces on the shell, and the centrip-
etal forces on the internal structures and furnishings. The
chart shows the working stresses in megapascals ranging
from 1 to 10,000 on the logarithmic y-axis. The x-axis shows
the outer rim radius of the rotating station ranging from 100
to 20,000 meters. The station is rotating at a speed to produce
1g at the outer rim. The chart includes the material stresses
for four materials. The anhydrous glass has the largest tensile
strength and aluminum has the smallest. Steel, with the high-
est density, creates the largest working stress. The filled
structure, with the lowest density, creates the smallest work-
ing stress. Except for steel, all the materials support their
working stress below the rotation radius of 10,000 meters.
We use this radius as a maximum value because of material
strength.
Table 3-1 –Materials and Space Habitat Radius
Material
Tensile
Strength
(MPa)
Density
(g/cm3)
Radius
(km)
Molecular Nanotechnology 50,000 3.51 343.9
Anhydrous Glass (max) 13,800 2.70 123.4
Anhydrous Glass 3,000 2.70 42.8
Basalt fiber 3,000 2.67 27.1
Basalt rod (7mm) 2,471 2.79 21.4
Filled Structure 1,500 1.72 21.1
O'Neill Future 2,068 3.12 16.0
Titanium 1,450 4.50 7.8
Steel 1,240 7.80 3.8
Aluminum 352 2.65 3.2
Iron 275 7.20 0.9
Glass 7.0 2.50 0.1
Credit: Self produced using data from [O’Neill 1974] [McKendree 1995]
[Bell and Hines 2012]; [Facts]. Figure 3-5 – Space Station Stress Comparisons
1E-03
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
100 1000 10000
Stress
(MPa)
Rotation Radius (meters)
Stress Comparison - Air, Shell, Furnishings
(Cylinder, Structure Shell, Shell Thickness=20m)
Centripetal Hoop Air Pressure Circumferential
Centripetal Radial Air Pressure Radial
Centripetal Furnishings Air Pressure Axial

As shown in Figure 3-6, the material densities and tensile
strengths affect the working stress. We include a chart in Fig-
ure 3-7 to show the effect of the shell thickness on the station
stresses. We show the two largest stresses from Figure 3-5 –
the shell centripetal stress and the air pressure stress. The
chart shows the stresses on the y-axis and the shell thickness
on the x-axis. The chart includes data from a torus station and
a cylinder station. The torus is similar to the Stanford Torus
with a major radius of 830 meters and a minor radius of 65
meters. The cylinder is similar to the O’Neill C-3 design with
a radius of 1000 meters. With a higher ceiling and thicker
atmosphere, the cylinder air pressure stress is greater than the
torus air pressure stress. We use standard sea-level air pres-
sure at the outer rim. In both designs, the air pressure stress
decreases with the increasing shell thickness (σa is equal to
P R/t). The Stanford torus was designed to use ½ standard
sea level air pressure; as such, its air pressure marker is lower
than torus air pressure line. The Stanford Torus has a thin
shell of 1.68 centimeters [Johnson and Holbrow 1977]. We
design the C-3 cylinder with a thick shell of 20 meters. The
centripetal shell stress is slightly greater for the torus than the
cylinder. This is because the cylinder is made using the filled
structure shell and the torus is made with an aluminum shell.
The centripetal stress is proportional to the density and alu-
minum is denser than the anhydrous structure. Additional
analysis is recommended; however, this brief review of
structure stress suggests that large stations with thick struc-
ture shells are viable.
Population: We include in Figure 3-8 population estimates
from various reports [Johnson and Holbrow 1977] [O’Neill
et al. 1979] [Globus et al. 2007] [Brody 2013]. Everyone in
a space station needs space to support their living, working,
industry, and agriculture needs. Technical estimates of that
space ranges from 35 to 200 square meters of projected area
per individual. Historically, most designs use only projected
floor values using only a single floor on the outer perimeter
of the station for living space. The populations in this chart
have been normalized to a projected surface area allocation
of 67 square meters per person, which comes from a NASA
study [Johnson and Holbrow 1977].
Figure 3-8 includes four O’Neill cylinder models (C-1
through C-4) [Johnson and Holbrow 1977]. The lengths of
these cylinders are 10 times the radius. Figure 3-8 includes
the Kalpana One cylinder, which is a rotating cylinder with
a radius of 250 meters and a length of 325 meters [Globus et
al. 2007]. This cylinder is not on the cylinder line in the chart
because the Radius to Length (R/L) ratio for Kalpana One is
250/325 or about 3/4 instead of 1/10. The O’Neill cylinders
use two counter rotating cylinders to reduce precession. The
designers of Kalpana One used only one cylinder and re-
duced the length for rotational stability [Globus et al. 2007].
Figure 3-6 – Space Station Stress Comparisons
Figure 3-7 – Space Station Stress Comparisons
Radius and population of space habitats
Figure 3-8 – Space Stations Radius and Populations
1E+00
1E+01
1E+02
1E+03
1E+04
100 1000 10000
Pressure
(MPa)
Rotation Radius (meters)
Working Stress and Material Tensile Strength
(Working Stress: Sum of Air, Centripetal, and Furnishing Stresses)
Anhydrous Glass (3000 MPa, 2700 kg/m3) Steel
Structure (1500 MPa, 1720 kg/m3) Anhydrous Glass
Steel (1240 MPa, 7800 kg/m3) Aluminum
Aluminum (352 MPa, 2650 kg/m3) Structure
Tensile Strength Material Working Stress Material
C-1
C-2
C-3
C-4
Stanford Torus
Tiny Torus
Atira Torus
Ryugu Torus
Kalpana One
Globus
Cylinder
Elysium
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
100 1000 10000
Population
(67m2
per
person)
Major Radius (meters)
Cyl
Tor
C-1
C-2
C-3
C-4
Sta
Tin
Atir
Ryu
Kal
Glo
Ely

The chart in Figure 3-8 also includes various torus designs
for comparisons. We include the Stanford Torus and a Tiny
Torus from a NASA study [Johnson and Holbrow 1977]. A
1974 Stanford study detailed a rotating torus design with mi-
nor radius of 65 meters and a major radius of 830 meters
[Johnson and Holbrow 1977]. The Stanford Torus and the
Tiny Torus both fall along the torus line in Figure 3-8. We
include several of our study’s restructured asteroid torus sta-
tions in the graph for reference. These results are for the sin-
gle main floor of the torus. The Atira torus is above the torus
r/R line because of its elliptic cross section. We also include
the station from the movie Elysium [Brody 2013]. For con-
sistency, the Elysium population in Figure 3-8 uses the same
population density metric (67 meters squared per person).
We plan to use multiple floors and significantly increase the
available living space of our stations.
Multiple Floors: Adding floors to a structure greatly in-
creases the available floor space. Examples of multiple floor
structures include underground cities, submarines, cruise
ships, and skyscrapers. Historic and modern underground
cities exist [Garrett 2019]. Entrepreneurs have begun to con-
vert abandoned military missile silos into multiple floor
homes and underground cities [Garrett 2019]. Limited space
and costs in urban environments promote high rise living.
We contemplated whether there are other issues with creat-
ing and using many floors. Researchers and developers be-
lieve the biggest problems for underground cities are not
technical but social [Garrett 2019]. Studies have found that
people living in highrises suffer from greater mental health
problems, higher fear of crime, fewer positive social
interactions, and more difficulty with child rearing [Barr
2018]. Luckily, literature and the lessons learned from
highrise public housing failures offer knowledge and
experience to address such issues. NASA studies have
considered the oppressive closed-quarters ambience of a
space station to be a risk to the colonists’ psychological well-
being [Johnson and Holbrow 1977] [Keeter 2020]. Research-
ers offer approaches to address these risks. With proper
planning and space allocation, it seems that using many
floors is acceptable for space station habitation.
Figure 3-9 illustrates the cross-sections and the floor struc-
tures for an inner and outer torus. The inner torus has a cir-
cular cross-section in Figure 3-9a. The outer torus has an el-
liptical cross-section in Figure 3-9b. We use this level of de-
tail in our analysis to compute the mass of the station and the
floor surface area. We hope to use this level of detail in a
future stress analysis.
For large space stations, we feel the number of floors be-
comes excessive. The material in an Atira sized asteroid can
support the construction of a circular torus with a major ra-
dius of 5.5 kilometers and a minor radius of over 800 meters.
With a 5-meter spacing between floors, this torus could have
80 stories underground. We feel many of the lower floors
would not be desirable for residential use. Over the course of
our study, the cross-section of our torus shaped station
evolved from a circle to an ellipse. This reduced the number
of floors. It increased the surface area and improved the vista
on the main floor. We believe the elliptical cross section will
provide much of the structural strength of a circular cross
section. We also lowered the main floor – again reducing the
number of floors and improving the vista. The outer torus in
Figure 3-9b illustrates an example station with the ellipse
cross-section and a lowered main floor. For scale, the spoke
of the elliptical torus is the same diameter as the inner torus.
Multiple Floor Population: We use the space station geom-
etry to compute the available surface area. In a torus, the
main floor surface area is the floor width (twice the minor
radius) times the station circumference (two pi times the ma-
jor radius). As we go deeper into the torus, the floor width
decreases as the square root of the depth. The floor circum-
ference increases linearly with the radius (depth). We sum
these floor areas to compute the total square footage for the
station. We produce a population estimate by dividing that
total by a floor space allocation metric. We use the same
analysis approach on the other station geometries.
a) Cross-section of inner torus b) Cross-section of outer elliptic torus
Figure 3-9 – Torus Cross Sections – Multiple Floors and Elliptical Design
150m
1100m
150m
45m
45m
20m
20m
b=400m
150m
a=1200m a=1200m
1150m
150m
2700m
2400m
100m
b=400m

We compare the population of stations with a single floor and
with multiple floors in Figure 3-10. This chart includes the
potential populations for some of literature’s cylinder and to-
rus geometry space stations [Johnson and Holbrow 1977]
[Globus et al. 2007]. We show the major radius of the station
along the horizontal axis in Figure 3-10. This chart extends
the data from Figure 3-8 and for consistency we continue to
use the population density of 67 square meters per person.
The torus stations assume the outer half of the torus is filled
with floors. We limit the number of cylinder floors to better
compare to the torus geometries and to retain the open view
in the cylinder. For both the cylinder and torus geometries,
adding floors dramatically increases the square footage to
support larger populations. The elliptic Atira torus design has
a major radius (R) of 2116 meters and minor radii of 1003
meters and 334 meters (r). Because it has an elliptical cross
section and r=R/6.33, the station supports more population
than the r=R/10 line. The top floor supports almost 400,000
people using the 67 square meters per person. It supports a
maximum population of 21.5 million and a realistic popula-
tion of 3.5 million.
We again include the station from the movie Elysium. Ely-
sium is a torus with a major radius of 30,000 meters and a
minor radius of 1500 meters [Brody 2013]. In the movie,
Elysium has a population of 500,000 and that provides 1131
square meters of space for each individual. Using only 20 of
the multiple floors possible, Elysium would increase its floor
area from 565 square kilometers to 11,852 square kilometers.
With 67 square meters per person, the 20 floors of Elysium
would support 177 million people. Using the generous 1131
square meters per person used in the movie, it would still
support over 10 million people.
Multiple Floor Visualization: To help visualize these
floors, we include a cut through diagram in Figure 3-11. This
torus station has major radius of 2300 meters. The torus has
an elliptic cross section with minor radii of 400 meters and
1150 meters. The top floor is 100 meters below the major
radius distance. There are 17 floors under the top floor with
15 meters between each floor. There are 82 floors in the sky-
scraper towers with 6 meters between each floor. The shell
is 20 meters thick. The ceiling in the torus is 500 meters
above the top floor. This provides an open vista of 6 kilome-
ters over the curved top floor. The top floor in this station
would have 33.6 million square meters of floor space. The
18 floors in such a station would have 487 million square
meters of floor space. Using 155.2 square meters per person
[Johnson and Holbrow 1977], the floors of this station could
support over 3 million people. The projected floor area den-
sity of 67 square meters per person would support over 7 mil-
lion people. Other constraints (such as gravity ranges and
psychological well-being) will impact the floor space and re-
duce the population to a lower and more realistic value.
Station Mass: For our analysis, we use the masses of both
the station and the asteroid. Our analysis leads to charts
showing population as a function of mass and station geom-
etry. The station mass uses the volumes of the towers,
spokes, outer shells, floors, fill, and the shuttle bay. We de-
rived the mass of those components from material densities
and volume of individual panels, tiles, rods, and fill. In some
analysis, we use different densities for the components and
materials. The basalt tile density is assumed to be 2,790 kil-
ograms per meter cubed. The asteroid densities vary depend-
ing on composition and porosity and ranges from 1,192 to
2,566 kilograms per meter cubed. The fill material uses that
asteroid material and is packed and includes melted regions
for stability. We set the fill material density to 1,721 kilo-
grams per meter cubed. This is in the density range of gravel.
We use that as the density of our fill structure too. In some
analyses, we compute and use the density of complete struc-
tures in the station. We include example densities of the
Population shows significant gains with multiple floors
Figure 3-10 – Torus and Cylinder Populations
Credit: Self produced with Blender using Background Milky Way:
ESO/Serge Brunier, [Brunier 2009] [CC BY-4.0]
Large Torus Space Station: Cut through diagram showing
17 subfloors and 82 floors in spoke towers
Figure 3-11 – Exploiting Floors in Space Stations
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
100 1000 10000
Population
(67m2
per
person)
Radius (meters)
Cylinder (R=L/10)
Cylinder with Floors
Torus Projected (r=R/10)
Torus with Floors (r=R/10)
C-3
Stanford Torus (1 Floor)
Kalpana One
Atira (Max)
Atira (Realistic)
C-3
Kalpana
Stanford
Elysium
(1 Floor)
(Max)
(Realistic)
(1 Floor)
(1 Floor)
(Realistic)
(Max)
(Max)
(1 Floor)
(20 Floors)
Atira
(20 Floors)
(1 Floor)

shuttle bay, spokes, and different floor spacings in Table 3-2.
We sum the volume and mass of the individual pieces in the
components of the station. Figure 3-9 illustrates the level of
detail for this analysis. The mass includes the material
needed to construct the trusses, to fill the exterior walls with
regolith, and to cover the exterior and floors with panels.
We show in Figure 3-12 the summed masses from this anal-
ysis. This includes mass estimates for the four station geom-
etries. All four of the geometries use a thick filled outer shell.
This chart shows the radius along the x-axis and the station
mass along the y-axis. It is close to a linear relationship be-
tween the radius and the mass. It is not linear because our
analysis varies the dimensions of structures (such as shells
and tethers) with the changing radius. These dimension
changes provide additional support, strength, or radiation
protection. Additional structures (such as spokes and towers)
are also added to provide strength in large stations.
Floor Allocation Usage: A NASA design study included
surface usage metrics such as 49 square meters per person
for residential, 10 for open spaces, 12 for transportation, and
61 square meters per person for agriculture [Johnson and
Holbrow 1977]. Their total surface area was 155.2 square
meters per person of surface area. Some structures, including
houses, used multiple stories to support that requirement. Us-
ing multiple stories results in 67.0 square meters of projected
surface area per person. Another NASA study allocated
157.1 square meters per person and 70.5 square meters of
projected area [O’Neill et al. 1979].
We include this space usage distribution in Figure 3-13. We
organize their categories into open areas, support, agricul-
ture, industry, and residential. This chart also includes our
estimates for different floors spacings. With a fixed floor
spacing of 15 meters, our updated space allocation provides
each individual a similar 65.5 square meters per person. Us-
ing this metric on previous example station, the 33.6 million
square meters of the first floor by itself would support a pop-
ulation over 500,000 individuals.
Like the NASA studies, we also use multiple story structures
to support our usage requirements. We also account for the
multiple floors in our station designs. We consider floor
spacings of 5, 10, and 15 meters. Different usage metrics are
shown for the categories and floor heights; see Figure 3-13.
NASA used various heights for the different space categories
(an average height of 11.2 meters).
Even with the different floor spacings, many of our detailed
categories use the same volume; as such, their space require-
ment simply scales with the changing floor distance. As an
example, the agriculture allocation increases from 13 to 39
square meters per person as the floor distance decreases from
15 to 5 meters. The total agriculture volume remains constant
at 195 cubic meters per person.
We increase the open space in the NASA study from 10
square meters per person to 18.7 square meters per person.
This includes some of the public areas in the support cate-
gory and adds an extra 5 square meters per person. The top
floor is more suited for open space, tourism, and recreation.
The top floor in our example station could meet the open
space requirement for over 1.8 million people. Lower floors
may also be used for residence and leave more of the top
floor open to help meet the open space requirement of 18.7
square meters per individual. In large stations, the top floor
can often meet the open space requirement. There is also op-
portunity to be creative and use low and high gravity regions
to create additional open areas.
Table 3-2 – Densities of Station Components
Density Value (kg/m3) Density Value (kg/m3)
𝜎𝑏𝑎𝑠𝑎𝑙𝑡 2790 𝜎𝑠𝑝𝑜𝑘𝑒 337.4
𝜎𝑟𝑜𝑑 2790 𝜎𝑓𝑙𝑜𝑜𝑟5 32.2
𝜎𝑝𝑎𝑛𝑒𝑙𝑠 2790 𝜎𝑓𝑙𝑜𝑜𝑟10 17.0
𝜎𝑏𝑎𝑦 2291 𝜎𝑓𝑙𝑜𝑜𝑟15 11.2
𝜎𝑓𝑖𝑙𝑙 1721 𝜎𝑎𝑖𝑟 1.23
Figure 3-12 – Station Mass Summed from Individual
Station Components Figure 3-13 – Floor Space Requirements per Person
1.0E+08
1.0E+09
1.0E+10
1.0E+11
1.0E+12
1.0E+13
1.0E+14
1.0E+15
100 1000 10000
Mass
(kilograms)
R - Rotation Radius (meters)
Station Mass
(Half Floors; fd=5m; Structure Varies with Radius)
Cylinder - R=a; l=1.3a
Ellipsoid - R=6.33a; c=0.8165a
Torus - R=6.33; c=2a
Dumbbell - R=6.33a; c=2a
48.6
34.7
21.2 12.1
12.1
6.1
4.0
2.0
39.0
19.5
13.0
20.3
25.9
12.9
8.6 22.6
18.7
18.7
18.7
10.0
144.2
91.9
65.5 67.0
0
20
40
60
80
100
120
140
160
Floor Spacing
fd=5m
Floor Spacing
fd=10m
Floor Spacing
fd=15m
1977 NASA
fh=11.2m
Space
Requirement
(Square
meters/Person)
Projected Floor Space Requirements per Person
Open
Support
Agriculture
Industry
Residence

The average home size has increased by 50% since the
1970s; as such, we increased the requirements for the resi-
dence. We increased the industry area requirements. This
will be important to make the station self-sufficient with ex-
port products.
NASA studies [Johnson and Holbrow 1977] [Bock, Lam-
brou, and Simon 1979] and more recent studies [Soilleux and
Gunn 2018] [Fu et al. 2016] have evaluated the use of agri-
culture and plants in a closed system environment. We de-
creased the requirement for agriculture using those recent
metrics. The biggest change is in the height of the agriculture
areas. The NASA studies used conventional farming and as-
sumed heights of 15 meters. We use short stacked shelves of
growing areas. We can even stack multiple shelves of agri-
culture in the 5 meter floor spacing. These changes reduced
the required agriculture volume from 915 to 195 cubic me-
ters. There are also even more recent advancements in hy-
droponics, aeroponics, and new biological approaches
[Kersch 2015] [Cornall 2021]. Those advancements offer
more reduction to the crop growing requirements. We con-
servatively do not include those most recent reductions in our
estimates.
Floor Space Allocation Examples: We evaluate an example
torus station with a major radius of 2300 meters and an ellip-
tic cross-section with minor radii of 400 meters by 1150 me-
ters. It also includes two inner tori, each with a radius of 1100
meters and a cross section radius of 75 meters.
This design has over 34 square kilometers of floor space on
the elliptic main floor alone. With a floor spacing of 15 me-
ters, there are 18 floors with 487 square kilometers in the
outer torus. The 15-meter spacing provides room for some
multistory buildings. This design has two inner torii and cre-
ates 8 dividers, 8 towers, 16 spokes, and two shuttle bays;
see Figure 1-1. Including all surface area on all the floors and
structures there is a total of 1070 million square meters of
projected floor space.
Some regions of the space station are not conducive to long
term habitation. Other regions are ideal for parks and recrea-
tion. We show in Figure 3-14 the space available in the major
components of the Atira station. With the total of 1070 mil-
lion square meters and a floor space allocation of 65.5 square
meters per person, we find that the station could hold a max-
imum of 16 million people.
We show a bar chart in Figure 3-15 as a final preview of the
station floor space allocation. The chart continues with the
same example torus station. The chart example uses the en-
tire space station to support a large population. With the floor
spacing of 15 meters, there are 18 floors. We assign the top
6 floors to be the habitable region and the bottom 12 floors
to be the lower ellipse region. By adjusting the portion used
in each of the station components, the chart in Figure 3-15
shows this station could comfortably support 10 million peo-
ple. Most of the population lives on the first six floors of the
station. This region has the most Earth-like gravity. We ex-
pect most of the top floor would provide the open recreation
regions for psychological well-being. Below the top floor,
facilities such as aquariums and botanical gardens could cre-
ate more open regions. Agriculture is likely to be in the lower
portions of the station. Industrial manufacturing is highly au-
tomated and requires few people to support and could reside
in the least desirable regions such as the higher-gravity low-
est floors and the low gravity spokes. Even with 10 million
people, there is still significant space available for storage.
This storage would initially be used for the inventoried met-
als and volatiles from the asteroid restructuring process. It
could be later used for more growth, tourism, industry, or ag-
riculture. Conservatively, we aim to support a population of
700,000. It is comforting to see that this station could support
many more people.
3.2.2 Geometry Rotational Stability
In the Elements of Spacecraft Design, Charles Brown recom-
mends that the desired axis of rotation should have an angu-
lar moment of inertia (MOI) at least 1.2 times greater than
any other axis to provide rotational stability [Brown 2002].
This constraint is important in developing the geometry
sizes. A recent paper investigated the rotational instability of
long rotating cylinder space stations [Globus et al. 2007].
Figure 3-14 – Space Available on Station Components
Figure 3-15 – Atira Station – Space Allocation
3.36E+07
3.57E+08
5.49E+08
1.98E+07
1.37E+06
5.03E+06
7.05E+05
1.87E+07
2.06E+07
6.09E+07
2.48E+06
1.070E+09
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
1.0E+10
Area
(square
meters)
Atira Elliptical Station - Floor Space
(Radii Radius: Major=2300; Minor A=1150; Minor B=400; Floor Spacing=15)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
Population
(Count)
Millions
Floor Space Allocation Category (square meters)
Atira Elliptical Station - Population Supported
(Radii: Major=2300; Minor A=1150; Minor B=400; Floor Spacing=15)
Habitable
Ellipse
Lower
Ellipse
Inner
Torus
Spokes
and Bay
Towers

That study imposed a limit on the cylinder length to passively
control the rotational stability. The study also mentioned that
a perfect sphere has a similar issue with rotational stability.
We have extended the Global cylinder analysis to three other
geometries. We show the cross sections of the four geome-
tries in Figure 3-16. The diagrams show the floors half filling
the station with labels on the radii and other dimensions. We
have analyzed using thick and thin shell stress equations. We
present our results using thin shell hollow geometries. Our
20 meter thick shells are “thin” compared to our large station
radii. We provide terse overviews of the Globus Cylinder
Station analysis [Globus et al. 2007] and our Oblate Ellipsoid
station analysis. We include only final summary statements
for the Torus and Dumbbell geometries.
Flat-capped cylinder: The cylinder is short and squatty
(hatbox) and has a rotation radius (R) larger than the height
(h); see Figure 3-16a. The moment of inertia (MOI) for the
cylinder uses the mass (M), radius (R), and height (h). Along
the longitudinal axis (the x-axis in Figure 3-16a) the inertia
is Ix=MR2
for a cylinder without endcaps. Along the other
two axes, the inertias are Iy=Iz=(1/2) MR2
+ (1/12) M h2
. To
be stable, Ix >= 1.2 Iy and we find h<=2R. With endcaps, we
must include the MOIs for those end disks. Globus uses a
thin shell and assumes the disks and shell have the same
thickness and density. For the total system Ix = M R2
(1 +
R/2h) and Iy = M (R2
/2 + h2
/12 + R3
/(4h) + Rh/4). The end
caps have a detrimental effect on stability. Globus finds the
system would be stable when h=1.3R with the endcaps in-
stead of 2R without the endcaps [Globus et al. 2007].
Oblate Ellipsoid: An oblate ellipsoid has two major axes
that are the rotation radius length (a=b) and a third minor axis
with a length (c) that is shorter than the other two; see Figure
3-16b. The moment of inertias for the oblate ellipsoid uses
the mass (M) and the rotation radii (a, b, and c). The ellipsoid
rotates about the minor axis. The MOI of the ellipsoid around
the x-axis is Ix = (2/3) M a2
Along the other two axes, the
inertia is Iy = Iz = (1/3) M (a2
+ c2
). To be stable, Ix >= 1.2
Iz and we find the length of the minor axis c must be less
than 0.8165 times the major axis (a or b) length. This math-
ematically validates that a sphere would not be stable.
Dumbbell: We analyzed a dumbbell with spherical nodes;
see Figure 3-16c. For typical designs, the dumbbell will al-
ways be rotationally stable.
Torus: We also analyzed tori with circular and with elliptic
cross sections. The drawing in Figure 3-16d shows the ellip-
tic cross section. We have found torus designs would always
be rotationally stable for typical dimensions of elliptic and
circular cross section.
Table 3-3 contains a summary of our current stability equa-
tions for the four station geometry types. These equations
represent moments of inertia for thin-shell hollow geome-
tries. We evaluated hollow and solid geometries and found
minimal (or no) difference in the MOI results. This suggests
that the half-filled station will have the same stability MOI
characteristics. We have begun a similar analysis using the
shell, air, and floor densities (see Table 3-2) with these mul-
tiple floor geometries (see Figure 3-16).
3.2.3 Station Gravity Ranges
We cover three aspects of centripetal gravity in the following
paragraphs. We review the health impact of gravity, viable
ranges of gravity in the multiple floor rotating stations, and a
specific station example for its centripetal gravity.
Gravity Health Impact: Earth’s surface gravity ranges from
0.996g to 1.003g. Our human bodies have adapted to this
narrow range. We need to consider what range of gravity in
the space station will be acceptable for the colonists’ health.
Astronauts in the International Space Station (ISS) experi-
ence microgravity. This microgravity negatively affects hu-
man health by weakening bones and muscles. This increases
the risk of osteoporosis and cardiovascular problems.
Planned habitats on the moon will subject the residents to
0.16g. Habitats on Mars will subject residents to 0.38g.
These gravities may be insufficient to prevent the related
health problems [Boyle 2020].
a) Cylinder Station b) Ellipsoid Station c) Dumbbell Station d) Elliptic Torus Station
Figure 3-16 – Station Cross Sections – Floors Half Filling Station

There could be issues with high gravity too. A recent paper
determined a muscle strength upper limit of 1.1g [Poljak,
Klindzic and Kruljac 2018]. They also found gravity maxi-
mum tolerance could be increased by a factor of four to 3g
or 4g (with the strength of a few elite athletes).
Geometry Gravity Ranges: We can design the station with
different radii and rotation rates. This will vary the gravity
values over the station. The 1977 NASA study used a gravity
range to 0.9g to 1.0g and offered a relaxed constraint range
of 0.7 to 1.0g [Johnson and Holbrow 1977]. In the paper Ad-
vanced-Technology Space Station for the Year 2025 [Queijo
et al. 1988], the authors designed a torus station with a grav-
ity range from 97% to 103% Earth gravity. They felt this
range would not have any significant influence on human
physiology and performance. Our main concern is the grav-
ity range over the habitable portions of the station. We focus
on the gravity values from the top floor to the outer shell of
rotating stations.
To provide multiple floors, we also advocate relaxing the
gravity range constraint. We typically design a gravity range
of 0.95g to 1.1g for most of our half-filled multiple-floor de-
sign in the large restructured asteroid stations. The top floors
are where most of the population will spend most of their
time. We want these floors to have the most Earth-like grav-
ity. We aim for a gravity range of 0.95g to 1.05g over those
floors to minimize the health risk to the residents. We note
that some “higher” regions on the curved floor of spheres,
spoke towers, cylinder endcaps, and torus dividers will pro-
vide lower gravity environments. Only the “lowest” floors
near the outer rim of the designs will have the higher gravi-
ties. We recognize the larger gravity values on the outer rim
will require stronger materials and structures in the station
design.
We consider two classes of rotating stations. One class ro-
tates about an axis outside the habitable region and includes
the torus and dumbbells. The other class rotates about an axis
inside the habitable region and includes the cylinder and el-
lipsoid. We also vary the number of floors in the station vol-
ume. In one case we fill the habitable volume halfway and
the other case we fill the volume completely. We include Fig-
ure 3-17 to illustrate these classes and cases. Figure 3-17a
shows a half-filled volume rotating about an external axis.
Figure 3-17b illustrates a half-filled volume rotating about an
axis internal to the habitable volume. Figure 3-17c shows a
fully filled volume rotating about the external axis. The cir-
cular outer shells in the figures should be squished to repre-
sent the elliptical cross section for the torus or the prolate
ellipsoid for the dumbbell. The circular outer shell in Figure
3-17b should be squared to represent the cylinder.
We first consider the half-filled stations in Figure 3-17. We
have taken liberty in the term “half-filled.” The geometry
shape and providing a habitable gravity range determines the
actual fraction filled. In Figure 3-17a and b, we see that the
major radius is R to the floor at the center of the space station.
The centripetal gravity at the outer shell will be gmax and will
be equal to (R+h) ω2
, where ω is the station rotation rate in
radians per second. The minimum gravity, gmin, will be at the
top floor and will be equal to Rω2
. We create a relationship
between the distance h and the distance R. The radius R is a
multiple, m, of the distance h; i.e. R=mh. On a torus, this will
be the ratio of the major and minor axes. We first find the
minimum and maximum gravities for half-filled volumes as
shown in Figure 3-17a and b as 𝑔𝑚𝑎𝑥 = (𝑅 + h)𝜔2
and
𝑔𝑚𝑖𝑛 = 𝑅𝜔2
. Reorgnizing we find:
𝑚ℎ𝜔2
𝑔𝑚𝑖𝑛
=
(𝑚 + 1)ℎ𝜔2
𝑔𝑚𝑎𝑥
Divide each side by h and ω2
and reorganize, we find the
scaling factor would be:
𝑅 ℎ
⁄ = 𝑚 = g𝑚𝑖𝑛 (g𝑚𝑎𝑥 − g𝑚𝑖𝑛)
⁄
For the fully filled station with the external rotation axis in
Figure 3-17c, the maximum centripetal gravity would be at
the radius R+h and the minimum at the radius R-h. With a
similar analysis, we find for the Figure 3-17c the scaling
factor would be:
𝑅 ℎ
⁄ = 𝑚 = (g𝑚𝑎𝑥 − 2g𝑚𝑖𝑛) (g𝑚𝑎𝑥 − g𝑚𝑖𝑛)
⁄
We do not include a drawing of the full-filled internal rota-
tion axis in Figure 3-17. The minimum gravity, gmin, would
be at the center on the rotation axis and be 0g. The floor on
the outer rim would be gmax and be equal to Rω2
. The scaling
factor, m, would not be defined because h would be equal to
zero. The low gravity near the center would make this region
not habitable for long term residence. Acceptable gravity re-
gions can be determined using the equations and the scaling
factor of the half-filled station analysis.
We include Table 3-4 to illustrate the variation of the scaling
factor, m, for different minimum and maximum gravities.
Table 3-3 – Geometries and Rotational Stability
Geometry Key Stability Factor Rotational Stability Notes
Cylinder c < 0.65 a Hatbox cylinders can be stable Flat endcaps
Ellipsoids c < 0.8165 a Oblate ellipsoids can be stable Sphere stations are not stable
Dumbbell
r (tether) << a (spheres)
R > 0.365 a
Dumbbells are stable for our designs
where R>=6.33a
Tether mass and radius are much
less than the spherical nodes.
Elliptical
Torus
R2 > 0.75 (c2-a2) or R>1.4a
c<3.6056 a
Elliptical tori are stable for our designs
where R>=6.33a and c=2a or c=3a
Torus only – inner docking station
and spokes not included
Credit: Self produced by extending cylinder concepts from [Globus et al. 2007] [Facts]

This chart is for the half-filled stations shown in Figure 3-17.
We show the minimum gravity values across the top of the
chart and the maximum gravity values along the left side.
The gravity in the floors areas of our designs is between
0.95g and 1.05g. For a half-filled station, we find that the
scaling factor, m, would be equal to 0.95/(1.05-0.95)=9.5 and
the rotation radius of the station would be 9.5 times the dis-
tance h. In Table 3-4, the scaling values range from 2 to large
values when the gmin and gmax are almost the same value. We
highlight two values in the table: 9.5 and 6.33. These repre-
sent a minimum of 0.95g on the top floor and a maximum of
1.05g or 1.1g on the outer rim. We use those values and grav-
ity ranges extensively throughout our research.
Example Station Centripetal Gravity: We consider a sta-
tion design where the main floor of the outer elliptic torus is
2400 meters from the center of the station. The main floor of
the inner torus is 1100 meters from the center of the station.
The station will rotate once about every 1.6 minutes. This
will produce the sensation of Earth like gravity on the main
floor of the large outer elliptic torus. Centrifugal force from
the rotating frame of reference produces this artificial or
pseudo gravity. We show in Figure 3-18 the centripetal grav-
ity in this rotating space station. On the right side of the chart,
we show the gravity for the Earth, Moon, Mars, and Atira.
The bottom floor of the outer torus has the highest gravity of
1.06g. In the outer torus, the divider top floor and the tower
top floor has a gravity of 0.89g. The main floor of this design
has a gravity of 1.0g and only increases to 1.03g on the 20th
floor below the main floor. Most of the 700,000 residents
will live and work in this region between 1.0g and 1.03g.
Figure 3-18 also shows the inner torus will provide a gravity
greater than Mars but less than Earth. The small shuttle bay
at the center will provide a gravity more like the Moon.
Station Gravity Summary: When possible, we aim for a
gravity range of 0.95g to 1.05g in the most occupied areas of
the station. We believe this gravity range should minimize
the health risk to the residents. We reserve the upper-half,
low-gravity regions of the space station to serve as open
space. This open space provides good vistas and beneficial
aesthetics for the residents and visitors. Regions with gravity
near Earth-like (1g) are used for living, recreational, and
working quarters. The centripetal gravity increases with
depth into the station. Higher-gravity regions could provide
high strength training, filtration systems, and higher gravity
research. A recent space station design used an entire deck
Table 3-4 – Half Filled Floor Scaling Factor for Various
Centripetal Gravities
Figure 3-18 – Centripetal gravity in Atira Station
a) Half Filled External Rotation b) Half Filled Internal Rotation c) Full Filled External Rotation
Figure 3-17 – Gravity Ranges in Half and Full Filled Volume

as a large ventilation duct [Soilleux and Gunn 2018]. We
would place this ventilation deck (or two) in the higher-grav-
ity region. This saves space on the 1g regions to support a
larger population. Other functions could be placed in the
lower, high-gravity, decks including machinery, storage, and
agriculture. With today’s understanding, working in the
higher and lower gravities should be kept to a minimum and
avoided or perhaps done in shifts. Our hope is the chosen
gravity range and limited exposure to lower and higher grav-
ities will have no impact on the inhabitants’ health.
3.2.4 Geometry Adaptations
Most historic studies use only the outer shell of their geom-
etry for living space. We review in this subsection our station
geometry adaptations when using multiple floors and provid-
ing a reasonable gravity range over those floors. The chart in
Figure 3-10 illustrated the significant gains from using mul-
tiple floors on cylinders and tori. We include in Table 3-5
eight example stations from the literature [O’Neill 1976]
[Johnson and Holbrow 1977] [Bock, Lambrou, and Simon
1979] [Globus et al. 2007]. We selected two example stations
for each of the four geometries. The top half of the table pre-
sents the original floor surface area, the population density,
and the population for the eight stations. The bottom half of
the table presents the multiple floor version of those stations.
The following paragraphs focus on one example from each
of the four geometries.
Dumbbell Adaptations: We consider a station covered in
the 1977 NASA study [Johnson and Holbrow 1977]. In that
study, they use a projected surface area equal to the center
cross-section of the dumbbell sphere. Their baseline dumb-
bell station design had two sphere nodes. Each had a 65-me-
ter radius and a 13,273 square meter cross-section. They al-
located 67 square meters for each individual and this station
could support 396 people.
The dumbbell sphere nodes could have multiple floors. If we
leave the top half of the sphere open for aesthetic reasons,
the bottom half could have 13 floors separated by 5 meters.
The dumbbells would have 243,002 square meters of floor
space. Allocating 67 square meters for each person, we find
that the two spheres with 13 floors could hold a population
of 3627 people – almost 10 times the single floor version. A
more comfortable density is 144.2 square meters per individ-
ual; see Figure 3-13. At this density, the dumbbell station
would support a population of 1685 people. If we were to
rotate the two 65-meter-radius spheres at 1.2 RPMs about a
radius of 618 meters, the cross-section floor would experi-
ence 0.95g and the outer floor would experience 1.05g.
We see in Table 3-5 that the multiple floors increase the
available surface floor area of the spheres in the dumbbell
designs. Each of the small spheres increase from 13,273
square meter to 121,501 square meters. The 1977 NASA
study [Johnson and Holbrow 1977] also describes a single-
floor dumbbell with a radius of 316 meters to support a pop-
ulation of 10,000 people. We include in Table 3-5 a multiple
floor dumbbell design to support 10,000 people. Compared
to the 316-meter radius design, the multiple floor design has
a smaller radius of 118.6 meters. These spheres would rotate
at a radius of 1127 meters and produce gravities at 0.95g and
1.05g at the top (center) floor and bottom (outer rim) floor.
Sphere Adaptations: Researchers and writers have consid-
ered spherical space stations for over 100 years. Gerard
O’Neill proposed two spherical stations in his book The High
Frontier: Human Colonies in Space [O’Neill 1976]. The first
was called Island One, had a diameter of 500 meters, and
could support 10,000 people. The second was called Island
Two, had a diameter of 1800 meters, and could support
75,000 people. Even though spherical space stations are ro-
tationally unstable [Globus et al. 2007], our analysis shows
that ellipsoid space stations can be rotationally stable. In the
following paragraphs, we provide a brief comparison of the
spherical station to a similar ellipsoid station.
We use an oblate ellipsoid, and it rotates about the minor
axis. The minor axis length is less than 0.8165 times the
length of the major perpendicular axes to provide the rota-
tional stability. For Island Two, we keep the diameter of the
major axes at 1800 meters and set the minor axis diameter to
1469.7 meter. This ellipsoid would be rotationally stable.
Table 3-5 – Restructuring Improvement Examples for Space Station with Four Geometries
Single Floor Design Units Tiny Stanford Kalpana One Model 3 Island One Island Two NASA 65 NASA 10K
Major Axis (R) meters 190 830 250 1,000 250 900 650 3,002
Minor Axis or Length meters 33.5 65.0 325 10,000 250 900 65 316.0
Population count 10,000 10,000 3,000 2,000,000 10,000 75,000 396 10,000
Floor Area meters2
276,485 678,000 510,508 125,663,600 350,000 2,625,000 26,546 670,000
Population Density m2 / person 27.6 67.8 170.2 62.8 35.0 35.0 67.0 67.0
Max Ceiling Height meters 67.0 130.0 500.0 2,000.0 500.0 1,800.0 130.0 632.0
Multiple Floors Units Tiny Stanford Kalpana One Model 3 Ellipsoid One Ellipsoid Two NASA 65 Pop=10K
Floors count 7 12 5 20 4 18 13 24
Minor Axis or Length meters 33.5 65.0 325.0 1,300.0 204.1 734.9 65.0 118.6
Top Floor Radius meters 190.0 830.0 226.2 904.8 226.2 814.3 617.5 1,126.7
Population count 13,715 70,051 16,723 2,047,560 6,546 278,693 1,685 10,000
Floor Area meters2
1,977,703 10,101,300 2,411,457 295,258,152 943,981 40,187,494 243,002 1,442,000
Population Density m2 / person 144.2 144.2 144.2 144.2 144.2 144.2 144.2 144.2
Max Ceiling Height meters 33.5 65.0 452.4 1,809.6 452.4 1,628.6 65.0 118.6
Torus Cylinder Sphere Dumbell

The outer surface would be at a radius of 900 meters, and we
set the top floor at 814.3 meters. The gravity would range
from 0.95g to 1.05g with the station rotating at 1.02 RPMs.
There would be 18 floors with a total surface area of 40.2
million square meters. O’Neill wrote that Island Two could
support a population of 75,000. This assumed 35 square me-
ters per person and all agriculture was in an adjacent banded
torus “crystal palace” structure. With 18 floors, the Ellipsoid
Island Two station could support 600,000 people at 67 square
meters per person. Using the 144.2 square meters per person
density would eliminate the separate agriculture structure
and still support 278,693 inhabitants.
We see in Table 3-5 that the multiple floors increase the Is-
land One floor area from 350,000 to 943,981 square meters.
The Island Two size station population increases from
75,000 to 278,693 people. Using the same major radius and
a smaller minor radius, the exteriors of these oblate ellipsoid
stations are a little smaller than the O’Neill spherical station
designs. The population density is improved considerably
from 35 to 144.2 square meters per individual. There is still
reasonable openness and vistas on the top floor.
Cylinder Adaptations: Multiple reports from the 1970s and
1980s used cylinder lengths that were 10 times the radius. A
recent paper investigated the rotational instability of long ro-
tating cylinder space stations [Globus et al. 2007]. That study
imposed a limit on the length to passively control the imbal-
ance of the rotating structure [Globus et al. 2007]. To meet
this imbalance metric, they found the cylinder length should
be less than 1.3 times the radius.
We show artwork of the Model 3 O’Neill cylinder space sta-
tion [O’Neill 1974] in Figure 3-1. This cylinder was 10,000
meters long and had a radius of 1000 meters. O’Neill ex-
pected it hold 200,000 to 2 million people. Two counter-ro-
tating cylinders were attached to eliminate gyroscopic effects
and precession. Using the Globus imbalance metric, a rota-
tionally stable version of a single cylinder with a radius of
1000 meters would have a length of 1300 meters. We would
design the bottom floor (outer cylinder) at 1000 meters ra-
dius and the top floor (inner cylinder) at 904.8 meters radius.
This would support 20 floors spaced 5 meters apart. The sta-
tion would rotate at 0.97 RPM and provide 1.05g at the bot-
tom floor and 0.95g on the top floor. This version of cylinder
would not have the windows or complex mirrors like the
Model 3 station. The top floor would house 51,250 people at
144.2 square meters per person. The 20 floors would support
2,047,560 people. With its multiple floors and with a more
comfortable population density, this single cylinder would
hold as many people as the much bigger and double O’Neill
Model 3 cylinders.
We compare in Table 3-5 the single floor and a multiple floor
version of the Kalpana Station. Globus and his team designed
the Kalpana One space station and found it could support
3000 people [Globus et al. 2007]. The Globus team mentions
multiple floors doubling the surface area. We find adding 5
floors, each separated by 5 meters, would increase the floor
space from 510,508 square meters to 2,410,000 square
meters. The station would rotate at 1.94 RPM and the outer
hull would have 1.05g and the top floor would have 0.95g.
Given 144.2 square meters per person, the multiple floor
Kalpana station would house 16,723 people.
Torus Adaptations: Table 3-5 includes the rotating station
from a 1974 Stanford study. The Stanford Torus has a major
radius of 830 meters and a minor radius of 65 meters [John-
son and Holbrow 1977]. This torus rotates at 1 rpm to pro-
duce the effect of one Earth gravity on the outer surface.
Their study suggested 47 square meters of projected area for
each inhabitant. They also determined that agriculture re-
quires an additional 20 square meters for each person and
brings the total population density is 67.8 square meters per
resident. The Stanford Torus surface area would be 678,000
square meters and support a population of 10,000.
Our multiple floor Stanford Torus still uses a circular cross
section with an 830-meter major radius with 65-meter minor
radius. There could be 12 floors spaced 5 meters apart in the
outer half of the torus. The station would rotate at 1.01 RPM
and the top floor would have 0.96g while the bottom floor
would have 1.03g. The top floor would support 4,412 people
at 144.2 square meters per person. Using the 67 square me-
ters per person metric, the top floor would support 9,496 peo-
ple. We find the maximum population would be 70,051 peo-
ple including the area of all 12 floors, spokes, and shuttle
bay. A more realistic population would be 42,465 and would
primarily have inhabitants living on the top 10 floors.
Table 3-5 also includes a Tiny Torus from the 1979 O’Neill
Study [O’Neill et al. 1979]. This torus had a major radius of
190 meters. It had 276,485 square meters of floor space and
could support 10,000 people [Bock, Lambrou, and Simon
1979]. Using 7 floors, the floor space increases to almost 2
million square meters.
To better compare the single floor and multiple floor torus,
we use a consistent population density of 144.2 square me-
ters per person. We see the supported population increase
from less than 2,000 to more than 13,000 people on the tiny
torus station with only 7 floors. The population increases
from 4,701 people to over 70,000 people with a Stanford To-
rus size station with 12 floors. We note the perceived height
to the ceiling would be cut in half for the inhabitants. The
vista in the rotation direction would remain about the same.
The ceiling height reduction would be noticeable for small
stations; however, the ceiling height reduction would be hard
to perceive in larger stations. In our opinion, the gains in pop-
ulation and the improved population density outweigh the
loss in ceiling height.
Restructuring Population Improvements: The examples
in the previous paragraphs and in Table 3-5 illustrate the ben-
efits from using multiple floors in the space stations. It is
possible to maintain acceptable gravity levels from the top
floor to the outer rim (0.95g to 1.05g). A station designed to
be rotationally stable typically has a smaller dimension on
one of the axes. Multiple floors increase the population and
compensate for that smaller dimension. With the increased
floor space, the station design can be simplified by bringing

the agriculture in the station (instead of an external “crystal
palace”). Even with the simpler design and the internal agri-
culture, the stations can support greater populations than a
single floor design.
3.2.5 Station Mass
The previous subsection detailed the impact of using multi-
ple floors with the four geometries using historic stations. In
all cases there were significant improvements in the popula-
tion supported. We now overview the relationships between
population, station radius, and mass.
Example Asteroids: We consider the effect of construction
material mass and geometries on the supported population.
This assessment uses the same four geometries, thick shells,
and the station volume half filled with floors. In the previous
asteroid section, we chose 5 asteroids with a good range of
sizes for our study; see Figure 2-1. We use these same 5 as-
teroids to illustrate the available oxide building material. We
show in Table 3-6 their characteristics and the resulting pro-
cessed material. In our building material estimate we account
for asteroid porosity, processing losses, and asteroid compo-
sition. The asteroid density varies with the asteroid size and
type. We derived porosity and processing metrics of 48.3%
and 24.4%. The asteroids are assumed to contain 84.9% ox-
ides, 4.0% volatiles, and 11.1% metals. We designed the sta-
tions to use 30% of the volume of asteroid oxides as building
material. This results in using only 10% to 13% of the total
asteroid mass to create the station construction material.
Mass and Radius: We show Figure 3-19 the radius of the
same four station geometries and their required construction
material. We show along x-axis the amount of building ma-
terial in kilograms. This is the processed oxide material from
the asteroids. We show the 5 example asteroids along the axis
at the mass of their station oxide building material. We show
along the y-axis in Figure 3-19 the radius of the station that
can be constructed with each of the geometries.
We include a line for the minimum radius at 224 meters,
which when rotating at 2 revolutions per minute produces 1g
Earthlike gravity. We include a line at the maximum radius
(10 kilometers) in Figure 3-19. We included in Table 3-1 dif-
ferent materials and the maximum rotating station radius
given material density and strength [McKendree 1995].
O’Neill envisioned stations up to 16 kilometers using future
materials [O’Neill 1974]. Basalt rods and fibers could be that
type of future material and could support a station radius over
20 kilometers. We envision using anhydrous glass tiles and
beams to support even larger station radius. We reviewed the
properties of these materials in Table 3-1. We conservatively
set 10 kilometers as a maximum radius on this graph. We
earlier found that most of our considered materials can sup-
port our station working stresses with this radius.
We see in the chart that the dumbbell station has a much
larger radius given the same amount of material. This makes
sense because the other geometries encircle the center of ro-
tation. The dumbbell has two nodes at the radius distance
from the center. Given the lower and upper limits, we see in
Figure 3-19 that dumbbell geometries are viable for small to
medium sized asteroids. Dumbbell geometries are not viable
for large asteroids because their rotation radius would exceed
our maximum 10-kilometer metric. The building material
from the asteroid Šteins would create a huge dumbbell sta-
tion with a large radius exceeding that limit. We also see in
Figure 3-19 that cylinders and ellipsoids are not viable for
small asteroids because their radius would be smaller than
our minimum 224-meter radius. The building material from
the asteroid Bennu would create a cylinder station with too
small of radius.
Mass and Population: The charts in Figure 3-20 compare
the population supported by the four geometries. For refer-
ence, we show the mass of five asteroids along the horizontal
axis of the chart. Many parameters such as the radius, floor
count, and support structures vary with the available mass.
The charts in Figure 3-20 combine all those parameters. It
combines many assumptions, requirements, and design deci-
sions. Its value is more for comparative than absolute results.
Table 3-6 – Available Building Material
Asteroid Bennu Ryugu Moshup Atira Šteins
Mass (kg) 7.3E+10 4.5E+11 2.5E+12 4.1E+13 1.5E+14
Volume (m3) 6.2E+07 3.4E+08 1.6E+09 2.2E+10 7.6E+10
Mean Radius (m) 241 448 659 1928 2580
Asteroid Type S-Type S-Type S-Type S-Type E-type
Density (kg/m3) 1192 1324 1537 1875 1908
Packed (m3) 3.2E+07 1.8E+08 8.4E+08 1.1E+10 3.9E+10
Processed (m3) 2.4E+07 1.3E+08 6.3E+08 8.6E+09 3.0E+10
Oxides (m3) 2.0E+07 1.1E+08 5.4E+08 7.3E+09 2.5E+10
Volatiles (m3) 9.6E+05 5.3E+06 2.5E+07 3.4E+08 1.2E+09
Metals (m3) 2.7E+06 1.5E+07 7.0E+07 9.5E+08 3.3E+09
Station (m3) 6.1E+06 3.4E+07 1.6E+08 2.2E+09 7.6E+09
Mass Used (%) 12.3% 11.7% 11.3% 10.8% 10.1% Figure 3-19 – Preview - Radius and Mass Comparison
1E+02
1E+03
1E+04
1E+10 1E+11 1E+12 1E+13 1E+14
Station
Radius
(meters)
Station Mass (kg)
Station Radius as Function of Station Mass
Dumbbell - R=6.33a; c=2a Torus - R=6.33a; c=2a
Ellipsoid - R=6.33a; c=0.8165a Cylinder R=a; l=1.3a
Max Radius = 10km Building Material (30% Oxide)
Min Radius = 224m (1g at 2 RPM)
Bennu Ryugu Moshup Atira Šteins
3E+03
3E+04
3E+02

The chart in Figure 3-20a shows a logarithmic horizontal x-
axis measuring mass in kilograms. We show two masses for
the 5 example asteroids along the x-axis in Figure 3-20a. One
is the mass of the asteroid and the other is the mass of the
constructed station. The difference would include losses,
margin, and surplus. The logarithmic vertical y-axis shows
the supported population of the four station geometries. For
the five asteroid masses, the maximum populations range
from 8,000 to 200 million. At logarithm scales, two groups
of two geometries appear to support nearly the same popula-
tion for a mass of material. For a given mass, the cylinder
and ellipsoid geometries support less population than the to-
rus and dumbbell. To better compare the different geome-
tries, we normalize the populations to the torus geometry
population; see Figure 3-20b. The chart shows that, except
for the smallest masses, the dumbbell geometry supports the
largest population compared to the other geometries for a
given mass of building material.
Station and Population Details: We include in Table 3-7
population details for stations constructed from the same five
asteroids. We include an asteroid station Stanford in the list
for comparison to the O’Neill Stanford Station. The table
contains the computed radii and populations for torus sta-
tions. The radius column shows the major radius and the mi-
nor radii. Smaller stations only have one torus, and they have
a circular cross section. Larger stations have an inner torus
and an outer torus. For the larger stations, we only show the
three outer elliptical torus radii in the table. The floor count
assumes the torus is half filled with floors. We use a space of
5 meters between each of the floors. We also design the top
floor with additional thickness to support soil, forests, and
vegetation.
Our maximum population is generated using all floor space
in the station and a density of 144.2 square meters per person.
The “realistic” population uses only a small percentage (5%)
of the spoke, inner torus, and shuttle bay for habitation. We
also include the population of the top floor of the station in
Table 3-7. This top floor population provides a comparison
to historic single floor designs.
Population Details: Figure 3-21 shows the populations for
those six space habitats and uses the data from Table 3-8. We
include results showing the maximum population, a more re-
alistic population, and the population supported on the mid-
dle (top) floor of the torus. The maximum population uses all
the available space in the stations. This includes space on
lower floors, in spokes, and in the shuttle bay. These
population estimates use a density of 144.2 square meters per
person. Using this density and Bennu as an example, we find
the station would support a maximum of 8,273 people in its
torus. The Ryugu station would support 33,150 people. Con-
structing and using floors in the Stanford Torus, we find it
could support a maximum of 70 thousand people. The Atira
station could support 10 million people. The Šteins station
would support a maximum of 70 million people.
a) Station Population versus Mass
b) Station Population (Normalized) versus Mass
Figure 3-20 – Preview - Population Comparison
Table 3-7 – Example Radius and Populations for Torus Stations from Asteroids
Asteroid
Station
Radius (meters)
(Major & Minor Radii)
Floor Count
(fd=5m)
Maximum
Population
Realistic
Population
Top Floor
Population
Bennu (205,32) 5 8,273 2,771 450
Ryugu (354,56) 10 33,150 16,475 1,531
Stanford (830,65) 12 70,051 42,760 4,412
Moshup Inner (937,148) 28 371,267 123,418 11,096
Atira Double (2116,1003,334) 60 10,009,838 1,625,065 184,912
Šteins (4042,1915,638) 120 69,769,913 5,790,393 674,557
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
1.0E+10 1.0E+11 1.0E+12 1.0E+13 1.0E+14
Population
(count)
Mass (kilograms)
Station Mass to Population
(Top Floor 0.95g; Outer Rim 1.1g; fd=5m; 144.2 m2/person)
Torus - R=6.33a; c=2a
Building Material Mass
Asteroid Mass
0.0
0.5
1.0
1.5
2.0
1.0E+10 1.0E+11 1.0E+12 1.0E+13 1.0E+14
Population
(Normalized
to
Torus)
Station Mass (kilograms)
Station Mass to Normalized Population
(Top Floor 0.95g; Outer Rim 1.1g; fd=5m; Pop Dens=144.2m2/person
Torus - R=6.33a; c=2a
Building Material Mass
Bennu Ryugu Moshup Atira Šteins

We include a more “realistic” population metric in Figure
3-21. Low gravity and high gravity regions are excluded
from the population estimate. The Bennu and Ryugu stations
can realistically support about 2,771 and 16,475 people.
Larger stations have more than 50 floors and it is unlikely
that people will want to live in the lowest levels. The realistic
population metric limits the living region to roughly the top
10 floors. It also uses a small percentage (5%) of the spoke,
inner torus, and shuttle bay for habitation. The Atira station
would support a realistic population of 1.6 million people.
The large Šteins station with a double set of spokes and inner
tori can support a realistic 5.8 million people.
We also include the population estimates using the Stanford
Torus dimensions. We include the population supported us-
ing only the top floor of the torus. With the Stanford design,
this top floor nearly matches the projected surface area esti-
mates of earlier NASA studies [Johnson and Holbrow 1977].
The Stanford Torus was expected to support a population of
10,000 people. We find our top floor of the Stanford Torus
supports 4,412 people using the 144.2 square meters per per-
son. This would be 9,496 people with a density of 67 people
per square meter. There can be a dozen floors in outer half of
the Stanford Torus. This would support a maximum popula-
tion of 70,051 people and a realistic population of 42,760
people. These examples continue to highlight the value of
using floors to increase the available population on stations.
Population and Radius Details: We include additional data
in Table 3-8 from our population analysis. This includes
populations for torus and dumbbell geometries. This table in-
cludes the five asteroids with their mean radius and mass.
Again, we include a fictitious asteroid Stanford in the list for
comparison with the Stanford Station. We show the amount
of building material used in each of the stations. This repre-
sents 30% of the volume of the available construction mate-
rial (oxide) of the asteroids; see Table 3-6. We computed the
population using a density of 144.2 square meters per person
from Figure 3-13. The station mass uses the volumes of the
towers, spokes, outer shells, floors, fill, and the shuttle bay.
We include the maximum and realistic populations for the
torus and the dumbbell geometries. There are many esti-
mates, curve fittings, and extrapolations in these population
estimates. These estimates should be considered a first ap-
proximation and mainly for comparative purposes.
Population and Mass Equations: We have developed equa-
tions that estimate the radius and the population of stations
based on the available asteroid mass. The Station Mass sub-
section of §3.2.1 Station Characteristics detailed our ap-
proach to compute the station mass. We derived and summed
the volume and mass of the individual pieces in the compo-
nents of the station. We derived the population in this same
analysis by summing the floor spaces.
We took the results of these detailed estimates to create sim-
ple equations to estimate the population, radius, and mass.
We fit a power curve to the data in Figure 3-12 to derive ra-
dius to mass equations. The data for Figure 3-12 was gener-
ated using earlier, slightly different station metrics. We have
also fit power curves to the data in Table 3-8. We extrapo-
lated results from both set of power curves to create our equa-
tions. We show those equations for the four geometries in
Table 3-9. These equations subsume many parameters and
reduce the estimates to a single variable – the station mass.
We define that the station is filled with multiple floors. In
these cases, the equations were generated with floors sepa-
rated by 5 meters and the population density is 144.2 square
meters per person. The geometry design metrics in Table 3-9
produce rotationally stable space stations and Earth-like
gravity ranges over the floors. The stability and range con-
cepts were detailed in previous subsections. The major rota-
tion radius is typically scaled from one of the minor rotation
radii. The dumbbell is designed with two prolate ellipsoid
nodes and the ellipsoid station is designed as an oblate ellip-
soid. The equations show that the mass from the radius equa-
tion is not a quite a volume relationship. We see that the
Figure 3-21 – Populations with Station Alternatives
Table 3-8 – Estimate Radius and Maximum Population for Station Geometries Asteroids
Asteroid
Mean
Radius
(m)
Mass
(kg)
Station
Material
(kg)
Torus
Radius
(m)
Torus
Maximum
Population
Torus
Realistic
Population
Dumbbell
Radius
(m)
Dumbbell
Maximum
Population
Dumbbell
Realistic
Population
Bennu 263 7.33E+10 9.03E+09 205 8,273 2,771 245 7,766 2,521
Ryugu 448 4.50E+11 5.28E+10 354 33,150 16,475 433 32,614 15,871
Stanford 502 7.02E+11 8.31E+10 830 70,051 42,760 502 85,400 54,324
Moshup 659 2.49E+12 2.81E+11 937 371,267 123,418 659 396,325 126,903
Atira 1928 4.11E+13 4.45E+12 2,116 10,009,838 1,625,065 1,736 11,944,304 1,822,202
Šteins 2580 1.98E+14 1.98E+13 4,042 69,769,913 5,790,393 2,628 88,939,570 6,778,960
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
Bennu Ryugu Stanford Moshup
Inner
Atira
Double
Šteins
Population Population for Station Alternatives
(Population Density = 144.2 square meters per person)
Maximum Population
Realistic Population
Top Floor Population

station mass is a 2.4 to 2.6 power function with the thick
shells, the half-filled station, and the open regions between
the floors. The station mass is between a surface area (quad-
ratic) and a volume (cubic) relationship with the station ra-
dius. As one would expect, the population is a volume or cu-
bic relationship with the station radius. The population of the
station increases faster than the mass of the station with in-
creasing radius. We see that the population is a 1.20 to 1.25
power function of the mass.
Using these equations, we can now estimate the radius and
population of a station given the mass of the asteroid. Again,
we note that many parameters such as the radius, floor count,
floor spacing, population densities, and support structures
can be varied. Material densities, asteroid porosity, and con-
struction processes will all affect the results. This section has
introduced the supporting details on those parameters. Given
the multiple extrapolations and sources of data, these
equations should be used for comparative purposes only.
Station Mass Summary: This brief assessment does not
consider many issues. A qualitative issue example is that
dumbbells do not have the open views that the other geome-
tries offer. A construction and scheduling issue example is
that small asteroids have limited surface area for building
construction equipment. We plan additional evaluations of
these types of issues.
The data of this subsection serve to highlight two important
observations. First, using multiple floors produces stations
that can support large populations even with small asteroids.
Second the different geometries support similar populations
for the same mass of building material. For a given mass,
dumbbells support the largest population. The torus geome-
try supports the next largest population. Cylinders and ellip-
soids support similar but smaller populations than the torus
and dumbbell geometries. The dumbbells may provide the
largest population; however, they have other limitations that
need to be considered.
3.3 Space Stations – Results
We refined slightly the set of typical space station geometries
to address rotational stability and gravity issues. We use el-
lipsoids instead of spheres; short cylinders instead of long
cylinders; elliptical cross-section torus instead of circular
cross-section torus; and a single dumbbell instead of a com-
posite dumbbell structure. We design the space stations with
multiple floors to significantly increase the supported
population. The design provides near Earth-like gravity over
the habitable floors.
In this section we focus on the details and geometry of a spe-
cific space station for a restructuring mission. We provide
details on the selected space station and cover its character-
istics, construction materials, and population.
3.3.1 Specific Space Station
As previously reviewed, there are many ways to evaluate and
select a station geometry. These earlier assessments and se-
lections were typically based on thin space station shells. In
our asteroid restructuring, we use thick shells to provide
structural integrity, radiation protection, and safety from de-
bris collisions. We use the abundant asteroid material to
build the thick shell.
These historic reviews were also typically based on a single
projected floor. We design our station with many floors and
support greater populations. Our assessment uses these ge-
ometries with thicker shells and many floors. A preview of
this assessment was in Section 3.2.5 and results were in-
cluded in Figure 3-20. The charts provided the population as
function of the available asteroid mass and the different sta-
tion geometries. That section provided some of the underly-
ing assumptions and we offer more assumptions and details
in this section.
As shown in Figure 3-20, in general, the dumbbell geometry
supports the largest population compared to the other geom-
etries for a given mass of building material. The next best
geometry is the torus. Like other studies, we have been ex-
cluding the dumbbell geometry stations because they are typ-
ically a small design with limited vistas. The limited views
of small dumbbells could create an oppressive ambience and
be a risk to the psychological well-being of the colonists
[Keeter 2020]. There could also be structural issues with
large dumbbell nodes at the end of long tethers.
Ultimately, we need to consider qualitative and structural
metrics in selecting a station geometry. Based on our current
analysis, we suggest that an elliptical cross-section torus is
the preferred geometry for our restructuring effort.
3.3.2 Station Characteristics
We have reviewed historical studies on space stations. We
have explored many shaped and sized space station with our
simulations and our analysis. In this section, we focus on a
rotating torus as our habitat. We use an elliptical cross sec-
tion instead of circular. The elliptical shape reduces the
Table 3-9 – Equations to Estimate Population and Mass
Geometry Cylinder Ellipsoid Torus Dumbbell
Design Metrics R=a; l=1.3a R=6.33a c=0.8165a R=6.33a; c=2a R=6.33a; c=2a
Mass (m) from Radius (r) m = 80681 r 2.4430 m = 52811 r 2.4340 m = 12391 r 2.5471 m = 2121 r 2.4551
Population (p) from Mass (m) p = m1.2533 / 1.284E+9 p = m1.2533 / 1.676E+9 p = m1.2017 / 1.538E+8 p = m1.2435 / 4.165E+8
Population (p) from Radius (r) P=r 3.0618/1187.7 P=r 3.0506/1546.8 P=r 3.0609/1854.7 P=r 3.0530/30414.3
Station Metrics: Mass (m) in kilograms; Population (p) in count; and Radius (r) in meters

excessive number of floors in large stations, increases the
station floor space, and maintains a good station vista. This
example torus has a major radius of 2400 meters and an el-
liptical cross-section with radii of 1200 meters and 400 me-
ters. The cross section is half-filled with floors. The spacing
between the floors ranges from 6 meters to 15 meters in dif-
ferent station components. We presented an internal drawing
of a similar station in Figure 3-9. The external view of this
station is like the one shown in Figure 1-1. This version of
the station has two inner tori. Each of the inner tori has a
radius of 1100 meters. This station rotates about once every
100 seconds and produces an Earth-like gravity on the main
outer-torus floor.
We show in Table 3-10 an earlier set of population estimates
for this example torus. The table includes the number of
floors, the surface area, and population for the station com-
ponents. On some of the floors, we use multistory construc-
tion to increase the usable surface area. Even using the full
surface area allocation of 157.1 square meters per person
from [O'Neill et al. 1979], we find the station could support
6 million people. Even larger populations could be supported
using the allocation of 67 square meters per person.
We do not recommend living in low gravity or high gravity
regions for medical reasons. We also do not recommend liv-
ing in the deep bowels of the station for physiological rea-
sons. In the rightmost column of Table 3-10, we show a pop-
ulation estimate with colonists living only on the first five
floors of the outer elliptic torus, and in part of the dividers
and the skyscrapers. The main top floor is used exclusively
for openness, public areas, and recreation. As stated in the
NASA SP-413 study [Johnson and Holbrow 1977], habitats
with large living space “would be settled with much lower
population densities, so as to permit additional “wild” areas
and parkland.” A population density metric of 547 square
meters per individual can support a population of 700,000.
There is still significant usable space despite the generous
density metric. This extra space could support recreation,
tourism, and other “wild” uses.
3.3.3 Station Construction
The first asteroid restructuring task is to construct additional
spiders and a web of trusses to access raw materials. We il-
lustrate in Figure 3-22a many trusses over the surface of the
asteroid. Each truss is 1 meter wide and 20 meters long. The
web provides a stable and less varying surface for the vehi-
cles. Navigation is much simpler on this web compared to
the natural surface of the asteroid.
There are multiple station components to build. The external
view of this station is like the one shown in Figure 1-1. We
show in Figure 3-22b an interior view of a similar space sta-
tion. We label the major components of the station in this
rendering. This is a view of almost 2 kilometers distance and
3 kilometers across. The spokes and dividers in the distance
have 32 stories. The rendering tool was programmed to draw
a 100-meter grid on the main floor of the torus for reference.
In our rendering code, we include almost 100 parameters to
define the station and the asteroid. Changing these parame-
ters produce different renderings. The rendering tool also
outputs a summary report with statistics about the surface
area, volumes, heights, and counts for the major components.
We use multiple tools in our investigation to create details
and cross check results. The rendering tool and our simula-
tions allow us to evaluate different size stations. We can vary
many parameters on the station elements including their ra-
dii, depths, widths, and thicknesses.
3.3.4 Station Materials
To simulate the restructuring of the asteroid, we need to un-
derstand the amount of construction material available from
the asteroid. We also need to understand the amount of con-
struction material required to build the station. Previous sub-
sections previewed our analysis of the available asteroid ma-
terial. We detail in this subsection the amount of construction
material in the station. We described in the previous subsec-
tion how we analyzed the structure as shown in Figure 3-9.
We have developed estimates for the material needed to con-
struct the trusses; to fill the exterior walls with regolith; and
to cover the exterior, walls, and floors with panels.
Table 3-10– Population Estimates for Atira Ellipse Station
Station Component Part Floors
Floor Surface
Area (m2)
Height
(m)
Useable
Surface Area
(m2) Count
Total Surface
Area (m2)
Max
Population
(157 m2)
Target
Population
(547 m2)
Inner Torus Main Floor 1 684,239 55 684,239 2 1,368,478 8,711 -
Lower Floors 5 2,515,401 8 2,515,401 2 5,030,802 32,023 -
Dividers 8 352,657 6 352,657 2 705,314 4,490 -
Shuttle Bay Center 8 1,238,541 10 1,238,541 2 2,477,082 15,768 -
Spoke Floors (Beyond Inner Torus) 158 1,503,299 6.67 1,503,299 16 24,052,778 153,105 -
Floors (Inside Inner Torus) 242 2,302,780 6.67 2,302,780 16 36,844,482 234,529 -
Outer Torus Main Floor 1 33,973,140 470 33,973,140 1 33,973,140 216,252 -
Lower Floors 5 161,732,128 15 323,464,256 1 323,464,256 2,058,970 591,802
Lowest Floors 11 248,683,950 15 497,367,899 1 497,367,899 3,165,932 -
Dividers 32 1,238,470 15 2,476,940 8 19,815,520 126,133 36,254
Spoke Skyscraper Floors 77 2,339,240 6 2,339,240 8 18,713,920 119,121 34,239
Adjacent Skyscraper Floors 82 2,576,110 6 2,576,110 8 20,608,880 131,183 37,705
Population Density Square meters per individual 157.1 547
Total 459,139,954 870,794,502 984,422,551 6,266,216 700,000

We compare the material provided by the asteroid and used
by the station. The asteroid is about 4.8 kilometer in diame-
ter. The total volume of material in the Atira asteroid is al-
most 22 billion cubic meters. By our estimates, it would pro-
duce about 8 billion cubic meters in usable raw material. For
comparison, we use the same previous example torus station.
Details on the material supply and requirement is shown in
Figure 3-23. That station requires 2.6 billion cubic meters of
the oxide building material. The fill and structure of the large
outer torus uses nearly all that processed oxide material. We
include estimates of the metal and volatiles that would be
harvested from the asteroid. Not all of the asteroid would be
mined to produce the required building material. Another ad-
ditional 5 billion cubic meters of building material could be
produced from the unused surplus of the asteroid. Our plan
is to use the oxides as the building materials and not the
metal. Only 9000 cubic meters of metal is needed to con-
struct the station. There should be almost a billion cubic me-
ters of metal in the Atira asteroid and 341 million cubic me-
ters of metal will be harvested. The station has over 2.5 bil-
lion cubic meters of storage space. The unused metals will
be inventoried and stored in the station for future colonists.
3.3.5 Station Building Materials
We show in Figure 3-24 the estimated volume of material
used in an Atira torus station design as we vary the major
radius. The horizontal axis shows the major radius from 1200
meters to 4000 meters. The minor radii of the elliptic outer
torus are proportional to the major radius. The smaller minor
axis length is about 1/6 the size of major axis. The other mi-
nor axis length is 3 times the smaller minor axis. This design
includes an inner torus that is positioned halfway between
the shuttle bay and the outer torus. The inner torus has a mi-
nor radius of 75 meters. This simulation assumes 20-meter-
thick exterior walls. The Atira asteroid could produce 7.3 bil-
lion cubic meters of material for construction. This is after
compressing out the porosity and assuming over 20% loss in
processing. This only includes the bulk stony material and
does not include the metal or volatiles. The vertical axis of
Figure 3-24 shows the required construction material ranging
from 0.8 billion cubic meters to 7.3 billion cubic meters. This
represents from 11% to almost 100% of the available con-
struction material. The chart shows the outer torus uses the
a) Web trusses on Atira b) Inside station – tower, divider, and spokes
a) Credit: Self produced using Blender, Image ESO/Serge Brunier [Brunier 2009] [CC BY-4.0], and Doug Ellison model [Ellison 2018] [CC BY-4.0]
b) Credit: Self produced using Blender
Figure 3-22 – Atira Space Station – Web Development and Interior View
a) Material from Atira Asteroid
b) Material Used by Station
Figure 3-23 – Building Material for Space Station
2.19E+10
1.13E+10
8.57E+09
7.27E+09
9.51E+08
3.43E+08
0.00
7.85E+09
4.06E+09
3.07E+09
2.60E+09
3.41E+08
1.23E+08
5.50E+09
1.0E+07
1.0E+08
1.0E+09
1.0E+10
1.0E+11
Atira Packed Regolith Building Metal Volatile Surplus
Volume
(cubic
meters)
Asteroid Materials
(Atira Asteroid; Elliptic Torus, R=2,332m, a=368m, c=1,105m, fd=5, m=6.333)
Asteroid Atira Volume
Station Atira Material
1.45E+05
5.72E+07
2.70E+08
1.38E+08
2.14E+09
2.60E+09
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
1.0E+10
1.0E+11
1.0E+12
Web Shuttle Bay Spokes Inner Torus Outer Torus Total
Volume
(cubic
meters)
Station Construction
(Elliptic Torus, R=2,332m, a=368m, c=1,105m, fd=5, m=6.333)

most material of all the station elements. The volume in-
cludes the material needed to construct the trusses, to fill the
exterior walls with regolith, and to cover the exterior and
floors with panels. Our space station structure will use anhy-
drous laminates in structural beams and as skin, regolith as
fill, and basalt fibers as cables for additional strength and ri-
gidity. We find that the structure is 95% basalt fill (like
gravel), 4.7% anhydrous glass beams and panels from the
basalt materials, and 0.3% basalt fiber cables. Most of the
material is used to fill the exterior shell of the outer torus.
3.3.6 Station Population
Figure 3-25 shows the population supported as the major ra-
dius of the station is changed. The maximum population as-
sumes all interior surface areas are used, the floor spacing is
5 meters, and each person is allocated 144.2 square meters.
For a 1200-meter radius station we see the maximum popu-
lation is over 2 million. For a 4000-meter radius station, the
maximum population is about 64 million.
Many areas of the station are not desirable for long term hab-
itation. Figure 3-25 includes a more realistic population esti-
mate where smaller percentages of the surface areas are used.
Most individuals will reside in areas with near Earth-like
gravity. As an example, few people will live in the higher
gravity depths of the outer torus nor in the lower gravity be-
tween the top of the outer torus to the shuttle bay. In Figure
3-25 we used the top 10 floors of the outer torus surface area,
5% of the inner torus surface area, 5% of the spokes surface
area, and 2% of the shuttle bay surface area. We see the pop-
ulation varies from 570,000 to 5.660,000 individuals. With
the increasing radius, the area used by the realistic population
estimate ranges from 30% to 10% of total available surface
area. We envision that the unused surface area could be used
for tourism, manufacturing, agriculture, and storage.
3.4 Space Stations – Summary
In this section, we reviewed space station background infor-
mation and introduced features for our restructuring. These
features included the multiple floors, rotationally balanced
geometries, and Earthlike gravity ranges. To support these
restructuring features, we refined slightly the set of typical
space station geometries to address rotational stability and
gravity issues. Spherical stations become ellipsoidal stations;
long cylindrical stations become short hatbox stations; and
circular cross section torus stations become elliptical cross
section torus stations. We also reviewed features of the inte-
rior environment such as the surface area allocation to living
quarters, public areas, industry, and agriculture. The analysis
included computing the floor surface areas, the volume of
construction material, and the mass of the station. Sizes, den-
sities, and quantities of the individual pieces of the major sta-
tion components were summed to produce the details for this
analysis. We recognize that there could be structural issues
with some of these stations. Ultimately, we need to consider
qualitative and structural metrics in selecting a station geom-
etry. Based on our current analysis, we believe that an ellip-
tical cross-section torus is the preferred geometry for our re-
structuring effort. We finished this section with more details
on an example of that station.
4 Asteroid Restructuring – Robotics
Asteroid restructuring mandates understanding space sta-
tions, asteroids, and robotics. We have covered the asteroid
and materials that will be used to construct the station. We
have covered the type of space station that will be created by
the asteroid restructuring process. In this section we cover
robotics and the technologies that will be used to construct
the station. We include multiple subsections to cover the ro-
botics background, analysis, and results. We offer details on
robots, autonomous systems, and self replication.
4.1 Robotics – Introduction
Our initial robotic workers will use 21st century technologies
including solar cells, miniature efficient motors, advanced
computing, robotic software, and state-of-the-art artificial in-
telligent software. In a lunar factory study, Metzger advo-
cated to first produce tools and support equipment using
technologies from the 1700’s [Metzger et al. 2012]. We
agree with that recommendation. Our initial robots will be
Figure 3-24 – Construction Material Estimates Figure 3-25 – Station Population Estimates
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Station
Building
Material
(m3)
Billions
Outer Torus Major Radius (meters)
Elliptic Torus Station Material Requirement
(Varying Major Axis R=1200m to 4000m; Minor Axes a=R/6.33, b=3a)
Web
Shuttle Bay
Spokes
Inner Torus
Outer Torus
Atira Building Material
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
Station
Population
(Count)
Outer Torus Major Radius (meters)
Torus Population Varying Outer Torus Radius
(Varying Major Axis R=1200m to 4000m; Minor Axes a=R/6.33, b=3a)
Max Population (Pop Density)
Torus Floors Pop (Pop Density)
Realistic Population (Pop Density)
Top Floor (Pop Density)

able to make these tools and equipment with a modest set of
supplies and without industrial infrastructure or operator di-
rection. Our manufacturing techniques will reach a technol-
ogy level of the 1800’s. Most of the space station framework
will be produced with lower quality material and with low
precision. We have no goal to build advanced technologies
such as solar cells or computer chips. The end goal is to build
a rotating space station framework with a rich store of cata-
loged volatiles and metals. The rotation will produce centrip-
etal gravity. The thick shell enclosing this framework will
provide radiation protection. We envision this framework
and catalog will attract and support follow-up missions with
crews bringing more advanced manufacturing technologies.
We provide a brief overview of the background and technol-
ogies of robots. This includes example systems for space ex-
ploration and mining. We provide a set of background credits
supporting our robotic technologies. To operate in the aster-
oid environment and perform the complicated restructuring
process, the robots will use autonomous system software.
The restructuring process of an asteroid represents a huge
construction task. To support this huge restructuring project,
we will need the equivalent of millions of robots. It is too
costly to ship the millions of robots; as such, we use a tech-
nology called self replication. We provided detail on a ver-
sion called productive self-replication where robots (replica-
tors) can make copies of themselves and produce products.
We introduce the concept of having the robots make special-
ized tools (helpers) to improve their productivity. Many of
the tools are mechanical robots (or automatons) programmed
with simple state machines. We include our mathematical
analysis of the performance of these replicators and helpers.
We describe our simulations of these robots and systems.
The results of these simulations show that asteroid restruc-
turing is a viable approach to create a space station from an
asteroid.
4.2 Robotics – Background
The restructuring process uses autonomous robotics instead
of manual or teleoperated labor. Robots are comprised of six
major components: Program, Sensors, Actuators, Effectors,
Locomotion, and Power. Our asteroid restructuring robots
requires all these components. To introduce robotics, we pro-
vide background examples of robots used or planned for
space exploration and mining. Besides background and ex-
amples on robots, we also include background on important
supporting technologies: autonomous system software and
self replication.
4.2.1 Robotics – Background Credit
For our background on robotics, we present important topics
with their researchers and their work.
• Robotics: NASA projects provide a wealth of infor-
mation for robotics. Lunar vehicles have evolved from
the 1950s [Koelle and Williams 1959], 1970s [Nishioka
et al. 1973], to recent ideas in the 2020s for Mars and Lu-
nar missions [Artemis 2022]. We use this information as
a foundation for our asteroid restructuring mission. We
also credit concepts to RASSOR (Regolith Advanced
Surface Systems Operations Robot) [Mueller et al. 2013]
and to ATHLETE (All-Terrain Hex-Limbed Extra-Ter-
restrial Explorer) testbed [Volpe 2018b].
• Space Technologies: NASA has funded industry part-
ners to advance robotic technology for space. The space
industry company Made in Space plans to use their
Archinaut spacecraft in Earth orbit to manufacture struc-
tures. Their technology includes 3D printing in the zero
gravity of space and could be commercially operational
by the 2020s [Wall 2017]. Honeybee Robotics was
funded to develop the Spider Water Extraction System as
part of the NASA World Is Not Enough (WINE) program
[Honeybee 2019]. This system has demonstrated the abil-
ity to gather water from asteroid-like materials under
thermal vacuum conditions.
• Self Replication Projects: NASA projects have detailed
self-replication projects on the moon [Freitas and Gil-
breath 1982] [Metzger et al. 2012]. Lewis-Weber de-
scribes a lunar self-replicating system [Lewis-Weber
2016]. We overview these projects’ concepts, tools,
schedules, and costs. The projects include concepts such
as teleoperation, seeds, and closure.
• Tracks for Navigation: Several studies have considered
using tracks for self-replication systems to simplify navi-
gation and locomotion [Lackner and Wendt 1995] [Mo-
ses et al. 2014]. Our restructuring process builds a web of
trusses over the asteroid to provide this simpler work en-
vironment instead of the natural asteroid terrain. This
simplicity better supports our mechanical computing au-
tomatons.
• Artificial Intelligence: The replicators (and base station)
must have the “intelligence” to meet assigned goals in a
complex and dynamic environment. In the author’s ca-
reer, he studied and published multiple papers and pro-
posals to apply cognitive processing to defense products
[Jensen 1996]. We offer a short credit to the long history
of artificial intelligence. In our studies, we have captured
history and details of cognitive architectures from
[Brooks 1985] [Boyd 1987] [Albus 1997] [Sifakis 2018].
The cognitive system for our asteroid restructuring might
easily be extended from current self-driving autonomous
systems [Liu et al. 2020]. We offer only a brief introduc-
tion of our intelligent system in this paper.
• Mechanical Automatons: Our restructuring process cre-
ates mechanical automaton using 18th and 19th century
technologies and materials. One example of mechanical
computers and automatons is a mechanical monk built in
the 1560s by Juanelo Turriano using springs, cams, and
levers [King 2002]. Another example is the Babbage Dif-
ference Engine built in 1822 [Copeland 2000]. A recent
NASA funded study considered using mechanical com-
puting for the harsh environment on Venus [Good 2017]
[Sauder 2017]. NASA also funded another study project
(RAMA) and found it is possible to build mechanical
computing on an asteroid [Ackerman 2016] [Dunn and

Fagin 2017]. The primitive mechanical control is simpler
to manufacture than semiconductors and electronics.
We also present new concepts discovered during this restruc-
turing research. In later sections, we provide more details on
these robotic technology discoveries.
• Parallelism and Specialization: Our asteroid restructur-
ing uses exponential growth of replicators and uses spe-
cialized tools to improve the process performance. Paral-
lelism provides a speed-up in the execution time using
multiple Replicators (Spiders) and Helpers (Tools and
Equipment). Specialization provides a speed-up in the
task execution time using the Helpers (Tools and Equip-
ment). We recognize this growth as a form of self repli-
cation called productive replicators [Freitas and Merkle
2004]. The extensive use of parallelism and specializa-
tion may represent a somewhat novel approach to self-
replication.
• System Analysis Extension: We review and extend anal-
ysis concepts from [Hall 1999] to our replicators (Spi-
ders), helpers (Tools), and products (Construction Mate-
rial and Structures). Hall did not explicitly cover multiple
types of tools. Our productive self-replication creates dif-
ferent tools and different products at different rates. The
Hall analysis evaluated a system where the self-replica-
tion and the product production were at the same rate
[Hall 1999]. We apply and extend Hall’s analysis to in-
clude different products and rates.
4.2.2 Robotic Examples
There is good background on robotics for our restructuring
effort. Multiple robotic systems have been proposed and de-
signed to support lunar or asteroid mining. Simulations have
been performed, papers published, and prototypes have been
built. We offer in this section an overview of those systems.
Our approach in the restructuring effort is to use existing and
historic technologies. It is not our goal to create today’s ad-
vanced manufacturing capabilities on the asteroid; instead,
we will use a limited number of 21st century robots to con-
struct 18th century mechanical automata. The following sys-
tems are examples of early 21st century robotic technology.
The NASA Jet Propulsion Laboratory (JPL) has multiple
space robotic projects [Volpe 2018]. One of those robots is
the LEMUR (Limbed Excursion Mechanical Utility Robot).
The second version of this system, LEMUR IIa, consists of
six limbs arranged around a hexagonal body platform [Volpe
2018a]. These limbs incorporate a feature that allows the
rapid change of its end-effector tools [Volpe 2018a]. We
show in Figure 4-1 two pictures of this robot. Our spider (ro-
bot) will be similar to this design with its multiple arms, re-
placeable end-effectors, sensors, and frame.
The NASA Innovative Advanced Concepts program funded
a mechanical rover in 2015. Jonathan Sauder proposed the
Automaton Rover for Extreme Environments (AREE) to op-
erate in the harsh environment of Venus [Sauder 2017]. This
clockwork mechanical robot would explore the Venus sur-
face and only use primitive components such as levers and
gears. The mechanical technologies could survive in the Ve-
nus conditions where most electronics would simply melt.
We include an image of the AREE rover in Figure 4-2 [Good
2017] [Sauder 2017]. Our restructuring process takes ad-
vantage of mechanical computing because it can be built us-
ing impure materials with millimeter tolerances. Semicon-
ductor electronics require more pure materials with microm-
eter tolerances.
NASA has been studying and documenting space missions
since the 1950s. These reports offer great detail and con-
cepts, often studied for years or decades before implementa-
tion. One historic 1973 document is entitled Feasibility Of
Mining Lunar Resources for Earth Use: Circa 2000 A. D.
[Nishioka et al. 1973]. This long memorandum details the
technologies and systems required to establish the mining
base, mine, refine, and return the lunar resources to earth for
use. They also include gross equipment requirements such as
weights and costs. We include a sketch of an automated
miner vehicle from that study in Figure 4-3. Some of our ro-
botic helpers have characteristics similar to this miner. We
use many concepts from this wealth of NASA information
throughout our restructuring process.
4.2.3 Robotics and Autonomous Systems
The robots will have autonomous system software to operate
in the asteroid environment and to perform the tasks in the
dynamic and complicated restructuring process. The
a) LEMUR IIb climbing b) LEMUR IIa
Image Credit: NASA, JPL, [Volpe 2018a] [JPL Image Public Domain]
Figure 4-1 – NASA JPL LEMUR II Robot
Image Credits: NASA/JPL-Caltech [Good 2017] [JPL Image Public Domain]
Figure 4-2 – NASA JPL-Caltech Mechanical Rover

software framework of the robots will integrate real time pro-
cessing, artificial intelligence, image processing, knowledge
bases, and more.
Our restructuring effort will need an embodiment of an au-
tonomous system. Our plan is to integrate individual artifi-
cial intelligent algorithms and instantiate the building blocks
of the autonomous system architectures. Our replicator (and
base station) must have a complete plan and the “intelli-
gence” to meet assigned goals. The autonomous system com-
bines five complementary capabilities: Perception, Reflec-
tion, Goal management, Planning, and Self-adaptation [Si-
fakis 2018]. Such capabilities started with research in the
1980s [Brooks 1985] [Boyd 1987].
Many years ago, we architected an autonomous system as a
military hierarchy of nodes [Jensen 1996]. There is value in
such a hierarchy. The restructuring process software will
communicate as a hierarchy of nodes executing through
crews of spiders, lead spiders, the base station(s), an orbiting
system, and terrestrial support computers. Eight years later
we enhanced our 1996 design to become a cognitive system
with building blocks of sensory processing, world modeling,
behavior generation, and situation assessment. Design and
proposal work was performed with planning experts [Nau et
al. 2003] and with multi-agent and blackboard experts
[Lesser and Corkill 2014]. The system in each node was to
be built using multiple intelligent agents working through a
common blackboard system.
Today, new software environments and standards exist to
support our restructuring software system. The cognitive sys-
tem for asteroid restructuring might easily be extended from
current self-driving autonomous systems [Liu et al. 2020].
For reference, we have added building blocks to support
communication and a heartbeat for self-awareness to our ear-
lier autonomous system designs. We follow many of the ar-
chitecture concepts from [Sifakis 2018]. We illustrate the ar-
chitecture with those new building blocks in Figure 4-4. This
architecture highlights the building blocks necessary to sup-
port a restructuring process. Agents represent those building
blocks. These intelligent agents provide an interface to phys-
ical devices (such as sensors, actuators, and communication),
software algorithms (such as simulations, planning, and op-
timization), architecture databases (such as world model,
concepts and rules, experience, and policies), architecture
system modules (such as observer, orient, decide, and act
[Boyd 1987]), and real time control capabilities [Albus
1997]. The cognitive system architecture in Figure 4-4 in-
cludes hierarchy layers of building blocks. The layers repre-
sent a cognitive hierarchy with reactive, routine, and reflec-
tive levels [Sterritt and Hinchey 2005]. They also represent
an autonomous system hierarchy with automation, autono-
mous, autonomic, and cognitive layers. We do not delve into
the implementation details in this paper.
4.2.4 Robotics and Self-Replication
Self replication will produce many robotic units. Buzz Aldrin
stated: “It’s amazing what one person can do, along with
10,000 friends.
”We find it’s amazing what a single probe and
26,500 restructuring units can accomplish. It may not be
launching a man to the moon, but we found those units can
restructure a large asteroid into a rotating space-station
framework in 12 years,
The original seed probe with its 4 spiders and a few supplies
creates quite a legacy of equipment. The restructuring pro-
cess builds thousands of robotic spiders, tools, and equip-
ment using the seed package and the raw materials of the as-
teroid. Our baseline example simulation created almost 3000
spiders and over 23,500 other pieces of equipment. In about
12 years, an asteroid the size of Atira would be restructured
into the enclosed framework of a space station.
It would be very costly to launch thousands of robots, mining
equipment, and construction equipment to accomplish this
goal. Self replication provides the capability for a system to
create a copy of itself. The restructuring of an asteroid repre-
sents a huge construction task. Launching a probe with the
right tools and building that equipment at the asteroid is es-
sential from a cost standpoint. These thousands of units are
produced with productive replicators. This is a form of self-
replication where the replicators can make copies of them-
selves and produce products. In our restructuring system we
Credit: NASA, [Nishioka et al. 1973] Figure 5-1 [NASA Report Public Domain]
Figure 4-3 – Automatic Lunar Miner
Cognitive Architecture for Restructuring Mission
Figure 4-4 – Cognitive System Architecture
Communicate
Real World
World Model
Sensors Actuators
Heartbeat
Learn
Predict Profiles,
Policies
Experience,
History
System Manager / Blackboard System
Internal
Sensors
Evaluate
State
Orient
Analyze
Observe
Monitor
React Act
Execute
Decide
Plan
Concepts,
Rules
Reactive
Routine
Reflective

include Replicators (Spiders). They produce Helpers (Tools
and Equipment). Combined they produce the final Products
(Construction Material and Station Structures). Self replica-
tion allows us to not launch the thousands of pieces of equip-
ment, and instead, build them at the asteroid.
Self Replication – Introduction: The goal of the restructur-
ing process is to use a single rocket launch to send a seed
probe to an asteroid. The restructuring process exploits self-
replication to reduce launch costs and construction times. We
use robotics, image processing, and artificial intelligence to
completely automate the restructuring process. Other than a
modest seed package of materials, we use only the bulk ma-
terial of an asteroid to build our station. With that modest
seed package of materials and tools, robotic workers use the
asteroid material to create copies of themselves, create more
tools, and other forms of vehicles and automata.
Our restructuring concept is a form of self-replication. Our
seed probe includes a small set of 21st
century robots along
with fabrication and testing equipment. It includes sufficient
supplies to support the construction of a few thousand robots
and some materials to support the construction of other
equipment. The robot frames are built from local asteroid
material. The supply of robotic electronics and actuators are
installed in those frames. By themselves, thousands of these
robots would take many centuries to build a large space hab-
itat. An innovation of the restructuring process is to provide
the robots with many tools and equipment to complete the
space habitat. These robots construct tools and equipment us-
ing processes available during the first industrial revolution.
Many pieces of equipment will be powered with Stirling en-
gines and/or clock springs. Heat and furnaces will be solar
powered. Instead of large industrial complexes, overwhelm-
ing numbers of small mining and construction equipment re-
structure the asteroid into a space habitat.
Self replication and the restructuring process reduce the seed
probe costs. We do not need to develop and bring processes
to manufacture 20th
or 21st
century technologies such as sem-
iconductors, solar cells, electrical wiring, and HVAC com-
ponents. Instead, we need to develop processes to manufac-
ture 18th
or 19th
century technologies like shovels, plows,
wagons, trusses, and bridges. Using in-situ material to build
the tools, equipment, and habitat reduces the weight of the
seed probe and launch costs.
Self Replication – History: Original historic details on self
replicating systems first appeared in the 1950s and 1960s by
John von Neumann [von Neumann 1966] and Edward Moore
[Moore 1962]. In the 1970s, Freeman Dyson developed con-
cepts for four terraforming self-replicating systems [Dyson
1970]. NASA commissioned a study detailing a lunar self-
replicating system in 1980 [Freitas and Gilbreath 1982]. This
study describes a 100-ton probe with over a dozen systems
including paving robots, mining robots, warehouses, compu-
ting, and fabrication. Robert A. Freitas Jr. and Ralph C.
Merkle wrote an extensive book on Self-Replicating Ma-
chines [Freitas and Merkle 2004]. A study in 2012 describes
a more modern version of a self-replicating lunar industry
[Metzger et al. 2012]. Their study reduced the initial seed
probe weight to 7.7 tons and includes a similar set of systems
such as excavators, chemical plants, refineries, and solar cell
manufacturing. This newer study includes 3D printers. The
authors of that paper believe that this lunar industry will rev-
olutionize the human condition. Those lunar self-replicating
examples require teleoperation initially and periodic supplies
from the Earth.
The restructuring process alone cannot accomplish every-
thing envisioned by the 1980 NASA study [Freitas and Gil-
breath 1982] or the 2012 bootstrapping study [Metzger et al.
2012]. Their designs resulted in manned stations with all the
supporting environment and technologies. This is with many
high-cost launches and with considerable astronaut labor in
low gravity and unprotected radiation environments. The re-
structuring process can construct a space station framework
at a lower cost and with less technical support. The restruc-
turing process finishes the enclosed framework that rotates
to provide centripetal gravity, has a thick shell to provide ra-
diation protection, and includes an inventoried store of met-
als and volatiles. Follow-up missions are required to make
the station habitable. The workers and then colonists of those
missions will be able to work in this framework environment
without negative effects from microgravity and radiation.
Our restructuring approach and study agrees with the con-
cepts, direction, and benefits captured by Metzger, Freitas,
Gilbreath, and their colleagues; however, our restructuring
approach increases the amount of automation, eliminates the
human teleoperation, and reduces the costs.
Self Replication - Equipment and Tools: We considered
using and building a single type of robot to perform all tasks.
This approach quickly ran into complexity, performance, and
production bottlenecks. We found many of the restructuring
tasks are simple, repetitive, and constrained to well defined
areas. This led to the concept of building specialized tools to
offload that repetitive work and reduce the required number
of spiders (replicators). The launch cost limits the number of
spiders while building simple tools and equipment is essen-
tially free and unlimited using in-situ asteroid material. Our
approach evolved over the course of this research to include
multiple types of tools to manage larger volumes of material
and specialization to perform specific tasks more efficiently.
In the replicating process, these helpers (tools and equip-
ment) are mechanical automata built from in-situ material
and use 18th and 19th century processes. The mechanical au-
tomata are sophisticated state machines using hardware such
as gears, levers, springs, and cams. The primitive mechanical
control is much simpler to manufacture than semiconductors
and electronics.
Eventually, the replicators (spiders) only need to load, mon-
itor, unload, wind springs, and adjust settings on those helper
pieces of equipment. These helpers are mechanically de-
signed to perform repetitive operations. A spider would ad-
just levers and knobs on equipment to control and tune the
operation. A recent NASA funded study considered using
mechanical computing in the harsh environment of Venus

[Good 2017] [Sauder 2017]. The RAMA asteroid project
also plans to use a purely mechanical analog computer and
use things like gears, rods, and levers linked by chain belts.
Jason Dunn from Made In Space [Ackerman 2016] com-
ments that “This is all very old technology, but it's also well
understood, reliable, and easy to build from simple parts.”
Project RAMA felt most of the fundamental technologies al-
ready exist. The NASA funded study found it is possible to
build an asteroid spacecraft using mechanical computing
[Dunn and Fagin 2017].
Electronics can survive in the asteroid environment and
could be used. Electronics could perform many of the same
operations as the mechanical computing. The advantage of
mechanical computing for restructuring is the required man-
ufacturing materials and tolerances. Building semiconductor
electronics requires pure materials and micrometer toler-
ances. Mechanical computers could be build using impure
metals or ceramics with millimeter tolerances. Our restruc-
turing process builds in-situ mechanical devices to perform
the repetitive restructuring operations. The large number of
mechanical automatons provide an immense productivity
gain. Building equipment on the asteroid with in-situ mate-
rial dramatically reduces the launch costs.
Our spiders and equipment build and operate on a web of 1-
meter-wide trusses. This web provides a simpler navigation
environment for the mechanical computing than the natural
asteroid surface. A similar set of tracks were considered for
self-replication to simplify navigation and locomotion in a
1995 study [Lackner and Wendt 1995].
Self Replication – Closure: Closure is a metric that
measures the ability of a replicator to gain access to the re-
sources required for replication [Freitas and Gilbreath 1982].
A self-replicating system with 100% closure has access to all
the materials require to self-replicate. We send sufficient
supplies “vitamins” to produce 3000 replicators (Spiders) us-
ing only in-situ asteroid material. Those replicators build
tools and equipment using only the asteroid material and
very limited supplies from the initial probe. The replicators
and helpers are primarily built from in-situ material (95% to
99%) with a small percentage of vitamins (1% to 5%). We
have 100% closure using the few supplies from the single
space probe until the “vitamins” are exhausted. Once com-
pletely exhausted, no additional tools can be built.
Self Replication – Tool Production: Our asteroid restruc-
turing approach can be compared to the effort of early pio-
neers. A wagon heading west in America in the 1800s could
not carry enough supplies to support a family for the journey
or at the destination. These pioneers brought tools with them
to be self-sufficient [Williams 2016]. Our restructuring relies
on self-replication, but more important, on the production of
tools to make the restructuring effort self-sufficient and suf-
ficiently productive.
Our restructuring process relies on productive replicators.
These replicators can make copies of themselves and can
also make other products [Freitas and Merkle 2004]. The rep-
licators are the “spider” robots. Four of these spiders are sent
with the initial bootstrapping probe. The seed probe lands on
one of the asteroid poles and becomes the base station for
early operations. The base station can process regolith and
produce structural rods, tiles, and panels. The probe contains
enough supplies to support the construction of 3000 spiders.
The supplies are small and lightweight; they include small
electro-mechanical modules and solar cells. The housings
and frameworks for these spiders and solar panels are built
with local asteroid material. The spiders assemble the solar
cells into frames to create solar panels. The modules and so-
lar cells are designed to clamp easily to the frames. The seed
probe includes sets of connectors. Spiders use these connect-
ors to interconnect the electro-mechanical modules, jigs, and
legs. Legs are made from structural rods. The four initial
workers assemble the modules, regolith frames, rods, solar
panels, and connectors to produce more spider robots.
The base station includes a few hundred jigs for the spiders
to start the restructuring process. The spiders use these jigs
to build these housings and frameworks. Testing jigs are used
to measure material samples for inventory and storage. The
base station also includes testing capabilities.
The spiders will also create other products (helpers/tools and
equipment) to support the restructuring effort. Early simula-
tions quickly determined that thousands of robotic workers
would be insufficient to build a large station in a reasonable
length of time. We found spiders were performing numerous,
repetitive, time-consuming tasks in our simulations. We be-
gan to build helper systems to augment the initial robotic
workers. Trucks can haul materials to and from processing
stations. Diggers can work on breaking rocks and producing
loose regolith. A Sun Tracker can aim mirrors for solar fur-
naces as the asteroid rotates. Under the spider supervision,
simple clockworks and mechanical settings provide the con-
trol for these helper systems. The spiders build larger tools
such as vehicles - trucks and movers. The spiders will also
build mining equipment such as jaw crushers, filters, and so-
lar furnaces. They build more complex manufacturing de-
vices such as truss builders, harvest units, and tile placement
units. Power for these helper systems comes from springs
(for clockworks) and from Stirling engines (for motion).
Navigation on an asteroid’s surface is difficult because of the
low gravity and rugged diverse terrain. The robotic spiders
build a web of trusses to provide a much simpler navigation
surface. The spiders make the trusses using regolith rods or
tiles manufactured initially by the base station. Spiders weld
the tiles together using a Fresnel lens jig to form trusses and
panels. Initially simple legs provide the locomotion on those
trusses in the near zero gravity environment. The simple legs
are augmented with wheels and rollers to adapt to the in-
creasing centripetal gravity on the rotating station.
The base station manufacturing is eventually relegated to
other pieces of equipment built by the robotic workers. Many
new pieces of equipment are built to crush rocks, filter mate-
rial, extract metal, and produce tiles and panels.
The spiders will use 21st century technologies including so-
lar cells, miniature efficient motors, advanced computing,

robotic software, and state-of-the-art artificial intelligent
software. We agree with Metzger that the first produced tools
and support equipment should be more like technology from
the 1700’s or 1800’s [Metzger et al. 2012]. The advanced
spider workers will be able to make these tools and equip-
ment without additional supplies, infrastructure, or operator
direction. Most of the framework and tools will be mass pro-
duced with lower quality material and with low precision.
With asteroid restructuring, we have no goal to build ad-
vanced technologies such as solar cells or computer chips.
Our restructuring goal is not to build a self-replicating sys-
tem. Our goal is to build the framework of a space habitat.
We do not attempt unlimited self-replication and we strive to
minimize human direction. The end goal is to build a rotating
space station framework with a rich store of cataloged vola-
tiles and metals. We envision this enclosed framework will
attract and support follow-up missions with colonists and/or
robots. These groups will then develop more advanced man-
ufacturing technologies.
Self Replication – Summary: It would be wondrous to send
a self-replicating system to an asteroid. Multiple studies and
science fiction stories promote self-replicating systems. A
single self-replicating system creates create copies of itself.
The number of units increases exponentially and would
quickly provide the “labor” to restructure the asteroid. Mul-
tiple studies describe self-replication with units ranging in
size from nanobot assembles (nanotechnology) [Drexler
1986] to von Neumann machines [von Neumann 1966] to
large factories [Metzger et al. 2012]. We introduced self-rep-
lication with a review of a 1980 lunar self-replicating system
[Freitas and Gilbreath 1982] and a more recent self-replicat-
ing lunar industry [Metzger et al. 2012]. Both these self-rep-
licating systems require teleoperation initially and periodic
supplies from the Earth. Our restructuring concept assumes
complete autonomous operation and does not require addi-
tional supplies from the Earth. Our restructuring process uses
units called Productive Replicators [Freitas and Merkle
2004]. We increases productivity using parallelism and spe-
cialization. We advocate that launching a probe with the right
tools and building equipment on the asteroid is viable and
very cost effective.
4.3 Robotics – Analysis
We provide in following subsections the results of our self-
replication analysis. We first extend a historic mathematical
analysis to model replicators, helpers, and products. We re-
view a specific example of our replicator, helper, and product
model. We then provide the restructuring results using pro-
duction rates of the replicators and helpers. We include our
approach to analyze and simulate the entire restructuring of
the asteroid. We describe our simulators, the restructuring
equipment, and the initial seed package. We conclude this
section with a summary.
4.3.1 Mathematical Analysis
Our initial probe lands on the asteroid Atira. The probe
serves as a base station and has some communication, sensor,
computing, and manufacturing capabilities. It only has 4 ro-
botic systems (spiders). The robots have 21st
century tech-
nologies like sensors, motors, solar panels, processors, ad-
vanced software, and communication capabilities. We do not
intend on building these 21st
century technologies on the as-
teroid. We include with our probe several thousand small
modules with robotic electronics and actuators. We build
frames for the robots using in-situ materials to support this
module. We analyze the restructuring self-replication
growth. In particular, we consider the growth using different
production and self-replication rates
Background: A historic analysis evaluated such a system
where the self-replication and the product production were at
the same rate [Hall 1999]. This analysis produced an equa-
tion to define the time in generations to complete the self-
replication and production task:
2𝑘
𝑆𝑢 = 𝑆𝑝𝑙𝑛2.
In this equation, k is the number of generations; Su is the size
of the universal constructor (Spider); Sp is the size of the
product. Robots and tools will produce different products at
different rates. The productive replicator can produce copies
of itself or produce different products. In our restructuring
process we have different production rates for building tools
and for tools building products. We initially only consider
two production rates. This produced an equation to define the
time in generations to complete the self-replication and pro-
duction task:
2𝑘
𝑆𝑢 =
𝜆𝑢
𝜆𝑝
𝑆𝑝𝑙𝑛2.
In this equation, we include λu and λp as the production rates
of the constructor and the product. The minimum time occurs
when the total construction volume (2k
Su) is equal to total
production volume times 69.3% and the ratio of the produc-
tion rates λu/λp. Universal constructors self-replicate until
generation, kmin, and then all replicators, 2kmin
, work on pro-
ducing the product Sp. This analysis is obviously a simple
extension to the previous Hall equation.
Productivity Gains: Our restructuring process takes ad-
vantage of productivity gains from both parallelism and spe-
cialization. Parallelism, the number of replicators, is the tra-
ditional improvement of self-replication and provides only
part of our productivity gains. The replicators (spiders) also
offload tasks to helpers (specialized tools and equipment).
The helpers are designed to perform simple and repetitive
tasks much faster than the general-purpose replicators. This
specialization speeds up the execution of the tasks, improves
the productivity, and frees the replicators to perform more
complex tasks and management functions. There are similar-
ities in the analysis of this system’s parallelism and speciali-
zation to our analysis of system-on-a-chips [Jensen 2008].
We have developed many tools to support the spiders and
improve the space station production rate. We analyze the
product production in our system. We can use spiders to
build the product, or we can use a helper tool to build the
product. We first analyze the production mathematically and

then with simulations. The results of this effort illustrate the
trade-off between using sophisticated robot spiders and lim-
ited capability mechanical tools.
Mathematical Analysis: We mathematically evaluated this
problem assuming the restructuring effort first builds all the
spiders, then builds all the helpers, and finally builds all the
product. There are many options to overlap the building ef-
forts. This sequential approach simplifies the analysis and
provides a conservative estimate for the productivity im-
provements. We provide a summary of the analysis equa-
tions produced from this analysis in Table 4-1. The equations
on the left side of the table define the length of time required
to build spiders, helpers, and products. Our analysis has
found the minimum times for each of those tasks and those
equations are in the center column. We also include in the
right column of the table the equations that define the quan-
tity of produced spiders, helpers, and products.
We summarize the parameters with example values in Table
4-2. Our descriptions are for an early example of our restruc-
turing system. This system describes spiders (replicators)
self-replicating to produce other spiders. The spiders build
truss building units (TBUs), which are specialized pieces of
equipment (helpers). The spiders and TBUs build trusses
(products). We consider the construction of all the trusses re-
quired for our Atira space habitat.
The first four parameters in Table 4-2 describe the time re-
quired to build the individual pieces of equipment. The next
three parameters represent the number of spiders, helpers,
and product. The next set of parameters are the production
rates for the system. The next set of parameters define the
size (or complexity) of the equipment. The last parameters in
Table 4-2 define maximum counts for the system. There is
good correlation to Hall’s analysis and syntax of self-repli-
cating systems [Hall 1999].
Summary: We have extended a historic system analysis
[Hall 1999] to better represent the self-replicating spiders
and tool construction environment of the restructuring pro-
cess. Hall determined that replicators benefit more from spe-
cialization and pipelining than they do from parallelism [Hall
1999]. We agree with that insight. We keep the universal
constructor (spider) conceptually simple in our restructuring
process. The spiders cannot do everything efficiently, and
they do not construct the entire station. They can build addi-
tional spiders using vitamins from the seed unit. They can
build multiple tools and pieces of specialized equipment.
Parallelism and specialization increase the restructuring
productivity dramatically.
The performance can be calculated given the parameters of a
system and a selection of the number of spiders to dedicate
to the production. In the next subsection, we apply the devel-
oped equations using counts, maximums, rates, and sizes
from an example restructuring system.
4.3.2 Replicator, Helper, and Product Example
The previous subsection analyzed a system that self-repli-
cated spiders, built helper tools, and produced product. We
apply that analysis to a restructuring system example in the
following paragraphs.
We use previous analytic results and the specific values from
Table 4-2. We illustrate those production timing results for
the spiders and the truss building units. The graph in Figure
4-5 shows the time spent producing trusses for the space hab-
itat. The purpose of this chart is to illustrate the minimum
production time as a function of the number of helpers. The
space habitat uses 27,382,485 meters of trusses, which is
7,097,540 cubic meters of material. The y-axis shows the
production time in hours. The x-axis shows the number of
truss building units (TBUs) in the system. The chart includes
the time taken to build the spiders (replicators), build the
helpers, build the product, and the total time. These form the
relationship of the main equation of the previous subsection,
t = ts+th+tp. We use a maximum of 1000 spiders and the spi-
der build time of 120 hours. We see in the chart that the time
to build the spiders is a constant of 120 log2(1000) or 1196
hours. This example assumes all the spiders are built, then all
the helpers, and then the product. A single spider would take
10,550 hours to build the Truss Building Unit (TBU) and we
would have 1000 spiders building it. The build time for the
Truss Building Unit (helper) is an average of 10.55 hours.
The total helper build time, th, grows linearly from zero at
hour zero at the rate of 10.55 hours per helper unit. The time
to build the product (trusses), tp, is the total amount of prod-
uct divided by the production rates of the spiders and helper
units. The number of spiders is constant, and the number of
Table 4-1 – Minimize Production Time with Helper Tool
Activity Time Equation Minimum Time Equations Quantity Equation
Total to
Build
𝑡𝑡 = 𝑡𝑠 + 𝑡ℎ + 𝑡𝑝 𝑡𝑡𝑚𝑖𝑛 = 𝑡𝑠 + 𝑡ℎ𝑚𝑖𝑛 + 𝑡𝑝𝑚𝑖𝑛
𝑁𝑢𝑛𝑖𝑡𝑠 = 𝑁𝑠𝑚𝑎𝑥 + 𝑁ℎ
𝑁𝑝 = 𝑆𝑝𝑚𝑎𝑥 𝑆𝑝
⁄
Build
Spiders
𝑡𝑠 = 𝑇𝑠𝑠𝑙𝑜𝑔2(𝑁𝑠) 𝑡𝑠 = 𝑇𝑠𝑠𝑙𝑜𝑔2(𝑁𝑠) 𝑁𝑠 = 𝑁𝑠𝑚𝑎𝑥
Build
Helpers
𝑡ℎ =
𝑁ℎ𝑇𝑠ℎ
𝑁𝑆
𝑡ℎ𝑚𝑖𝑛 = √
𝑆𝑝𝑚𝑎𝑥
𝑁𝑠
𝑇𝑠ℎ
𝜆ℎ𝑝
− 𝑇𝑆𝐻
𝜆𝑠𝑝
𝜆ℎ𝑝
𝑁ℎ =
𝑁𝑠
𝜆ℎ𝑝
(√
𝑇𝑠ℎ
√
𝜆ℎ𝑝
𝑁𝑠
− 𝜆𝑠𝑝)
Build
Product
𝑡𝑝 =
𝑁ℎ𝜆ℎ𝑝 + 𝑁𝑠𝜆𝑠𝑝
𝑡𝑝𝑚𝑖𝑛 = √
𝑁𝑠
𝑇𝑠ℎ
𝜆ℎ𝑝
𝑁𝑝 =
𝑆𝑝

truss building units increases with the x-axis values (help-
ers). The production time, tp, decreases monotonically with
the increasing number of helpers. The chart also shows a
black square at the minimum point on the total production
time. For this example, the minimum occurs with 604 helpers
and the entire production of trusses is built in 14,207 hours.
This is only 1.6 years while previous chapters have indicated
the space habitat would take 12 years to complete. This anal-
ysis only includes the building of the trusses. It does not in-
clude the mining, transportation, construction, and many
other tasks associated with the truss building units. We later
find that over 3500 TBUs are used in the full station restruc-
turing simulation. This chart and approach illustrate the op-
timization potential for restructuring in general and validates
our analysis with another simulation.
4.3.3 Production Rate Analysis Results
The previous subsection only included the building of the
trusses. It did not include the mining, refining, transportation,
assembly, and many other tasks. To optimize these activities,
it is important to match the input and output rates for each of
the stages of processing. A previous study by the author of
this paper found that:
“Finally, simple analysis of a proposed architecture
traffic patterns can provide immediate insights into po-
tential performance and bottlenecks. Using average de-
vice interface rates and uniform request distributions
can identify many system constraints.” [Jensen 1993]
Performing complex, detailed, and compute intensive simu-
lations clearly provides valuable results; however, early an-
alytic analysis and rate analysis can provide insights to guide
those simulation efforts. We provide in this subsection an
analysis of the self-replicating growth for the restructuring
system. In this system, the spiders are self-replicating. They
are constructed using a limited quantities of solar cells and
electro-mechanical subunits.
Production Rate Example: As an example, we consider the
initial Base Unit production. To maximize production, we
need to maximize the Base Unit input and output rates. We
capture in Table 4-3 the analysis of spiders digging and load-
ing regolith into the base station, the base station producing
tiles, and the spiders using those tiles to construct new spi-
ders. We use some input and output rates to analyze the sys-
tem. The simple analysis of the rates in Table 4-3 shows that
we would need Nd=33.3 spiders digging and delivering reg-
olith as input to the base station. It also shows we need
Na=64.6 spiders using the output to assemble spiders.
This simple assessment illustrates the value of such analysis.
We find that many spiders are required to keep the single
base seed unit filled and processing. We also find that even
more spiders are required to assemble new spiders and match
the seed unit tile output rate. Initially, there are not enough
spiders to keep the base unit loaded with regolith and oper-
ating continuously. Even if the base unit were operating at
100%, there would not be enough spiders to use all the output
tiles to build new spiders. The rates give us a good estimate
Figure 4-5 – Minimize Truss Production Time using Spi-
ders and Truss Building Unit Helpers
Table 4-2 – Parameters for Spider with Truss Building Unit (TBU) Helper Tool
Description Parameter Unit Example Value
Time for spider to build spider
Time for spider to build helper (TBU)
Time for spider to build product (1m of truss)
Time for helper (TBU) to build product (1m of truss)
Tss
Tsh
Tsp
Thp
hours
hours
hours
hours
120
10550
6.1
0.153
Number of spiders
Number of helpers (TBUs)
Number of products (meters of truss)
Ns
Nh
Np
count
count
count
4 to 1000
Optimization Variable
0 to 27,382,485
Production rate of spiders making spiders
Production rate of spiders making helper equipment
Production rate of spiders making product
Production rate of helper making product
λss
λsh
λsp
λhp
m3 / hour
m3 / hour
m3 / hour
m3 / hour
0.000153
0.002737
0.0425
1.700
Size (complexity) of spider
Size (complexity) of truss
Size (complexity) of helper
Size (complexity) of product
Ss
St
Sh
Sp
m3
m3
m3
m3
0.0184
0.2592
28.88
0 to 7,097,540
Production quantity maximum
Spider quantity maximum
Maximum count of spiders
Spmax
Ssmax
Nsmax
m3
m3
count
7,097,540
184 (Ss x Nsmax)
1000

of the system at full operation. We see the base unit is pro-
ducing 7 tiles per hour at full production. We now consider
in a simulation how to reach full operation from the initial
seed with 4 spiders.
Initial Seed Simulation: Our simulation begins with the
base unit and four spiders. We assign two spiders to dig and
deliver regolith to the base unit. The base unit processes the
raw regolith and outputs tiles. The other two spiders assem-
ble new spiders using those tiles and vitamins. We use the
rates and volumes previously described.
To introduce the simulation, we include the count of spiders
and their activity in Figure 4-6a. This chart shows along the
x-axis the passage of time in hours and covers almost 3
months. The y-axis of the chart shows the count of spiders.
The graph includes the total number of spiders in the system,
the spiders assembling other spiders, the number of spiders
digging and delivering regolith, and the number of idle spi-
ders. Additional assembled spiders not being used are con-
sidered idle; however, in a more detailed simulation they
would be working on other tasks.
In this example, as spiders are built, they are assigned to
work on filling the base unit or building new spiders. The
assignment simply considers the times being used currently
on the filling and building tasks and assigns the new spider
to the task using more time. The graphs in Figure 4-6 show
at first the number of build-spiders (building new spiders) is
increasing more rapidly than the number of fill-spiders (dig-
ging regolith and filling the base unit). All newly built spi-
ders are assigned to work on digging and delivering regolith.
We show the same simulation data in the more detailed chart
in Figure 4-6b. After 300 hours we see that the number of
fill-spiders begins to increase.
We see in Figure 4-6a that the number of fill-spiders plateaus
at a count of 34 shortly after the time 1000 hours. The num-
ber of build-spiders plateaus at a count of 66 spiders at about
time 950 hours. With these spider counts, the base unit is be-
ing filled and the tile product is being used at maximum rates.
Shortly after time 1000 hours, we see more spiders are being
built and those become idle spiders. At this point the base
unit is operating at 100% capacity with maximum regolith
input and tile output.
The simulation results closely match the counts analyzed and
presented in Table 4-3. These simulations allowed us to
delve into details of the spider and base unit activities. This
kind of detail has helped to identify bottlenecks and deter-
mine what types of tools and equipment to create. With these
simulations we could monitor many parameters. We monitor
the surplus of regolith arriving at the base unit hopper, the
regolith rate coming out of the base unit, and the regolith rate
being used to build spiders. We could track the tiles being
used to build the spiders. We measured the count of surplus
tiles in a pile near the output of the base unit. Many additional
simulations have been performed and results captured.
Tile Production Simulation: As an example, we were curi-
ous how much construction material could be produced with
the Base Unit and Spiders. We adjusted the simulation to
build 100 extra (idle) spiders and then start producing tiles;
see Figure 4-7. The extra spiders could use the tiles to begin
building other tools. As before, the 66 build-spiders and the
34 fill-spiders are complete shortly after the time 1000 hours.
We see in the chart that the extra spiders are completed in
less than 200 hours. The system is producing the spiders at
the maximum rate of 0.5 spiders per hour. This rate is ex-
pected given the 66 build-spiders and a 120-hour spider con-
struction time. The tiles are produced at a rate of 7 tiles per
hour. Looking at Figure 4-7, this production rate seems great
at first glance. After an initial setup period, the base unit and
the fill-spiders and build-spiders are all working at 100% ca-
pacity. We see the number of tiles growing rapidly and we
have 100 extra spiders to begin working on other equipment.
We consider how long it would take to harvest and convert
the Atira asteroid to tiles for the station using the 100 extra
spiders and producing 7 tiles per hour. Our example torus
space station requires 2.62 billion cubic meters of material;
see Figure 3-23. Each tile represents 0.01 cubic meters of
material. It would take 37.4 billion hours (or over 4 million
years) to produce the material at 7 tiles per hour. Given this
Table 4-3 – Example Rate Analysis for Restructuring Process
Phase Dig & Deliver Fill Bin Manufacture Tiles Assemble Spiders
Activity Obtain Raw
Regolith
Input Raw Regolith Output Tiles Tiles and Vitamins
Details 1 Shovel = 0.001
m3
1 Shovel per 20
minutes
Input Bin = 0.1 m3
One bin = 100 shovels =
33 spider hours.
1 Bin processed per
hour
Output = 0.07 m3
Tiles = 2m x 0.1m x
0.05m = 0.01 m3
7 Tiles per hour
14 meters per hours
1 Spider built with Na Spider in 120/Na hours
Na <= 4 Spiders overcrowding constraint
4 Spiders build 1 spider in 30 hours
1 Spider requires 26 m tiles = 13 tiles; 6 connectors;
1 electro-mechanical subunit; 8 solar cells
Rate 0.003 Nd m3 per
hour regolith
dug and
delivered
Inputting 0.1 m3 per
hour maximum
Outputting 14 meters
per hour or 7 tiles per
hour maximum
1 Spider / (120/Na) hours
(13 tiles * Na / 120) tiles per hour
Using 0.1083 Na tiles per hour
Output 7 tiles/hours = Build 0.1083 Na tiles/hour
Spider
Count
Nd Spiders Digging Nd = 33.3 Spiders Base Unit Production Na = 7/0.1083 = 64.6 Spiders; About 6 groups of 4
working on the tile

simple assessment, we see the base unit tile production is a
severe bottleneck for the asteroid restructuring process.
Our original plan was to build rods (or tiles) of basalt; later
we chose to build tiles of anhydrous glass laminates. We ref-
erence Rod Production Units (RPUs) in most of our analysis.
Re-evaluating this analysis with Laminate Production Units
(LPUs) instead of RPUs would be appropriate in the future.
For the current time, we freely interchange tiles and rods and
RPUs and LPUs. We do not expect significant changes in the
restructuring approach or general results given this change.
Because the base unit tile production is a severe bottleneck,
we need to build Rod Production Units (RPUs) to increase
the tile production rate. With additional RPUs, we quickly
find that the transport of regolith becomes time-consuming
for the spiders. We address this issue by making trucks to
offload that task from the spiders. Digging the regolith is also
time consuming for spiders and we build harvest units to dig
and load the trucks more efficiently. Finally, these tools will
quickly deplete the availability of loose regolith pebbles and
grains on the asteroid surface. We build Regolith Crushing
Units (RCUs) to produce more pebbles and grains.
Restructuring Tools: We show these tools with some of
their construction metrics in Table 4-5. Tools are shown as
acronyms in the table’s left column. Later subsections and
paragraphs provide acronym definitions and descriptions;
see Figure 4-10. We estimate that some of these tools will
take thousands of hours to build. Fortunately, they are com-
plex and multiple parts can be built at the same time with
many spiders. As an example, it takes 3,516 hours for one
spider to build the subunits and construct and assemble the
Regolith Crushing Unit (RCU). The material would take 140
hours to construct. With 32 spiders working on that tool, it
could be complete in only 250 hours. The table also shows
the quantity (length) of tiles required to build the tool. The
Rod Production Unit requires 4,768 meters of rods (or tiles).
At 7 tiles per hour or 14 meters per hour this would require
340 hours if they were produced with only the base unit. Tak-
ing over two weeks for the tiles seems excessive; as such, we
need to improve their production. Having other RPUs pro-
ducing tiles increases the tile production rate and reduces the
material time correspondingly.
We include Table 4-5 and Table 4-4 to provide a summary
of the construction time and material requirements for all the
tools and subunits. These are our current estimates and only
rough designs for most of these tools and subunits exist. We
created engineering estimates for the construction material
and time. We considered the general size estimates to evalu-
ate the number of tiles and trusses required. We plan on using
concentrated solar energy to weld the parts together. We
could consider a basalt “rivet” to connect the tiles together
after drilling (melting) a hole in the tiles with focused solar
energy. To estimate the build time, we counted the number
of welds required and conservatively assumed 30 minutes
per weld. We also doubled that build time for most tools to
a) Initial Spider Activity Matching Production Rates
b) Details on Spider Activity
Figure 4-6 – Spider Construction Analysis
Figure 4-7 – Surplus Tile Production
0
20
40
60
80
100
120
140
160
180
200
0 200 400 600 800 1,000 1,200
Spiders
(count)
Time (Hours)
Base Unit Regolith Processing
(4 initial spiders; 2 digging & filling; 2 Building new spiders)
Total Spiders
Build Spiders Count
Fill Spiders Count
Idle Spiders Count
0
5
10
15
20
25
0 50 100 150 200 250 300 350 400 450 500 550 600
Spiders
(count)
Time (Hours)
(4 initial spiders; 2 digging and filling regolith; 2 building new spiders)
Total Spiders
Build Spiders Count
Fill Spiders Count
Idle Spiders Count
0
1000
2000
3000
4000
5000
6000
0
20
40
60
80
100
120
0 500 1000 1500 2000
Tiles
(Count)
Spiders
(count)
Time (Hours)
(Maximum build and fill spiders; 100 idle spiders; Create surplus of tiles)
Build Spiders Count Fill Spiders Count
Max 100 Idle Spiders Tiles Instead of Idle Spiders

provide extra margin on the estimate. Some of the more com-
plicated tools have multiple Stirling engines and/or clock-
works. We add the construction time and materials from
those subunits to the total time. We also assume that it would
require 120 hours to assemble, attach, and integrate a subunit
to one of the tool housings. The total time also includes the
time to build the material assuming a production rate of 7
tiles per hour. We divide the truss length estimates by 14 me-
ters per hour to determine the material build time. We include
the characteristics of the subunits in Table 4-4. These subu-
nits have the same metrics as the tools. In these tables, we
sometimes explicitly show the subunit build time and other
times implicitly include the subunit build time in the equip-
ment build time.
4.3.4 Analysis Approach Using Simulations
We present in this section our approach to analyze and sim-
ulate the entire restructuring of the asteroid. We describe our
simulators, the restructuring equipment, the initial seed pack-
age, and expected technology advancements.
Restructuring Simulations: We have run hundreds of sim-
ulations to evaluate the restructuring concepts. These in-
cluded orbit and transfer simulations using Verlet integra-
tion, simulations using production rate analysis, and discrete
event simulations of the restructuring process. We gathered
and encoded accurate mathematic formulae for the station
physical characteristics. When possible we used comparable
values or engineering estimates for consumption and produc-
tion rates. We developed a tool to estimate the number of
welds for the various equipment built during the restructur-
ing process. In all cases, we used conservative estimates.
We used C++ and Python for various programming efforts.
We use Excel to simulate and produce many of our results.
We used Wolfram-Alpha to assist with mathematical analy-
sis. We used Blender to render the images of our asteroid and
torus station. The Blender station rendering was written in
Python code and has size parameters for key components of
the station. Not only does the Blender Python code render a
station but it also produces a report with details including pa-
rameter values, component sizes, number of floors, and sur-
face area. Using multiple tools provides cross checking of
results to identify issues and correct discrepancies. Many of
the simulation tool concepts were developed over the au-
thor’s 40-year engineering and research career. The discrete
event simulation software has its foundation from the 1990s
[Jensen 1993]. The orbit analysis approaches were part of a
more recent research effort. We used multiple approaches for
the scheduling and system engineering of this effort. The
analysis, decomposition, modeling, and building of complex
systems has been a successful part of the author’s career for
multiple products and research projects.
The restructuring process includes mainly mining, pro-
cessing, and construction. Our simulation effort evaluates the
Table 4-4 – Tool Subunits Characteristics
Table 4-5 – Equipment used in simulations
Subunits Material
Build w/
Margin
Build
Material
Detail
Complexity
Stirling
Engines
Clock-
works
Mirror
Units
Integrate
Subunit
Build Time
(Material &
Tool)
Maximum
Spiders to
Build
Minimum
Build Time
Metric (m) (hours) (hours) 60 hrs 659 hrs 217 hrs 318 hrs 120 hrs (hours) (count) (hours)
Fresnel Len Frame 11.2 139.8 0.8 0 0 0 0 0 141 2 70.7
Solar Panel Frame 12.8 145.8 0.9 0 0 0 0 0 147 2 73.8
Clockwork 28.0 95 2.0 120 0 0 0 0 217 4 55.8
Mirror 397.0 290 28.4 0 0 0 0 0 318 16 46.5
Stirling Engine 56.0 138 4.0 300 0 217 0 0 659 8 85.9
Connectors 1.2 2400 0.2 60 0 0 0 0 877 6 146.2
Sun Tracker 484.0 293.8 34.6 120 0 217 0 0 772 8 96.5
Tools Material
Build w/
Margin
Build
Material
Detail
Complexity
Stirling
Engines
Clock-
works
Mirror
Units
Integrate
Subunit
Build Time
(Material &
Tool)
Maximum
Spiders to
Build
Minimum
Build Time
Metric (m) (hours) (hours) 60 hrs 659 hrs 217 hrs 318 hrs 120 hrs (hours) (count) (hours)
Spider 26.0 120 1.9 0 0 0 0 0 122 4 31.86
Truck 114.4 148.4 8.2 0 659 0 0 120 936 8 124.10
Mover 95.1 111.3 6.8 0 659 0 0 120 897 8 118.08
Digger 93.6 330 6.7 0 659 0 0 120 1,116 8 145.31
RCU 1965.2 2400 140.4 0 659 217 0 240 3,656 32 250.25
HU 622.8 2496 44.5 0 2636 0 0 480 5,656 16 395.24
TPU 2872.2 916 205.2 60 659 1519 1910 1680 6,949 32 415.91
RPL 2086.4 4142 149.0 120 1318 868 0 720 7,317 32 373.03
TBU 5071.2 1630 362.2 120 659 2387 3184 2640 10,982 64 528.16
RPU 4768.8 148 340.6 120 2636 2387 3184 3000 11,815 64 519.92
SAU 6967.2 3300 497.7 0 659 2387 3184 2640 12,667 64 687.81
F&MU 6967.2 5494 497.7 120 659 2387 3184 2640 14,981 64 723.96
CPP 7450.8 6520 532.2 120 2636 2387 3184 3000 18,379 64 811.05

building and operation of equipment and tools. We do not
claim to have every issue resolved; however, we feel suffi-
cient progress has been made to present the restructuring pro-
cess for review. Our evaluation and analysis have run into
bottlenecks, but every time there has been an alternative so-
lution. We have evolved and adapted our approach a dozen
times during the development and execution of this effort.
Equipment Overview: Our simulations include the building
and operation of equipment and tools. The asteroid environ-
ment will pose problems for existing terrestrial equipment.
Design changes will be required for terrestrial equipment to
work in the asteroid environment. The design and modeling
of the restructuring equipment must consider a low gravity
and vacuum environment.
Earth gravity is important for the operation of terrestrial min-
ing equipment. Equipment tied to the earth or using cables to
move buckets have the least dependency on strong Earth-like
gravity. Anchoring equipment to the asteroid using harpoons
or spikes helps overcome some of the issues with low grav-
ity. Portable wheeled equipment used to move ore can oper-
ate well on a track with low gravity except for a risk of reach-
ing escape velocity on small asteroids. Portable wheeled
equipment on Earth that assert digging or scraping force on
the surface relies on their mass and gravity to counteract that
force. That equipment is highly dependent on gravity and
will require new designs.
We recognize there are other issues in the asteroid environ-
ment. The lack of an atmosphere means that waste heat can-
not be dissipated by atmospheric convection. No atmosphere
means lubricants such as oil and grease will evaporate in the
vacuum. No atmosphere means combustion engines would
no longer work without a separate supply of oxygen. The ex-
treme temperature changes will subject equipment to signif-
icant thermal stress. Another problem for the asteroid opera-
tions could be an abundance of dust from the regolith. Dust
contamination can obstruct and abrade moving joints in
equipment. We strive to address these issues but we recog-
nize they have not been fully addressed in our study. These
environment issues are problematic; however, solutions
could enable new approaches for mining and processing ore.
Additional research, testing, and development will address
these issues and refine our designs.
Self-replicating systems can create millions of units to per-
form a large task. Because of launch costs we could not send
millions of units or even the vitamins to build the millions of
units. Because we did not have millions of devices, we found
that our restructuring approach with replicators regularly hit
bottlenecks in the processing or transporting of material. Our
list of equipment for the simulations evolved from a single
device to over twenty unique pieces of equipment and subu-
nits. We have not completed the final formal design and
drawings for these pieces of equipment. We have good engi-
neering estimates on the size and required material. We in-
clude the primary 13 tools in Table 4-5 and the 7 support
subunits in Table 4-4. The tables include for each piece of
equipment its size in required length of regolith tiles and the
time to build with spiders. The simulation of these equipment
models includes other relationships such as the amount of
metal required to build, the production rate, travel rates, and
the equipment required to build. We hope to refine this sim-
ulation with additional detail and complete the final formal
estimates, designs, and drawings of the restructuring equip-
ment in the future.
Initial Seed Package: Our restructuring approach sends a
probe and seed package to an asteroid. This seed package
contains enough supplies to produce a limited number of spi-
ders and many tools. A 1980 study defined a 100-ton seed
package for a self-replicating system on the Moon [Freitas
and Gilbreath 1982]. A 2012 study defined a more modern
approach and estimated a total of 41 metric tons using six
launches of seed packages to the Moon [Metzger et al. 2012].
Both of these self-replicating systems used teleoperation in-
itially and periodic supplies from the Earth. We estimate that
our total seed package weighs 8.6 metric tons and requires
only a single rocket launch. We envision that our seed pack-
age is self-sufficient and does not need additional supplies or
direction from Earth.
Our restructuring process will construct hardware made from
in-situ materials. The produced tools will be more primitive
than the original seed equipment. Our 21st century robots
will be creating 18th and 19th century frameworks, trusses,
tools, and engines. We send enough solar cells and computer
modules to build the required number of spider robots. These
robots only perform a small fraction of the total work – prim-
itive trucks, diggers, crushers, and specialized units perform
most of the heavy lifting for the restructuring effort. Our goal
is to have full closure on the restructuring process – no addi-
tional materials beyond the original seed are required to ac-
complish the building of the space habitat framework.
We show in Table 4-6a Metzger’s list of the assets to produce
a self-replicating lunar industry. We show in Table 4-6b a list
of the assets required for the restructuring probe. The mass
of both probes is under the launch weight of a SpaceX Falcon
Heavy (16.8 metric tons) [SpaceX 2018]. Our seed probe in-
cludes different jigs such as shovels, Fresnel lens, cutting,
and test sensors. The number of jigs becomes a bottleneck in
many of the restructuring processes. Some jigs can be pro-
duced using the mongrel alloys and the asteroid regolith.
Many jigs are too sophisticated to build using the spiders,
asteroid material, and available seed package tools. Some
jigs are replaced with less sophisticated 18th
century technol-
ogy. One of those sophisticated jigs is the Fresnel lens. Its
function will be performed with solar concentrators built
from rods, panels, and a supply of silvered mylar.
We expect there could be additions to the asset list that will
increase the weight. Refinement of the assets should reduce
the individual weights of the tools. It is realistic to aim for a
probe weight of 8 metric tons. Using an ion engine and a
mission delta-v of 5 kilometers per second, we find we would
need almost 1 metric ton of fuel for the one-way mission to
a near-Earth asteroid. An eight-ton goal for the seed probe is
desirable. It becomes possible to send two probes – one for

the north pole and one for the south pole of the asteroid –
with a single launch. The two probes would require about
double the fuel and hopefully still meet the maximum pay-
load weight for a single launch.
4.3.5 Technology Advancements
The restructuring effort seed probe is smaller and less com-
plicated than those in detailed historic studies [Freitas and
Gilbreath 1982] [Metzger et al. 2012]. Our goal was to re-
duce (or eliminate) future transport of materials from the
Earth. The earlier 1980 study developed a 100-ton seed probe
that would require the launch equivalent of four Apollo mis-
sions to the Moon. The later 2012 study reduces that seed to
33.3 metric tons and could be accomplished in 5 Falcon
Heavy launches. These early studies included material and
support for astronaut crews. Self-replication systems that in-
clude crew support incur additional cost in materials, guid-
ance, and technology.
The advancement of technology provides our restructuring
effort with advantages over the 1980 study. The 1980 NASA
study also included multiple robots with the seed unit. Min-
ing robots, paving robots, repair robots, and transport vehi-
cles were included and weighed over 18 metric tons. The
1980 estimate for the mining robot has been reduced from
4.4 tons to less than 100 kilograms [Metzger et al. 2012]. In
1980 each robot computer weighed 50 kilograms [Freitas and
Gilbreath 1982]. Today such computers weigh less than a
few kilograms. Also, a processor today has over 250,000
times the performance of a 1980 processor. The required
power, size, price, cooling, and weight have all been reduced.
The restructuring process is different than the earlier ap-
proaches. We replace custom part manufacturing equipment
with 3D printing. We replace teleoperation with modern day
image processing and artificial intelligence. We replace large
complex pieces of manufacturing equipment with many
smaller and less efficient helper equipment designs.
We include in our probe enough supplies to build a modest
number of productive replicators. Beyond that limited num-
ber, we do not attempt any additional self-replication. Our
restructuring process relies on the production of tools and
equipment to extend the capabilities of the replicators (spi-
ders). With the limit on the number of spiders, our restruc-
turing seed would only be about 8 metric tons and launched
on one Space X Falcon launch. Ideally, our restructuring ef-
fort does not require any additional launches to complete its
mission. A Falcon Heavy rocket can lift 16.5 tons to trans-
Mars injection and could potentially deliver two of our seed
probes to an asteroid. Two probes would reduce mission
risks with redundancy and reduce the mission schedule.
4.3.6 Analysis Summary
We have used mathematical and simulation analysis of the
restructuring asteroid process. We extended a historic math-
ematical analysis to model replicators, helpers, and products.
We provided the restructuring results using production rates
of the replicators and helpers. We included our approach to
analyze and simulate the entire re-structuring of the asteroid.
We describe our simulators, the restructuring equipment, and
the initial seed package. We also included a section describ-
ing technology advancements that could improve our re-
structuring process.
The analyses of those subsections show that the production
and consumption rates have an impact on the system perfor-
mance and on design decisions. We also saw different parts
of the system becoming the bottleneck as the number of spi-
ders and tools were produced. As more tools and activities
are added, the analytic analysis and simulations become
more complex. Fortunately, with large numbers of units and
activities performing over longer times, our experience has
shown that using average production and consumption rates
will provide the insights we need to complete our analysis.
These early simulations identified different bottlenecks. Ini-
tially, there were not enough spiders to keep the base unit
operating at 100% efficiency. With enough spiders, once the
base system was operating at 100% efficiency, a surplus of
output indicated that the spider-building spiders had become
the bottleneck. More of these spiders addressed that bottle-
neck. We found that with many more spiders there would not
be enough material to build the station in a timely fashion.
The base-unit rod-production had become the bottleneck.
These simulations showed that there is a balance between
rapidly finishing one task and starting other tasks. Additional
Table 4-6 – Initial Probe Assets
a) Assets for Lunar Industry Probe
Credit: Self Produced using [Metzger et al. 2012] [Facts]
b) Assets for Asteroid Restructuring Probe
Credit: Self Produced
Metzger Assets
Qty. per
set
Total Mass
(kg)
Power Distrib & Backup 1 2000
Excavators (swarming) 5 445
Chem Plant 1 – Gases 1 763
Chem Plant 2 – Solids 1 763
Metals Refinery 1 1 1038
Solar Cell Manufacturer 1 188
3D Printer 1 – Small parts 4 752
3D Printer 2 – Large parts 4 1276
Robonaut assemblers 3 450
Total per Set 7675
Atira Asset
Qty. per
set
Total Mass
(kg)
Spider 4 340
Spider Control Units 3000 2100
Solar Cells 6000 900
Jigs 720 3064
Connectors 200 400
Base Unit 1 1039
Silvered Mylar 2000 200
Misc 1107 563
Total per Set 8606

units would reduce the time required to complete one task.
Often though, there is other equipment that is needed to com-
plete the station. For simple cases, mathematical analysis can
provide the optimal balance. Our self-replication system will
need to monitor progress and adjust assignments during the
building of the station. It may be beneficial to have the re-
structuring asteroid system simulate future versions of itself
to identify bottlenecks and provide guidance on tasks and as-
signments.
Our simulations have used the estimated resources and times.
We have seen the overall system performance rates improv-
ing from the parallelism and the specialization. From the in-
itial base unit production rates of only 7 tiles per hour and
construction taking 37.4 billion years, it is exciting to see the
scalability and productivity gains reducing this to about
100,000 hours (12 years).
4.4 Robots – Results
Our analysis in the previous subsections focused on the con-
struction of spiders, tiles, and trusses. We present in this sub-
section our analysis and simulation of the entire restructuring
of the asteroid.
4.4.1 Introduction
Our initial probe lands on the asteroid Atira and only has 4
robotic systems (spiders). The probe serves as a base station.
The first 4 spiders and the base station will build frames and
assemble new spiders. The spiders will also build other tools
and equipment from supplies and the asteroid material. Ini-
tially, the spiders will need to multitask on many different
tasks. Some of the early tasks include:
• Mining regolith
• Loading the base unit with regolith
• Removing manufactured regolith tiles from base unit
• Assembling solar panels from frames and solar cells
• Assembling spiders from frames and modules
• Assembling trusses from tiles
We show in Figure 4-8 a chart that illustrates this early mul-
titasking. This chart was produced early in our investigation
and shows the activity of spiders over the first 4000 hours on
the asteroid. The y-axis shows the count of the spiders. The
graphed lines show the different spider activity. The x-axis
shows the time in hours. During the first 500 hours in this
simulation, the spiders alternate between collecting regolith,
assembling solar panels, and assembling new spiders. This
simulation produced many idle spiders. By hour 1000, there
are only eight active spiders and 50 idle spiders. About this
time the supply of connectors included with the probe are
exhausted. Spiders begin to make new connectors (3D print-
ing with metal grains) and the number of idle spiders drop
significantly to support this effort. Groups of 20 spiders
begin to build rod production units at time 2600. We then see
more spiders begin to dig regolith to supply those units. This
simulation includes spiders producing trusses beginning at
about hour 3200. Near the end there are still almost 1000 spi-
ders not being used in this simulation. The chart in Figure
4-8 begins to highlight the different spider activities and the
changing bottlenecks. It also highlights the potential rapid
growth from the self-replication of spiders with sufficient
supplies.
4.4.2 Tool Construction
The first year and a half shown in our full restructuring sim-
ulations are based on results from the discrete event simula-
tions. The last 11 years of the simulations are based on the
production and consumption rates of the station materials.
This includes the trusses, panels, and fill. With larger num-
bers of entities in the simulation, we have reached a point
where the Theory of Large Numbers applies. It becomes vi-
able to use rates and averages instead of the discrete event
simulation.
We review one of those simulations to understand the tool
construction. This simulation found it took almost 12 years
to construct the Atira station. This version of the space habi-
tat had the elliptic outer torus with a major radius of 2332
meters and minor radii of 1105 meters and 368 meters. This
version had two sets of inner circular tori and spokes. The
inner tori have a radius of 1166 meters and minor radius of
75 meters.
The simulation limited the growth in spiders to 3000 units.
This is limited by the number of electronic modules and solar
cells sent with the probe. The spiders build 23,500 other
pieces of equipment. The equipment built by the spiders will
not have sophisticated electronic microprocessors; instead,
they will have mechanical state machines to control their op-
eration. Equipment and tools are supplied, emptied, and
managed by the spiders. We found in our simulations that
there is a limit when all spiders are occupied with managing
the existing equipment. Additional equipment would not be
Figure 4-8 – Early Spider Activity on Asteroid
1
10
100
0 500 1000 1500 2000 2500 3000 3500 4000
Count
Time (Hours)
Spider Multitasking Activity
Collect Regolith
Assemble Solar Panel
Assemble Spiders
Build RPUs
Build Connectors
Idle Spiders
30
300
3

used if built. We note that some earlier-built equipment is no
longer needed near the end of the station construction. The
retirement of that equipment will free some spiders. The re-
tired equipment is typically replaced with other equipment
necessary to finish the station.
4.4.3 High Level Schedule
The restructuring mission and process goes through a series
of activities. Previous sections included rendered images of
an example space station; see Figure 1-1 and Figure 3-22b.
Those images help to illustrate these major activities and
their associated components. These activities include:
1. Reach asteroid
2. Land seed probe
3. Start initial evaluation
4. Build web
5. Build spokes
6. Build shuttle bay
7. Build outer rim
8. Build inner torus
9. Build outer elliptic torus
Each of these restructuring tasks has been simulated in some
fashion. The tasks begin with landing the seed unit and finish
with attaching a skin of regolith panels to the exterior of the
large outer elliptic torus. We have performed analysis of all
the building tasks. Some analyses are detailed discrete event
simulations, some are detailed rate driven simulations, and
some are high level average rate estimates.
We include in Figure 4-9 a simple Gantt chart to illustrate the
restructuring schedule. The chart shows the web of trusses
being built over the asteroid in the first year and a half. The
process starts building the spokes, and that requires almost 5
years to complete. No equipment or tools exist at the start of
the restructuring process. It takes time to build the initial
equipment and tools and then the progress on the station
components improves. The shuttle bays at the north and
south poles of the asteroid tie the spokes together. This
schedule only assumes a single base station at one of the
poles. Two probes and base stations (two poles) would dou-
ble the number of spiders and improve the schedule. We see
in the schedule that the outer rim is started early. Once the
outer rim ties the station together, it is possible to begin
rotating the structure and produce some centripetal gravity.
Some tools require gravity (the Continuous Panel Production
Unit in particular) and mandate this early rotation. The inner
torus is started in the fifth year. Once sections of the inner
torus are complete, a construction crew can arrive to make
those sections habitable. The outer torus is built inward from
the outer rim and requires over six years to complete. As seg-
ments of the outer torus are completed, the manufacturing
crew can begin to make those segments habitable. More pop-
ulation arrives with the completion of the habitable seg-
ments.
For our example Atira asteroid model, this is an appropriate
order of tasks. For different shape asteroids or station geom-
etries, the order of the tasks may change. As an example, the
outer rim and outer torus may not be built with smaller aster-
oid. For some shaped asteroids, the outer torus may be built
before the inner torus. A dumbbell might only have a single
hub and no tori structures. It may be appropriate to surround
an asteroid with an ellipsoid station. The station could be
built to one side of the rotating asteroid. We also note that
there are issues with solar power, shadows, and rotation that
need to be addressed.
Figure 4-9 also shows the immigration of the station popula-
tion. The restructuring system is designed to work autono-
mously. The initial crew arrives in the seventh year. This is
before the outer elliptic torus is complete and before the sta-
tion has been spun up to full rotation speed. This crew would
start making portions of the station airtight, producing an at-
mosphere, and creating an air processing system. Their work
would initially be in a low gravity environment. The crew
would start work in the inner torus or the shuttle bay since
the outer torus would not be complete. Even without the crew
arrival, the restructuring system continues to autonomously
construct the station. We imagine that this initial crew would
bring a refreshed set of technologies that would enable a new
generation of robots, tools, and equipment to be built. The
catalog of stored materials and volatiles would guide the re-
search and selection of these new technologies.
Figure 4-9 – Schedule for Restructuring Asteroid Major Station Components
Year
Start
Web
Spokes
Shuttle
Outer Rim
Inner Torus
Outer Torus
Spinup
Inspection
Phase 1
Phase 2
Phase 3
Phase 4 Population: 700K
Outer Rim
Inner Torus
Crew: 300
Crew: 10K
Population: 100K
Outer Elliptic Torus
240 minutes to 1.55 minutes per rev
Crew: 12
Spokes
Shuttle Bay
13 14 15 16 17
Web
7 8 9 10 11 12
1 2 3 4 5 6

4.4.4 Total Equipment Built
Over the course of the simulation, the 3000 spiders were
built. We show in Figure 4-10 a bar chart with the maximum
number of key pieces of equipment created during this sim-
ulation. Spiders are the general-purpose robotic equipment.
Four of these are sent with the original base station and elec-
tronics are sent to construct a total of 3000 spiders. Regolith
is moved in Trucks that are covered to help reduce floating
debris in the low gravity. The equipment called Movers is
like a flatbed truck and used to move items other than rego-
lith such as trusses, panels, and tiles. Truss Building Units
(TBUs) are built to more efficiently build the standard
trusses used throughout the restructuring effort. Harvest
Units (HUs) have arms that gather loose regolith and convey
to the trucks. The base station probe initially produces the
rods and tiles from regolith; however, Rod Processing Units
(RPUs) are created to build rods and tiles. We are assessing
whether to replace the RPUs with Laminate Processing
Units (LPUs), which are smaller equipment helpers that con-
vert regolith to anhydrous laminates for construction. The re-
structuring process uses Fill and Melt Units (F&MUs) to fill
walls and floors with ground regolith and melt layers for ma-
terial containment and strength. Skin Attachment Units
(SAUs) are mechanical automatons that attach panels to the
shell, walls, and floors. As the name implies, the Regolith
Crushing Units (RCUs) take large regolith pieces (cobbles)
and crush them to pebbles and grains. Diggers use an attach-
ment like jack hammer chisels to reduce boulders and flat
rock regions for processing. These diggers hang onto the web
and slowly and autonomously move across the asteroid sur-
face. They leave behind a trail of smaller rocks. Early in the
restructuring process, Tile Placement Units (TPUs) attach
regolith tiles to structures to provide working surfaces, for
material retention, and for strength. TPUs also create panels
for equipment and floors. Once the outer rim of the outer to-
rus begins to rotate and provide centripetal gravity, we begin
to build Continuous Panel Production Units (CPPs). The
CPPs are large complex units that produce larger panels of
regolith to be attached to the shell, walls, and floors by the
SAU. LPUs may supplant the need for CPPs. Rotating Pel-
let Launchers (RPLs) are spinning arms that launch regolith
pellets at high speed [Johnson and Holbrow 1977]. The RPLs
are used to launch and quickly move regolith from the aster-
oid to the outer rim. This is a faster technique to move rego-
lith long distances instead of using trucks. We use this trans-
fer of mass (and momentum) to spin up the outer rim (and
ultimately the station) and reach the desired rotation rate.
About 26,500 pieces of equipment are constructed in the sim-
ulation. The chart does not include the subunits such as sun
trackers, parabolic mirrors, connectors, and Stirling engines.
Estimates for these subunits are included in the build time
and volume estimates for the other equipment.
4.4.5 Total Equipment over Time
Our simulations allow us to evaluate the quantity of equip-
ment needed to complete the station. The initial probe with
four spiders produce almost 26,500 pieces of equipment over
twelve years. This count is another way to evaluate progress
of the restructuring effort. We show in Figure 4-11 a running
count of the 13 types of equipment over the twelve years.
The y-axis shows the equipment count ranging from 0 to
30,000 pieces. The x-axis shows the passage of time in years
ranging from 0 to 12 years. Initially only spiders and the base
unit are available to do the work. Spiders use vitamins and
in-situ material to construct other spiders. Spiders build the
framework, connectors, subunits, tools, and equipment. Ulti-
mately, the spiders no longer build, and instead, are occupied
with managing the equipment. These simulations determine
how many pieces of equipment can be managed without ex-
ceeding the available 3000 spiders. The stacked graph chart
shows the quantity of units for each of the thirteen major
pieces of equipment. The legend shows those units, and the
stacked graphs are in the same order as the legend. We show
Spider – General Purpose Robot
Trucks – Mechanical Automaton
Movers – Mechanical Automaton
TBUs – Truss Building Units
HUs – Harvest Units
RPUs – Rod Production Units
F&MUs – Fill and Melt Units
SAUs – Skin Attachment Units
RCUs - Regolith Crushing Units
Diggers – Jack Hammer Diggers
TPUs - Tile Placement Units
CPPs – Continuous Panel Production
RPLs – Rotating Pellet Launchers
Figure 4-10 – Total Count of Equipment Used During Simulation
3,000
1,953
3,041
3,457
2,000
3,092
1,411
2,818
3,000
2,656
262
43
32
0 500 1000 1500 2000 2500 3000 3500 4000
Spiders
Trucks
Movers
TBUs
HUs
RPUs
F&MUs
SAUs
RCUs
Diggers
TPUs
CPPs
RPLs
Equipment (Count)
Equipment Created for Elliptic Torus Space Station Restructuring
(Atira Asteroid (2600x2400x1150m); S-Type; Station Major Radius 2332m; Minor Radii 1105m and 368m)

the maximum quantity in parentheses in the legend for each
piece of equipment produced in this simulation.
Exponential growth is characterized with slow initial growth
followed by rapid (almost unbounded) growth. The graph in
Figure 4-11 barely shows any activity during the first half
year. It takes time to build the initial web of trusses and the
first pieces of equipment with only four spiders and the base
unit. It shows a modest growth spurt from the sixth to the
nineth year. This is time spent preparing to build and starting
construction on the enormous outer elliptic torus. In the
nineth year, all 3000 spiders have been built and the self-rep-
lication ends. The last three years the spiders are fully occu-
pied with managing the tools and equipment. A fairly con-
stant set of equipment works on completing the outer torus.
We expect that additional refinement would shorten the over-
all schedule. We describe the activity at several yearly mile-
stones in the following paragraphs.
Year 1: Web Production: At the end of the first year, there
are 405 spiders active on the asteroid and station. There are
43 Rod Production Units (RPUs) active. We see 20 Harvest
Units (HUs) are digging regolith and many of the 362 Trucks
are bringing that regolith to the RPUs. There is only 1 Rego-
lith Crushing Unit (RCUs) active on the surface. Spiders and
Harvest Units process the innate loose regolith pebbles and
grains on the surface. We also find 48 Truss Building Units
(TBUs) are creating trusses that are being moved by the 1524
Movers. Spiders are using those trusses to extend the web
and build more equipment. Tile Placement Units (TPUs)
start being built to provide panels for the RPU, Jaw Crushers,
and other equipment.
Year 3: Spoke and Shuttle Bay Production: At the end of
the third year, there are 716 spiders active on the asteroid and
station. There are 74 Rod Production Units (RPUs) active.
We see 115 Harvest Units (HUs) are gathering regolith and
many of the 1892 Trucks are bringing that regolith to the
RPUs. We also find 82 Truss Building Units (TBUs) are cre-
ating trusses that are being moved by the 2305 Movers. Spi-
ders are using those trusses to build the station structure and
build more equipment. There are 153 Tile Placement Units
(TPUs) attaching tiles to the walls of the spokes and produc-
ing panels for other pieces of equipment. There are 259 Fill
and Melt Units (F&MUs) working on the outer walls of the
spokes.
Year 5: Spoke, Outer Rim, and Inner Torus: At the end
of the fifth year, there are 840 spiders active on the asteroid
and station. There are 277 Rod Production Units (RPUs) ac-
tive. We see 462 Harvest Units (HUs) are gathering regolith
and many of the 1953 Trucks continue to bring that regolith
to the RPUs. We also find 262 Truss Building Units (TBUs)
are creating trusses that are being moved by the 2311 Mov-
ers. Spiders are using those trusses to build the station struc-
ture and build more equipment. There are 257 Tile Placement
Spider – General Purpose Robot
Truck – Mechanical Automaton
Mover – Mechanical Automaton
TBU – Truss Building Unit
HU – Harvest Unit
RPU – Rod Production Unit
F&MU – Fill and Melt Unit
SAU – Skin Attachment Unit
RCU - Regolith Crushing Unit
Diggers – Jack Hammer Diggers
TPU - Tile Placement Unit
CPP – Continuous Panel Production Unit
RPL – Rotating Pellet Launcher
Figure 4-11 – Total cumulative equipment created during the restructuring process

Units (TPUs) attaching tiles to the walls of the spokes and
producing panels for other pieces of equipment. There are
372 Fill and Melt Units (F&MUs) filling the outer walls of
those structures as the panels enclose them. As the outer rim
becomes complete in the sixth year, some Regolith Pellet
Launchers (RPLs) would be manufactured and begin launch-
ing pellets from the asteroid to the outer rim. The outer rim
would begin to rotate faster than the asteroid, produce cen-
tripetal gravity, and some Continuous Panel Production
Units (CPPs) and Skin Attachment Units (SAUs) would be
built.
Year 8: Inner Torus and Outer Torus: At the end of the
eighth year, there are 1904 spiders active on the asteroid and
station. There is a significant increase in the number of
equipment units to construct the large outer torus. There are
2320 Rod Production Units (RPUs) active. We see 1579 Har-
vest Units (HUs) are gathering regolith and many of the 1953
Trucks are bringing that regolith to the RPUs. There are also
28 Regolith Pellet Launchers (RPLs) moving regolith from
the asteroid to the outer rim and torus. We also find 2617
Truss Building Units (TBUs) are creating trusses that are be-
ing moved by the 2864 Movers. There are 33 Continuous
Panel Production (CPPs) systems operating on the rotating
outer rim. The CPPs are producing panels that 476 Skin At-
tachment Units (SAUs) are welding to the shell, walls, and
floors. Panels from the CPPs are used instead of those built
by the Tile Placement Units (TPUs). As such, no additional
TPUs are built. Much of the original loose regolith is gone
from the asteroid and 2656 Diggers are creating the cobbles
for 2825 Regolith Crushing Units.
Year 10: Outer Torus: At the end of the tenth year the
equipment is only working on the outer torus. There are 2822
Spiders active on the asteroid and station. We find 1943
Trucks and 2949 Movers are active moving trusses, panels,
and regolith. We see 2000 Harvest Units (HUs) are gathering
regolith. There are also 32 Regolith Pellet Launchers (RPLs)
moving regolith from the asteroid to the outer torus. There
are still 2656 diggers creating the cobbles for 2909 Regolith
Crushing Units. There are 42 Continuous Panel Production
(CPPs) systems operating on the rotating outer rim. The
CPPs are producing panels that 2023 Skin Attachment Units
(SAUs) are welding to the shell, walls, and floors. There are
1016 Fill and Melt Units (F&MUs) filling the inner and outer
walls of the outer torus as the panels enclose them.
Year 12: Outer Torus: The station is completed at the end
of the twelfth year. All 3000 Spiders have been built and
have built and are managing 23,500 pieces of equipment.
4.4.6 Equipment Working on Station Structures
The chart in Figure 4-12 shows the total number of units
building various parts of the Atira space station. The vertical
axis shows the number of units, which includes spiders,
trucks, movers, and the other support equipment. The hori-
zontal axis shows the time in years when those units are
working on the building tasks.
The units are building the web, spokes, shuttle bay, outer rim,
inner torus, and outer torus. Each structure sees a similar pat-
tern of increasing number of units, a constant number work-
ing, and then a decreasing number of units. This simulation
uses the same rates and foundation as the previous simula-
tion. The y-axis of this graph is a logarithmic scale while the
y-axis of Figure 4-11 was linear. This chart includes recent
refinements. In the future, we plan to harmonize the two sim-
ulations and include refinements and additional details.
This chart shows the order of the major building tasks. The
web is built in the first two years. The spokes are started and
then the inner torus. The shuttle bay displaces the initial seed
unit and provides an axis point for the station rotation. The
outer torus ties together shuttle bays, spokes, and inner tori
on the north and south poles. At this point in the construction,
the process includes a spin up task (not shown). This spin-up
task increases the station rotation speed from one revolution
every 240 minutes to one revolution every two minutes. This
simulation shows the entire station could be completed in
twelve years. We expect that improvements in our process
(and simulations) will refine these schedule estimates.
4.4.7 Productivity Measure of Self Replication
Our initial thought was to only use replicators to restructure
the asteroid. Estimates quickly showed that it would take
thousands of spiders and thousands of years to complete the
effort. Many of the restructuring tasks are simple, repetitive,
and constrained to well defined areas. This led to the concept
of building tools to replace that type of repetitive work and
reduce the number of required spiders. Launch costs limit the
number of spiders while the number of tools and equipment
is essentially unlimited using in-situ asteroid material.
Our restructuring process takes advantage of productivity
gains from both parallelism and specialization. Parallelism,
the number of replicators, is the traditional improvement of
self-replication. We increase that parallelism with many
tools and pieces of equipment. The specialized tools and
equipment perform specific tasks much faster than the gen-
eral-purpose replicators. The chart in Figure 4-11 illustrates
the pieces of equipment being built over the construction of
Figure 4-12 –Units Building Major Station Components
1E+01
1E+02
1E+03
1E+04
1E+05
0 1 2 3 4 5 6 7 8 9 10 11 12
Units
(Count)
Time (Years)
Units Building Elliptic Torus Station Structures
(Atira Asteroid (2600x2400x1150m); S-Type; Station Major Radius 2332m; Minor Radii 1104m and 368m)
Web Outer Rim Inner Torus Total
Spokes Shuttle Bay Outer Torus

this space station. At the end of the restructuring effort, our
baseline simulation shows many spiders (3000) working
with even more support tools and equipment (over 23,500).
This represents a high degree of parallelism. Instead of a sin-
gle unit working on the space station, we have over 26,500
units working.
The specialization represents another productivity gain. We
use the example from our system analysis example of the
Replicator, Helper, and Product model; see §4.3.2. We esti-
mate that two spiders could build a truss in 127 hours. The
specialization of a Truss Building Unit (TBU) enables it to
build a truss in an average of 3.05 hours. Spiders need to load
rods or tiles into the TBU system, wind the clockwork
springs, tune the Stirling engines, and adjust the mechanical
programming as necessary. One spider on average can man-
age 5 TBUs. One spider by itself produces a truss in 254
hours on average. One spider with 5 TBUs can produce a
truss in 0.61 hours on average. It would take 416 spiders by
themselves to match the production rate of the single spider
with 5 TBUs. We measure this specialization productivity
gain as an “equivalent spider” metric of 416.
To compute the equivalent number of spiders, we must ac-
count for the tool productivity and the number of spiders sup-
porting those tools. We compute the tool productivity by
comparing the task time using only one spider to the time for
that same task using the specialized equipment. We show in
Table 4-7 this equivalent spider metric for the 13 pieces of
specialized equipment.
We also include in Table 4-7 the number of spiders monitor-
ing the equipment. This was estimated using the time to sup-
port the piece of equipment (position, program, load, and
empty) compared to the time the equipment is autonomously
performing its task. The reciprocal of this value would be the
number of pieces of each type of equipment that a spider can
monitor. Using the final equipment tally, we see that each
spider is monitoring about 7 or 8 pieces of equipment. Many
tools are mechanically programmed to perform a repetitive
operation. Spiders only need to be involved to load, monitor,
and adjust setting on those pieces of equipment. Some pieces
of equipment need constant supervision and monitoring (e.g.,
CPP and HU). Other pieces need little support from spiders.
They perform long duration tasks once they are positioned,
programmed, loaded, and later emptied (e.g., Trucks and
Diggers).
We also include in Table 4-7 a short description to provide
some insight on this equipment estimate. The improvements
shown in the table represent the decrease in spider-hours to
perform the tasks. This also represents the number of spiders
saved for each of the tasks. This could also be considered a
multiplier for equivalent spiders working on the station. Just
Table 4-7 – Tools and Spider Equivalence
Equipment
Equivalent
Spider
Monitor
Spiders
Description
Spider – General Purpose Robot 1 0 Original units for comparison – moving, building, digging, throwing, etc.
Trucks – Mechanical Automaton 10 1/10 A spider can travel at 10 meters per minute and the truck travels at 1 meter per mi-
nute.
Movers – Mechanical Automaton 50 1/10 Able to move larger loads (5x) and it still moves at 10% the speed as a spider.
TBU – Truss Building Unit 416 1/5 1 spider with 5 TBUs = 36.6 minutes / truss; 1 Spider = 254 hours/truss.
HU – Harvest Unit 500 1 Harvest Unit = 30 m3 / hour; Spider 0.0005 m3 shovel jig at 30 seconds * 60 sec/min
* 60 min/hr or 0.06 m3/hour.
RPU – Rod Production Unit 24 1/4 1 spider to spin, 1 spider to hold mirror, 1 to manage rod.
RPU builds 8x rods in same time.
LPU – Laminate Production Unit 96 1/2 1 spider to spin, 1 spider to hold mirror, 1 to manage tile.
LPU builds 32x tiles in same time.
F&MU – Fill and Melt Unit 1410 1/5 Spider Only - 5.31 hours per m3 of fill.
Spider & FM&U - 0.0038 hours per m3 of fill.
SAU – Skin Attachment Unit 240 1/24 Spider Only - 0.703 hours per m2 of panel.
Spider and SAU - 0.00293 hours per m2 of panel.
RCU - Regolith Crushing Unit 643 1/4 Rock Crusher Unit - Jaw crusher – 0.9 m3 every hour; 3 Jaw Crushers per RCU = 2.7
m3 / hour. Spider 1 rock per hour = 8.4 kg = 4195.6 cc = 0.0042 m3 / hour; Result
2.7 m3/hour divided by 0.0042 m3/hour = 643x.
Diggers – Jack Hammer Diggers 16 1/20 One chisel produces 0.72 m3 per 3.4 hours. Digger has 4 chisels running at 4x the
speed possible with a spider. Equivalent to 16x spiders.
1 shovel at 0.5 liter = 0.0005 m3 =10kg at 10 m/s = 100 kg m/s.
TPU - Tile Placement Unit 18 1/3 Spider Only - 0.877 hours per m2 of panel.
Spider and TPU - 0.0488 hours per m2 of panel.
CPP – Continuous Panel
Production Unit
8439 3 Unit produces panels at 10 meters per minute (200 m2/minute). Spider Tiles at 1 m2
per 0.703 hours = 0.0237 m2/minute. Equivalent=200/0.0237 = 8439x.
RPL – Rotating Pellet Launcher 2400 1/2 2 Spiders average to monitor RPL – load, program, adjust.
120 kg / minute over 2000 meters = 4000 kg-m/s (momentum).
Spider only handles 0.0005 m3 shovel jig. Using trucks and travel time to attain 2400x
improvement.

as an example, one of the most time-consuming tasks is the
Fill & Melt of the regolith. The previous example simulation
(Figure 4-10) used 1411 F&MUs to build the Atira station. It
would have taken about 2 million spiders to perform the fill
and melt tasks without those F&MUs. Instead, by using this
support equipment, we only need about 290 spiders to mon-
itor the 1411 F&MUs.
We use the equivalent spider metrics to determine how many
total equivalent spiders would be required to build the Atira
station. We use the maximum equipment counts in the chart
in Figure 4-10. We combine that with the Equivalent Spider
metric of Table 4-7. The Equivalent Spider total for each
piece of equipment is in Figure 4-13. The chart shows the
3000 spiders that were built including the 4 spiders that were
sent with the original launch. We find that the 1411 Fill &
Melt Units perform the work of almost 2,000,000 spiders.
The 3457 Truss Building Units are performing the work of
1.4 million spiders. These totals sum to 7,768,619 equivalent
spiders. With today’s launch costs, we could not justify send-
ing almost 8 million robots into space. With 7,768,619 equiv-
alent spiders given our 3,000 physical spiders, we find a
productivity gain of 2590 using the tools and equipment. We
harvest and process 6.57 billion kilograms of regolith with
those 8 million equivalent robots over 12 years. This implies
that each equivalent spider is processing 845.7 kilograms per
year or 96.5 grams per hour – a very reasonable rate! We
recall that the restructuring process began with a base unit,
only 4 spiders, 3000 spider electromechanical modules, and
a small assortment of jigs and supplies.
4.5 Robotics – Summary
Asteroid restructuring involves asteroids, space stations, and
robotics. Previous sections covered asteroids and space sta-
tions. This section covered robotic technologies. We in-
cluded a brief overview of the background and technologies
of robots. This included example systems for space explora-
tion and mining. To operate in the asteroid environment and
perform the complicated restructuring process, the robots
will need autonomous system software. The asteroid restruc-
turing represents a huge construction task. We used self-
replication to produce the labor to perform that construction.
We introduced the concept of having the robots make spe-
cialized tools to improve their productivity. We described
our simulations and their results show that asteroid restruc-
turing is a viable approach to create a space station from an
asteroid.
Our restructuring concept uses a form of limited self-replica-
tion called Productive Replicators [Freitas and Merkle 2004].
Our initial probe starts with a small set of 21st
century robots,
manufacturing capability, testing equipment, a modest num-
ber of robotic electronics and actuators, and some supplies.
The initial set of robots and equipment complete the con-
struction of robots using local material. These robots con-
struct tools and equipment using technologies available dur-
ing the first industrial revolution. Instead of large industrial
complexes, overwhelming numbers of small mining and con-
struction equipment restructure the asteroid into a space hab-
itat. A hierarchy of cognitive architecture nodes cooperate to
manage the restructuring process.
5 Asteroid Restructuring – System
Previous sections covered detail on asteroids, space stations,
and robotic technologies. We use those details in this section
to cover additional construction and system details. We re-
view the torus space stations constructed from six asteroid
sizes. We then overview the build time and population for
those same asteroids and stations. We include in this section
an estimate of the cost of a restructuring project. As a part of
the system analysis, we include subsections on our quantita-
tive and qualitative design.
5.1 Asteroids and Station Size
We varied the size of the space habitat and its components
for different asteroids. In Figure 5-1, we show the material
used for the major components of six space habitat versions.
We assumed the same S-Type composition for all the aster-
oids. For each asteroid, we found the largest station radius
using 30% of the available asteroid construction oxide mate-
rial. We include the same 5 asteroids with mean diameters
ranging from 490 meters to 4920 meters. For reference, we
include the material required to construct a station the size of
the Stanford Torus. Table 3-7 included the computed radii
and populations for torus stations.
Except for the Stanford Torus, we design elliptic torus sta-
tions that are half filled with floors. The rotation major axis
is 6.33 times the smaller minor axes in these stations. This
ratio provides a comfortable gravity range over the floors.
The gravity on the top floor (at the center) is 0.95g and on
the bottom floor (outer rim) is 1.1g. We could build a station
with a rotation radius of 205 meters and minor radius of 32
meters using the asteroid Bennu which has an equatorial ra-
dius of 241 meters. Ryugu, with a mean diameter of 896 me-
ters, could produce a single torus with a rotation radius of
354 meters and minor radius of 56 meters. The Stanford To-
rus has a major radius of 830 meters and a minor radius of
65 meters [Johnson and Holbrow 1977]. For Moshup, with a
diameter of 1317 meters, we can build a single torus with a
Figure 4-13 – Total equivalent spider effort from equip-
ment used during the restructuring process

radius of 937 meters. The Atira asteroid with a mean radius
of 1928 meters would support a large outer torus. We evalu-
ated the Atira station with a single, double, and triple set of
inner tori and spokes. We found with the double set of shuttle
bays, spokes, and inner torus; the elliptic outer torus would
have a major radius of 2116 meters and minor axes of 334
and 1003 meters. In Figure 5-1 we only show the results for
the double set. For a larger asteroid the size of Šteins with a
mean diameter of 5160 meters, we describe a double station
with a major radius of 4042 meters and minor radii of 1915
and 638 meters.
5.2 Build Time and Population
Most asteroid mining ventures focus on small asteroids – 10
meters to 100 meters. At this size, they consider towing it
back to an Earth orbit and/or processing it in place and re-
turning the mined product. Our restructuring goal is to con-
vert the entire asteroid into the framework of a space habitat
and leave that framework in the asteroid’s orbit. The equip-
ment and process are scalable and developed to restructure
asteroids that are several kilometers in diameter and create a
space station structure that can support a population of nearly
one million people.
Most of our simulations consider the asteroid 163693 Atira.
It contains almost 22 billion cubic meters of material, and its
mass is over 40 trillion kilograms. The space habitat uses
over 2.6 billion cubic meters of construction material. We
find the mass of the station would be 5.3 trillion kilograms
and would be about 13% of the mass of Atira. The restruc-
turing process could also inventory and store 123 million cu-
bic meters of volatiles and almost 341 million cubic meters
of metal for the future inhabitants. This example station is a
little larger than the Atira station in Figure 5-1. Its outer torus
has a major radius of 2332 meters. The elliptical-shaped
cross-section would have minor radii of 368 meters by 1104
meters. Again this is similar to the illustrations in Figure 1-1
and Figure 3-9. This station takes about 12 years to complete;
see Figure 5-2. At the end of the 12 years, we have a habitat
that is fully enclosed, is rotating to create Earth-like gravity,
and has meters of shielding to protect the initial work crews
and future colonists from radiation.
We show in Figure 5-2 a chart with the population and build
time of torus stations as a function of volume of material used
in their construction. We include five asteroids and their cor-
responding space habitats. Two space habitat structures were
considered in detail. The larger Atira station was analyzed
and takes about 12 years to restructure. We also evaluated a
smaller space habitat like the O’Neil Torus that can support
a population of 13,000 people. The smaller station requires
the material of an asteroid about the size of 162173 Ryugu
(896 meters in diameter). The restructuring takes about 5
years and creates a single inner torus with a major radius of
354 meters. The other asteroid values are extrapolated from
the analysis of those two asteroid designs.
The restructuring process scales to convert asteroids from
modest sizes less than 1 kilometer in diameter to those of al-
most 10 kilometers in diameter. Large asteroids begin to take
excessive time to restructure given our one seed and single
rocket launch. The Šteins asteroid in Figure 5-2 takes 25
years to process. The 3000-spider limit in one seed package
constrains the number of Replicators (spiders/productive
replicators) and ultimately the number of managed Helpers
(tools and equipment). Sending two base stations in the sin-
gle launch or a second launch would increase the number of
spiders and would decrease the processing time. Large struc-
tures will also be limited by the structural strength of the
trusses and panels.
We plan that the process will be completely autonomous. As
such it will be adaptable to different materials and construc-
tion issues. As an example, if the center of an asteroid were
a solid fragment of iron, the process would leave that core
for future inhabitants. There would be much less basalt ma-
terials and the overall size of the station would have to be
reduced. In Figure 5-2, the analysis assumes about 30% of
the asteroid oxide material will be usable for the station con-
struction. A large percentage of that material will be used for
shielding and will not need to be high quality.
5.3 Restructuring Cost
We compare this effort to O’Neill’s estimates for his space
cylinders [O’Neill 1974]. His estimates rely on a significant
Figure 5-1 – Material Allocation to Station Components
Figure 5-2 – Station Material Volume and Resulting
Population and Build Time
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
1E+10
Bennu Ryugu Stanford Moshup
Inner
Atira
Double
Šteins
Station
Material
Volume
(m3)
Elliptic Torus Station Material Requirement
Web Shuttle Bay Spokes Inner Torus Outer Torus
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
1
10
1E+06 1E+07 1E+08 1E+09 1E+10
Build
Time
(Years)
Population
Station Volume (m3)
Asteroid Volume Station Construction
Build Time
Build Time Trendline
Realistic Population
Population Trendline
Bennu Ryugu
Moshup
Atira
Šteins
Bennu
Ryugu
Moshup
Atira
Šteins
3
30

manual effort. He assumes 42 metric tons constructed per la-
bor-year, which is comparable to large scale construction on
Earth in the 1970s. The Atira station weighs 4.46e9 metric
tons or 106 million labor years. This would be over $43 tril-
lion in labor, which is not viable. We strive to reduce these
costs with automation. The concept of applying automation
to these efforts is not new. O’Neill stated:
“In the long run, space-colony construction is ideally
suited to automation. A colony’s structure consists
mainly of cables, fittings and window panels of stand-
ard modular form in a pattern repeated thousands of
times. The assembly takes place in a zero gravity envi-
ronment free of the vagaries of weather. By the time
that the colonies are evolving to low population den-
sity, therefore, I suspect that very few people will be in-
volved in their construction.” [O’Neill 1974].
The amount of automation used in the restructuring process
is more than most published space habitat building ap-
proaches. We recall that we have an equivalent of 7.77 mil-
lion spiders working at the end of 12 years on this project.
Summing the spider-years over the 12 years results in 45 mil-
lion spider years of continuous labor. It is comforting to see
a rough similarity to the 106 million labor years using
O’Neill’s estimate. There are multiple scaling factors that
should be applied to more accurately compare the two val-
ues. As an example, the restructuring process works more
than 8 hours per day. As a first estimate this adds to our con-
fidence that the restructuring approach using self-replication
with parallelism and specialization is viable.
We created a table using data from O’Neill’s Physics Today
article [O’Neill 1974]; see Table 5-1. This table includes his
details for the Model 2 Cylinder (population 150,000). In
1974, O’Neill was hoping his first station would be built in
1988. The second station would leverage the experience and
capabilities of the first station and be built eight years later
in 1996. With inflation, the 2019 dollars would be 6.1 times
the 1972 dollars. The cost of this station would be about $200
billion in 2019 dollars. O’Neill noted that the Apollo project
cost $33 billion in 1972 dollars. That would also be about
$200 billion in 2019 dollars.
The cost of space missions have decreased since the 1970s.
The estimated cost of the Artemis program [Artemis 2022]
is $93 billion compared to the $200 billion for the Apollo
program (in 2019 dollars). The cost of space probes have
been decreasing too. The New Horizon mission to Pluto cost
$700 million. The Osiris-REx mission to the asteroid Bennu
has a program cost of $800 million. The Hayabusa 2 mission
to the asteroid Ryugu cost $150 million. The recent Indian
Chandrayaan lunar mission cost $145 million. Tiny Cu-
beSats today can cost less than $1 million [Myers 2022].
We compare a self-replicating lunar industry [Metzger et al.
2012] and our restructuring effort to O’Neill’s estimates; see
Table 5-1. We use the Metzger’s list of assets from Table
4-6a with his mission descriptions to produce a self-replicat-
ing lunar industry [Metzger et al. 2012]. We used the New
Horizon costs for equipment in both the Atira and Lunar es-
timates. We multiplied by 6 for the Lunar Industry because
of the 6 required launches. We used our list of probe assets
from Table 4-6b to estimate our probe cost. The cost estimate
for the Atira mission probe is about $105 million. The cost
estimate for the six Lunar Industry payloads is $140 million.
We include 10,000 labor-years for research, development,
and support of the lunar industry. With less support, we in-
clude 8,000 labor-years for those activities for the restructur-
ing effort. There are still significant labor and research ef-
forts needed to see both missions to fruition. We also added
costs to the Lunar Industry for teleoperation and for manned
Moon support. This first initial estimate for the Atira restruc-
turing mission is about $4.1 billion. Our estimates are “back-
of-the-envelope” rough engineering estimates. We hope that
experts could refine and lower these estimates in the future.
We offer in this paragraph several funding comparisons for
the station. This station provides almost 1 billion square me-
ters of floor space and 383 million square meters of residen-
tial space. There are many ways to fund the $4.1 billion cost.
Each of the 1 billion square meters would cost $4.10 per
square meter. Table 3-10 shows a population of 700,000
Table 5-1 – Estimating Cost of Building Space Colonies (Compare at 2019 dollars)
Credit: Self produced using engineering estimates and concepts and data from [O’Neill 1974] [Facts] and [Metzger et al. 2012] [Facts]
1974 Total
1972
Total
2019 2012 Total
2019 2022 Total
2019
Unit cost (in $109
) (in $109
) Description (in $109
) Description (in $109
)
Launch vehicles $0.5 x 105
1.5 9.2 6 Space X Launches 0.3 Space X Launch 0.06
Transport E?L5 $250/lb 11 67.2 n/a n/a
People E?L5 $500/lb 8.8 53.8 n/a n/a
Transport E?M $500/lb 2.2 13.4 Lower launch vehicle costs 1.3 n/a
Equipment for Moon $400/lb 1.8 11.0 Similar to New Horizons (6x) 4.2 n/a
Equipment for L5 $400/lb 2 12.2 n/a Similar to New Horizons 0.7
Machines and tools (L5) $625/lb 2.8 17.1 Assets: $140M Estimate 0.14 Probe: $105M Estimate 0.11
Salaries (L5) 25% on Earth 2 12.2 Salaries on Moon 12.2 n/a
Research, Support, & Tele- Research & Support
operation (10,000 labor-years) (8,000 labor years)
Totals 34.1 208.4 22.3 4.1
4.1 3.3
Salaries (Earth) 30,000 labor-year 2 12.2
Atira Space Station
Metzger Lunar Industry
Description
Original Items
O'Neill Space Colony - Model 2

using 383 million square meters of residential space. The
700,000 people could invest in the $4.1 billion at $5857
apiece. Another alternative is for them to purchase their 547
square meters of residential space at a cost of $2243 and sell
other regions of the station to research and industry. The pop-
ulation would need 18 million square meters of agriculture.
This would cost $73.8 million in the station at $4.10 per
square meter. An acre of agriculture space in the station
would cost $16,592. This is a little more than the price of an
acre of good Iowa farmland in 2022. These comparisons
show that funding the station may not be excessive.
5.4 Station Quantitative Design Accuracy
In this project, we have researched and developed many en-
gineering estimates. We used many different weights,
speeds, rates, and costs. These metrics were used for equip-
ment, processes, and missions. When possible we used com-
parable values or published engineering estimates. These are
best effort values; however, we recognize that there is margin
for error in those values.
We appreciated the comment in the foreword of a historic
1973 NASA document entitled “Feasibility Of Mining Lunar
Resources for Earth Use: Circa 2000 A. D.” [Nishioka et al.
1973]. This long memorandum details the technologies and
systems required to establish the mining base, mine, refine,
and return the lunar resources to earth for use. It also contains
many estimates and metrics. We abbreviate the authors’ fore-
word comment: “Unfortunately, the quantitative results …
determined in these types of studies dealing with … the future
have a high probability of uncertainty and should thus be ob-
served cautiously.” [Nishioka et al. 1973]. We recommend
using the same caution with results of this paper.
5.5 Station Qualitative Design Evaluation
We again consider a torus station that has a major radius of
2400 meters and an elliptic cross-section with minor radii of
400 meters and 1200 meters. Figure 3-9 illustrated a cross-
section of this habitat. Using square footage from all floors,
this station could support over 10 million; see Figure 3-15.
We consider three views inside the large outer torus to ad-
dress qualitative metrics. A picture is worth a thousand
words and these inside views address qualitative criteria of
the environmental design. We previously showed in Figure
3-22b an interior view of the space station. That rendering
showed a wide field of view of one of the eight dividers in
the station. That view is 3-kilometer-wide from almost 2 kil-
ometers away. Each of the four entryways into the divider is
as large as the Arc de Triomphe in Paris. Two of the spokes
are within the divider. The divider includes 33 floors, each
15 meters in height. The dividers have over 1.5 million
square meters of floor space – enough to support 10,000 nice
size single home families. This scene has a fabulous view
with a vertical height of 500 meters. We include two other
views in Figure 5-3. The left picture is taken near one of the
dividers and includes a two-story house (stick figure) for
scale. The right picture is taken from the floor on the far-right
side of the large elliptic torus. The rendering tool was pro-
grammed to paint a 100-meter square grid on the main floor
– about the size of a city block. Along the side are some of
the 376 two story homes rendered to help with scale. From
this view we can see for 2.6 kilometers over the curved floor.
In the scene is a 77-story tower built into one of the station
spokes.
To further evaluate the potential of such a station, we con-
sider other design criteria from the Stanford study [Johnson
and Holbrow 1977]. The NASA SP-413 study explored
physiological, environmental design, and organizational cri-
teria for space stations. They felt these qualitative criteria
must be met by a successful space habitat for the colonization
of space. We show all three criteria in Table 5-2 updated with
evaluations of the Atira station. This station has the potential
to meet or exceed the design criteria of the Stanford station.
6 Asteroid Restructuring – Future
We offer in the following subsections several additional
thoughts. We consider a geometry alternative, an alternative
to shuttle bay landings, activities for the early colonists,
thoughts about the Atira moon, and future projects for re-
structuring. This section ends with our conclusions for aster-
oid restructuring.
6.1 Geometry Alternative
As an afterthought in our research, we decided to better re-
view the dumbbell structure. We noticed that the dumbbell
nodes are quite large for the asteroids that we are
Figure 5-3 – Qualitative Inside Views of Atira Station

considering. We found that the dumbbell supports the largest
population for a given asteroid mass; see Figure 3-20. The
torus geometry is the next best to support a large population.
We offer a comparison in Figure 6-1 between the dumbbell
and torus. The figure includes diagrams that are roughly to
scale for a torus and a dumbbell station created from the Atira
asteroid. We use our developed metrics and analysis to com-
pare key features. Both stations were designed to use the
same amount of building material. The Atira asteroid has
4.1e13 kilograms of mass and that quantity could support ei-
ther the elliptic torus or the ellipsoid node dumbbell. We de-
signed both stations to use 3.9e12 kilograms of material. A
simple stress analysis finds that the tether or trusses of the
dumbbell would need to have an equivalent truss cross sec-
tion of at least 3500 square meters using a tensile strength of
5500 MPa (filled structure metric). This would likely require
multiple truss tethers.
For both stations, the gravity is 0.95g on the main floor and
1.1g on the outer rim. The torus would have about 60 floors
and the dumbbell would have over 160 floors. For realistic
populations, the dumbbell supports about 12% more people
than the torus. Inhabitants on the main floor of the torus
would have a vista looking down a long valley that is 2 kilo-
meters wide and curves upward for 2.28 kilometers. The val-
ley would have a ceiling of 334 meters. Inhabitants in the
dumbbell would have a dome over them with a ceiling 820
meters above. The dumbbell would provide a smaller vista
of 1.6 kilometers by 0.8 kilometers from the center of the
Table 5-2 – Summary of Atira Station Design Criteria
Criteria Metric Atira Station Value / Comment
Summary of
Physiological
Criteria
Artificial Gravity (Centripetal Gravity)
Most living areas will be between 0.95g to 1.05g. Lowest lev-
els will reach 1.05g and the inner torus will be 0.7g.
Rotation rate 0.62 rpm
Radiation exposure <5 rem/year
Temperature TBD: 23o +/- 8o C
Atmospheric composition TBD: Asteroid composition
Summary of
Quantitative
Environmental
Design Criteria
Population 700,000 comfortable to 6,500,000 maximum
Projected area per person 144.2 square meters with 5 meter floor spacing
Projected volume per person 627.6 cubic meters (without open volume)
Open area per person 18.7 square meters per person
Agriculture area per person 39 square meters
Agriculture volume per person 195 cubic meters
Summary of
Qualitative Criteria
of Environmental
Design
Long lines of sight About 3.5 kilometers
Large overhead clearance 500 meters on main floor
Noncontrollable parts of environment TBD
External views of large natural objects Large open areas designed for aesthetics
Parts of interior out of sight of others Multiple floors and dividers
Natural light Chevrons, fiber optic skylights, LED supplement
Contact with the external environment Large open areas designed for aesthetics
Availability of privacy Private homes
Good internal communication Modern terrestrial wireless capabilities
Possible to physically isolate segments of habitat Multiple floors and eight major segments in design
Modular construction of habitat and of structures within habitat Future design
Flexible internal organization Future design
Details of interior design left to inhabitants Left to future colonists
Credit: Self produced using NASA SP-413 [Johnson and Holbrow 1977] [NASA Report Public Domain]
Elliptic Torus
Major Radius = 2116m
Minor Radii = 1003m and 334m
Building Material = 3.86E+12 kg
Habitable Volume = 7.49e9 m3
Realistic Population = 1.66 million
Rotation Rate = 0.63 RPM
Openness Ceiling = 334m
Vista = 2282m by 1002m
Ellipsoid Node Dumbbell
Major Radius = 5193m
Minor Radii = 820m and 1641m
Building Material = 3.86E+12 kg
Habitable Volume = 9.24e9 m3
Realistic Population = 1.86 million
Rotation Rate = 0.40 RPM
Openness Ceiling = 820m
Vista = 820m by 1640m
Figure 6-1 – Reconsidering Dumbbell Geometry

main floor. Both designs are quite habitable and provide
open space for psychological well-being. It is possible that
the dumbbell would be simpler to build. We need to identify
difficulties and benefits between the two geometry designs.
6.2 Landing on Runways
In the future, space tourism could reach tens of thousands of
launches per year - a rate comparable to the early decades of
aviation [Globus 2006]. Tourism to a large space station may
match international tourism to a city such as Washington DC.
Over 2 million international tourists visit Washington DC
each year and most are likely flying [DC 2017]. Assuming
40,000 flights to support this level of tourism, it is interesting
to consider how to accommodate the 100 flights per day to a
space station. A single docking station would have to accom-
modate over 4 flights per hour. This does not include flights
supporting maintenance, imports, exports, and business.
Most station designs use a central hub to support shuttle ar-
rivals, servicing, and departures. This single central hub be-
comes a bottleneck for the passengers and trade
Runways on the surface of the rotating station have been his-
torically avoided because of the perceived landing complex-
ity. We have found that the shuttle does not need to perform
a curved rotating approach to the station. The shuttle ap-
proach can be a straight vector. This minimizes fuel con-
sumption and landing complexity. The touchdown on the ro-
tating runway can be gentler than the touchdown of a large
commercial aircraft landing on a terrestrial runway.
A small station could become imbalanced with the landing
of a heavy shuttle. Some authors suggest landing two shuttles
on opposite sides of the rotating station to reduce this imbal-
ance impact. The Space Shuttle weighed about 2 million kil-
ograms. The Space X Falcon 9 Heavy rocket weights 3 mil-
lion kilograms. The smallest station in Table 3-8 was the
Bennu torus and weighted 9,030 million kilograms. With our
large station designs the shuttle mass is insignificant to the
station mass and should not affect the rotation balance.
Runways can be positioned anywhere along a radial axis of
the rotating space station. Dozens of runways could accom-
modate the higher traffic loads from tourism and from other
space habitats. To introduce this concept, we offer a diagram
and a chart in Figure 6-2. The diagram shows a cut through
view of half of a rotating torus station. The rotation axis is
along the right side of that diagram and show the rotation at
ω radians per second. We include landing runways on the top
(inner rim), on the middle side, and at the bottom (outer rim)
of the torus tube.
We include a simulation result from a shuttle landing on a
side runway on the station in Figure 6-2b. This station has a
major axis (R=2116 meters) and a minor axis (h=334 me-
ters). This is visually like the station shown in Figure 1-1.
The side runway is illustrated in Figure 6-2a. The x-axis
shows the horizontal distance, and the y-axis shows the ver-
tical distance from the center of the rotating station. The chart
shows the position of the runway at a radius of 2116 meters.
This side runway would not completely encircle the torus.
The chart in Figure 6-2b shows the shuttle approaching from
the right side and the station rotating clockwise. It shows a
portion of the runway at a radius of 2116 meters and the outer
rim at 2450 meters. The shuttle approach in Figure 6-2b
represents the last 7 seconds before landing. The shuttle is on
a straight path towards its landing spot. It is decelerating at
1g for the flight towards the station. During the last moments
of the approach, it decelerates at 2g in the y-direction. A
force of 2g is less than most roller coasters or similar to a
“hard” landing of a commercial air craft. The shuttle and run-
way edge both travel about 700 meters during the final ap-
proach. For most of the flight the shuttle is moving faster
than the rotating runway and overtakes the runway edge. By
design, the shuttle has a radial and tangential velocity (im-
pact velocities) of 0 meters per second at touchdown.
We show detail of the extra landing deceleration in Figure
6-3. This view is near the landing point and details the final
approach over the runway in Figure 6-2b. The graph axes
show the horizontal and vertical distance from the station
center. The markers on the shuttle and runway lines are
spaced at 0.05 seconds apart. The runway floor rotates at 0.62
RPM with a tangential velocity of 137.2 meters per second.
The shuttle approaches at a 14-degree angle; see Figure 6-2b.
It is traveling at 211 meters per second (or a relative 73.8
meters per second) when it passes the contact point. It con-
tinues to decelerate at 9.8 meters per second squared. The
shuttle decelerates at 2g for about the last two seconds. The
shuttle speed reduces from 211 to 137.2 meters per second
over six seconds. This angle and deceleration are designed to
land the shuttle at the tangential velocity of the runway; as
such, the shuttle lands at a relative 0 meters per second. This
would be a very “soft landing.”
The shuttle is initially moving faster than the runway floor.
The runway edge continues to rotate as the shuttle moves to-
wards the landing point. The chart in Figure 6-3 shows the
position of the contact point after it has rotated during the
shuttle landing as a red circle. When the shuttle lands, the
shuttle is over 100 meters beyond the contact point (the edge
of the runway). The shuttle lands with a forward velocity
matching the tangential rotation speed; as such, there is min-
imal shuttle rolling or braking after landing.
Approach Through Opening to Bottom Runway: We also
found that landings through openings along the outer perim-
eter of the rotating station are possible using this same
straight approach. The shuttle passes through the opening,
lands on the inner surface, and comes to a stop. Like the shut-
tle bay we enter through an opening and land inside the sta-
tion. Unlike the shuttle bay, we have gravity and a runway to
touchdown and decelerate like a commercial aircraft on
Earth. The runway touchdown and deceleration are like the
approach to other runway positions; see Figure 6-2b. Unlike
the other runways, this one is inside the station and the shut-
tle enters through an opening. This landing intuitively seems
like it would be complex and risky. This intuition appears to
be wrong. The shuttle can simply approach on a straight path
to the bottom of the station at a shallow angle. In the example

of this section, the shuttle approaches the bottom runway at
a radius 2450 meters at an angle of 16.5 degrees. We show
the shuttle crossing the 20-meter-thick shell of the outer torus
in Figure 6-4. The chart in Figure 6-4a shows the approach
in the station coordinate system and shows two openings.
The opening is shown at its position at 7.0 seconds before
touchdown (yellow and to the upper-right). The opening (and
station) is rotating clockwise and is also shown at its position
6.5 seconds before the shuttle touchdown (blue and to the
lower-left). The shuttle enters and exits the opening at these
times.
We design the approach and opening locations so the shuttle
enters at the center of the moving opening. The shuttle trav-
els about 100 meters at 16.5 degrees through the opening.
The opening rotates about 80 meters during that time. The
opening is angled in the spinward direction. The entrance is
designed so the shuttle exits at the center of the opening as it
passes through the 20-meter-thick shell.
We include the approach in coordinates relative to the rotat-
ing landing point in Figure 6-4b. Relative to the landing spot,
the opening is stationary. Figure 6-4b illustrates the same ap-
proach from the perspective of an observer near the landing
point. They would see the shuttle enter, ascend upwards, and
then descend to the landing spot. The distance to the runway
edge and the maximum ascent height are clearly visible.
We designed the approach to land 100 meters from the open-
ing edge. The shuttle approach appears to pass quite close to
the opening edges in Figure 6-4a. This is misleading because
the opening is rotating with the station. The same approach
in the coordinate system of Figure 6-4b shows the shuttle
passing about 40 meters from the edges of the opening.
This is one example of landing on the bottom runway. The
outer rim could have multiple openings and support several
simultaneous landings. The angle of the approach, the open-
ing size, the opening distance from the landing point, and the
height of the ascent can all be designed and be controlled.
Even with smaller and larger radius stations, the same type
of approach is possible. Simulation on multiple landing ap-
proaches for various station radii gives us confidence that
this outer shell landing concept works. We recognize that ad-
ditional study on the structural requirements of these run-
ways and landings is necessary.
6.3 Early Colonists
The restructuring process only creates an enclosed rotating
framework. The result is an environment that provides radi-
ation protection and gravity for early crews and colonists.
The process (currently) does not provide an atmosphere,
light, heating, or cooling. The restructuring process produces
regions of our example station ready for early colonists after
8 or 9 years. The Gantt chart in Figure 4-9 shows a crew of
12 arriving after 6 years. Portions of the station framework
are complete by this time. Those areas are shielded from cos-
mic radiation and are beginning to rotate to provide some
gravity. Those areas have no atmosphere, minimal light, and
no heat or cooling. The job of this initial crew is to make
those areas livable. The panels of the station shell are welded
Figure 6-3 – Final Landing Approach on Side Runway
a) Cross section of torus (or dumbbell) b) Simulation result of shuttle landing
Figure 6-2 – Runways on rotating station

together. The floors and walls are sealed with panels. Ideally
this would provide an airtight seal but the crew may need to
further seal the shell with an airtight coating. There will be
conduit, lighting, and door openings to space in the frame-
work. The crew must seal those openings with doors, chev-
rons, pipes, and light fibers. Producing atmosphere will be
next on the agenda for this early crew. The restructuring pro-
cess produces and inventories excess volatiles and metals.
The stored frozen volatiles have been tested and inventoried
and summaries sent to Earth. The initial crew will have a plan
on which volatiles to retrieve first and where to place for sub-
limation. Spiders, movers, and trucks will be assigned to
move the volatiles. Inside the station, the restructuring equip-
ment will require a new source of power or access to sun-
light. To melt the frozen inventory, heat will be needed.
Using the inventoried material available on the station, an
early crew will build a Heating, Ventilation, and Air Condi-
tioning (HVAC) system. Boiler systems could use parabolic
mirrors mounted on the exterior of the station to heat liquids
and transfer heat through pipes to the interior of the station.
The spiders and movers could move and mount those mirrors
to appropriate locations. With the right materials and new
equipment brought by the early colonists, solar cells could be
manufactured. These cells would produce electricity to drive
lights, the HVAC system, and new equipment.
The early colonists will need to bring additional equipment
and use the inventoried materials to spawn multiple indus-
tries. These industries are essential to make the station liva-
ble and may provide early exports from the station. These
industries could include:
• Solar Cells
• Heat/Boilers
• Pipes and Wires
• Fuel
• Agriculture
• Metal
There will be advances in artificial intelligence and robotics
while the first parts of the station are being restructured. The
spiders will be reprogrammed occasionally during the
restructuring process to take advantage of these advances.
The Earth-bound support groups will develop new equip-
ment and tools to take advantage of materials found during
the early restructuring process. Early progress and discover-
ies during the restructuring process may motivate earlier sup-
port and retrieval missions. Perhaps we would see a migra-
tion like the 1849 California gold rush.
6.4 Atira Moon
Many asteroids have moons. We offer a rendering in Figure
6-5 of the Atira asteroid moon from the surface of Atira. A
moon offers several future options for the colonists. This
moon represents another 0.52 cubic kilometers or 1.42 tril-
lion kilograms of material. Its proximity to the station (6 kil-
ometers) and microgravity makes it a potential lab for station
researchers. High risk industries could be stationed on the
moon instead of in the space station habitat.
Spiders, trucks, and other equipment could be moved to the
moon to begin a restructuring process on it. Building frame-
works for labs on the surface of the Atira moon is an obvious
extension to the Atira restructuring process. It might be val-
uable to spin up the lab created on the moon to provide grav-
ity. In this paper, we showed that a one-kilometer diameter
asteroid (the size of the Atira moon) has enough material to
build a small station. Such a station could remain in orbit
around Atira or moved further away as another colony or to
provide an additional safety margin for high-risk industry.
A similar thought for the moon would be using it as a seed
vessel. There will be a surplus of spiders and equipment after
the Atira restructuring effort is complete. Some spiders and
equipment will be needed to maintain the Atira station and
to support the early crews and colonists. The surplus equip-
ment and spiders could be moved to the moon and aug-
mented with additional circuit boards and supplies. Rotary
Pellet Launchers or fuel-based rockets could begin to move
the moon out of orbit towards another asteroid for
a) Shuttle Passing Through Opening in Rotating Outer Shell b) Relative Shuttle Position to Landing Spot
Figure 6-4 – Shuttle movement through bottom runway opening in rotating station

restructuring. The RAMA project developed a similar idea
[Dunn 2016]. The restructuring process would begin on the
moon enroute to the new asteroid. Upon arrival at the new
asteroid, a multitude of equipment would move to the new
asteroid and begin its restructuring process.
Colonists could leave the moon alone. The view of the moon-
rise would be spectacular; see Figure 6-5. Observation decks
on the exterior station wall could be fitted with electro-
chromic glass and electromagnetic shielding to reduce heat
and radiation. With a lunar orbit of 15.5 hours and the station
rotating once every two minutes, spectacular views of the
moon, sun, and stars would be enjoyed frequently during a
visit to an observation deck. One can envision these locations
as centerpieces for restaurants and other tourist activities.
6.5 Restructuring Future
We have focused on using the restructuring process to con-
vert an asteroid into a space station. If this process is viable,
other asteroids could be restructured. The concept of using
advanced technology robotic spiders (replicators) to build
and manage many simple mechanical automata (helpers) can
be used elsewhere. Reducing the risk to personnel and elim-
inating the expense of delivering equipment has ubiquitous
value. We plan to apply and study these concepts for use in
lunar, Titan, and Martian environments. There may also be
opportunity in using this restructuring process on the Earth
in less hospitable locations such as the Sahara, the Australian
outback, and the Antarctic. In the 1970s Freeman Dyson de-
scribed autonomous equipment to perform similar projects
[Dyson 1979] [Freitas and Merkle 2004]. His projects in-
cluded working on the Saturn moon Enceladus, Deserts, Ter-
restrial Industry, and Water projects. Our restructuring con-
cepts can enable these projects too.
6.6 Conclusions
The asteroids of the solar system have sufficient material to
build enough space stations to house more than the entire
world’s population. There are many large near-Earth aster-
oids to restructure and each could house one million people.
Researchers have been designing these stations for over 50
years. Two major obstacles have prevented the development
of these stations. First, the high cost of launching probes and
material into space. Second, the detrimental impact on peo-
ple from low-gravity and radiation in space.
We introduce in this paper the restructuring process where a
single modest-size probe lands on an asteroid and autono-
mously creates an enclosed space station framework. The
probe has a small number of robots that eventually create
thousands of robots, tools, and equipment. The restructuring
process improves the productivity using self-replication par-
allelism and tool specialization. The probe would land on a
large asteroid and potentially would take over a decade to
convert the regolith into basalt rods, tiles, trusses, panels, and
ultimately a complete space station. Metals and volatiles are
found during the regolith processing. These valuable com-
modities are tested, inventoried, and stored for future use.
At the conclusion of the restructuring process, an enclosed
space station framework is rotating in space and ready for
crews and then colonists. The rotating shell provides near-
Earth-like centripetal gravity. The station has many floors
and provides space for a large population. A thick shell pro-
vides protection from radiation and space debris. The single
launch and probe costs are small compared to the value of
this real estate. The restructuring asteroid process directly
addresses two major obstacles preventing the construction of
space stations.
We are at the stage where it appears that the restructuring
process is viable. Of course, we expect addition problems to
be identified during reviews. We also expect that experts and
future teams will be able to solve those problems and im-
prove on the work already done. The restructuring process
offers humanity the opportunity to truly become a space far-
ing society.
7 Asteroid Restructuring – References
[Ackerman 2016] Project RAMA: Turning Asteroids Into Catapult-Powered Analog
Spacecraft, Evan Ackerman, 20 Sep 2016, IEEE Spectrum, https://spec-
trum.ieee.org/tech-talk/aerospace/space-flight/project-rama-turning-asteroids-into-
catapultpowered-analog-spacecraft
[ADA 2010] 2010 ADA Standards for Accessible Design, Department of Justice, 15
September 2010, Americans with Disabilities Act,
https://www.ada.gov/regs2010/2010ADAStandards/2010ADAstandards.htm
[Albus 1997] 4-D/RCS Version 1.0: A Reference Model Architecture for Demo III,
James S. Albus, 27 June 1997, NIST Interagency/Internal Report (NISTIR), Na-
tional Institute of Standards and Technology, Gaithersburg, MD,
https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=823355
[Angelo 2014] Encyclopedia of Space and Astronomy, Joseph A. Angelo, 14 May
2014, Infobase Publishing, Science, https://books.google.com/books/about/Ency-
clopedia_of_Space_and_Astronomy.html?id=VUWno1sOwnUC
[Artemis 2022] Artemis: Why we are Going to the Moon, National Aeronautics and
Space Administration, NASA Official: Brian Dunbar, Accessed 11 November
2022, https://www.nasa.gov/specials/artemis/
[Barr 2018] The High Life? On the Psychological Impacts of Highrise Living, Jason
M. Barr, 31 January 2018, https://buildingtheskyline.org/highrise-living/
[Bell and Hines 2012] Space Structures and Support Systems, Larry Bell and Gerald
D. Hines, 2012, MS-Space Architecture, SICSA Space Architecture Seminar Lec-
ture Series, Sasakawa International Center for Space Architecture (SICSA), Cul-
len College of Engineering, University of Houston,
http://sicsa.egr.uh.edu/sites/sicsa/files/files/lectures/space-structures-and-support-
systems.pdf
[Bender et al. 1979] Round-Trip Missions to Low- Delta-V Asteroids and Implica-
tions for Material Retrieval, David F. Bender, R. Scott Dunbar, and David J. Ross,
1979, NASA SP-428 Space Resources and Space Settlements, pp. 161-172,
[O’Neill et al. 1979], https://ntrs.nasa.gov/api/citations/19790024054/down-
loads/19790024054.pdf
Credits: Self produced with Blender using Milky Way Image: ESO/Brunier
[Brunier 2009] [CC BY-4.0]; and Asteroid Model [Ellison 2018] [CC BY-4.0] modi-
fied/rescaled to match asteroid and moon dimensions
Figure 6-5 – Moonrise on Atira Asteroid

[Blacic 1985] Structural properties of lunar rock materials under anhydrous, hard vac-
uum conditions, J. C. Blacic, 1985, Papers Presented to the Symposium on Lunar
Bases and Space Activities of the 21st Century, p. 487. NASA/Johnson Space
Center, Houston., http://articles.adsabs.harvard.edu/cgi-bin/nph-iarti-
cle_query?bibcode=1985lbsa.conf..487B
[Bock, Lambrou, and Simon 1979] Effect of Environmental Parameters on Habitat
Structural Weight and Cost, Edward Bock, Fred Lambrou, Jr., and Michael Si-
mon, 1979, NASA SP-428 Space Resources and Space Settlements, pp. 33-60,
[O’Neill et al. 1979], https://ntrs.nasa.gov/api/citations/19790024054/down-
loads/19790024054.pdf
[Boyd 1987] Discourse on Winning and Losing, J.R. Boyd, August 1987, Air Univer-
sity Press, Curtis E. LeMay Center for Doctrine Development and Education,
https://www.airuniversity.af.edu/Portals/10/AUPress/Books/B_0151_Boyd_Dis-
course_Winning_Losing.pdf
[Boyle 2020] Can a Moon Base Be Safe for Astronauts?, Rebecca Boyle, 22 October
2020, https://www.scientificamerican.com/article/can-a-moon-base-be-safe-for-
astronauts/
[Bradley et al. 2012] Optimized Free Return Trajectories to Near-Earth Asteroids via
Lunar Flyby, Nicholas Bradley, Sonia Hernandez, and Ryan P Russell. Published
In Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, pages
3353–3369, 2013, CiteSeerX, http://citeseerx.ist.psu.edu/viewdoc/down-
load?doi=10.1.1.712.1087&rep=rep1&type=pdf
[Brody 2013] Not 'Elysium,' But Better 'Ringworld' Settlements Could Return Our
Future to Its Past (Commentary), David Sky Brody, 10 August 2013,
https://www.space.com/22326-elysium-movie-space-colonies-future.html
[Brooks 1985] A Robust Layered Control System for a Mobile Robot. Rodney A.
Brooks, September 1985, MIT Artificial Intelligence Laboratory, A.I. Memo 864,
https://people.csail.mit.edu/brooks/papers/AIM-864.pdf
[Brown 2002] Elements of Spacecraft Design, Charles D. Brown, AIAA Education
Series, Reston, VA, 2002. https://www.worldcat.org/title/elements-of-spacecraft-
design/oclc/850628450&referer=brief_results
[Brunier 2009] The Milky Way Panorama, Serge Brunier and European Southern Ob-
servatory, 14 September 2009, High-resolution images featured in the GigaGalaxy
Zoom project, 360 Degree Photograph of the Milky way, Credit: ESO/Serge
Brunier, [CC BY-4.0], https://www.eso.org/public/images/eso0932a/
[Carsley, Blacic, and Pletka 1992] Vacuum Melting and Mechanical Testing of Simu-
lated Lunar Glasses, J. E. Carsley, J. D. Blacic, and B. J. Pletka, 31 June - 4 June
1992, Engineering, Construction, and Operations in Space III, Vol 2, pp.1219
1231, Eds: Willy Z. Sadeh, Stein Sture, and Russell J. Miller, American Society of
Civil Engineers, https://archive.org/details/engineeringconst0000spac
[Copeland 2000] The Modern History of Computing (Stanford Encyclopedia of Phi-
losophy), B. Jack Copeland, 18 December 2000, Stanford Encyclopedia of Philos-
ophy, Retrieved 12 April 2018, https://plato.stanford.edu/entries/computing-his-
tory/
[Coriolis 1835] Sur les équations du mouvement relatif des systèmes de corps, (On
the Equations of the Relative Movement of Systems of Bodies), Gaspard-Gustave
de Coriolis, 1835, Journal de l'École Royale Polytechnique. 15: 144–154.,
http://www.bibnum.education.fr/physique/mecanique/sur-les-equations-du-
mouvement-relatif-des-systemes-de-corps
[Cornall 2021] Sophie's Bionutrients develops world's first dairy-free micro-algae
based milk alternative, Jim Cornall, 4 May 2021, NutraIngrediants.com,
https://www.nutraingredients.com/Article/2021/05/04/Sophie-s-Bionutrients-de-
velops-world-s-first-dairy-free-micro-algae-based-milk-alternative
[DC 2017] Destination DC, 2017 Visitor Statistics Washington, DC, 2017, 2017 Visi-
tor Statistics, https://washington.org/sites/default/files/2021-02/2017%20Washing-
ton%2C%20DC%20Visitor%20Statistics.pdf
[Deller 2017] Hyper-Velocity Impacts on Rubble Pile Asteroid, Jakob Deller, 2017,
Springer, 10.1007/978-3-319-47985-9, https://www.researchgate.net/publica-
tion/312008639_Hyper-Velocity_Impacts_on_Rubble_Pile_Asteroids,
https://kar.kent.ac.uk/54352/1/78Deller_2015_PhDThesis_screen.pdf
[Doody 2011] Basics of Space Flight, David Doody, 7 May 2011, Prepared at NASA
Jet Propulsion Lab (JPL), Public Domain, https://solarsystem.nasa.gov/basics/
[Drexler 1986] Engines of Creation: The Coming Era of Nanotechnology, K. Eric
Drexler, 1986, Anchor Books, Random House, Inc., http://wfmh.org.pl/en-
ginesofcreation/EOC_Chapter_1.html https://www.nanowerk.com/nanotechnol-
ogy/reports/reportpdf/report47.pdf
[Dunn 2016] How We Want to Turn Asteroids Into Spacecraft, Jason Dunn, May 31,
2016, Made In Space, Newsroom, https://medium.com/made-in-space/how-we-
want-to-turn-asteroids-into-spacecraft-e95d3214d787
[Dunn and Fagin 2017] Project RAMA: Reconstituting Asteroids into Mechanical
Automata, Jason Dunn and Max Fagin, 2017, NASA Innovative Advanced Con-
cepts, Made In Space, Inc., https://www.nasa.gov/sites/default/files/at-
oms/files/niac_2016_phasei_dunn_projectrama_tagged.pdf
[Dyson 1960] Search for Artificial Stellar Sources of Infra-Red Radiation, Freemann
J. Dyson, 3 June 1960, Science. 131 (3414): pp. 1667-1668, Bib-
code:1960Sci...131.1667D. doi:10.1126/science.131.3414, https://fermatsli-
brary.com/s/search-for-artificial-stellar-sources-of-infrared-radiation
[Dyson 1970] The twenty-first century, Vanuxem Lecture delivered at Princeton Uni-
versity, Freeman J. Dyson, 26 February 1970, Revised and reprinted as: Chapter
18 Thought Experiments [Dyson 1979], http://www.molecularassem-
bler.com/KSRM/3.6.htm
[Dyson 1979] Disturbing the Universe, Freeman J. Dyson, 1 January 1979, Chapter
18, Thought Experiments, Harper and Row Publishers, New York, 1979, pp. 194-
204., Extracts from [Freitas and Merkle 2004]. http://www.molecularassem-
bler.com/KSRM/3.6.htm
[Eisele 2001] Concentration of Useful Minerals from Asteroids, Timothy C. Eisele
Originally published 2001, Journal of the British Interplanetary Society, Vol. 54,
Part 7/8, pp. 277-288, [CC BY-4.0], https://www.researchgate.net/publica-
tion/260976297_Concentration_of_Useful_Minerals_from_Asteroids
[Ellison 2018] Asteroid Ryugu (July 11th, 2018), Doug Ellison, 3D Model, Sketch-
fab, Data Credit - JAXA, University of Tokyo, Kochi University, Rikkyo Univer-
sity, Nagoya University, Chiba Institute of Technology, Meiji University, Univer-
sity of Aizu, AIST., https://sketchfab.com/3d-models/asteroid-ryugu-july-11th-
2018-44876e2f0d314b05ba32b0472a1eddc6 [CC BY-4.0]
[Enos 2020] Enos - Bennu Pyramid, Heather Enos, 19 October 2020, OSIRIS-REx
Science and Engineering Briefing, NASA/Goddard Space Flight Center, Univer-
sity of Arizona, https://svs.gsfc.nasa.gov/13738
[Freitas and Gilbreath 1982] Advanced Automation for Space Missions: Proceedings
of the 1980 NASA/ASEE Summer Study held at the University of Santa Clara,
Robert A. Freitas, Jr., and William P. Gilbreath, June 23-August 29, 1980; NASA
Conference Publication 2255, 15 May 1981, NASA Ames Research Center, Mof-
fett Field, Publication Date: 1 November 1982, https://ntrs.nasa.gov/ar-
chive/nasa/casi.ntrs.nasa.gov/19830007077.pdf
[Freitas and Merkle 2004] Kinematic Self-Replicating Machines, Robert A. Freitas
Jr. and Ralph C. Merkle, 2004, Landes Bioscience, Georgetown, TX,
https://epdf.pub/queue/kinematic-self-replicating-ma-
chines90c44fd3e88ba39ff48389263e3f55434462.html
[Fritz and Turkoglu 2017] Optimal Trajectory Determination and Mission Design for
Asteroid/Deep-Space Exploration via Multibody Gravity Assist Maneuvers, Sean
Fritz and Kamran Turkoglu, 2017, International Journal of Aerospace Engineer-
ing, Volume 2017, Article ID 6801023, 12 pages, http://down-
loads.hindawi.com/journals/ijae/2017/6801023.pdf
[Fu et al. 2016] How to establish a bioregenerative life support system for long-term
crewed missions to the Moon and Mars, Fu, Y. L. Li, B. Xie, C. Dong, M. Wang,
B. Jia, L. Shao, Y. Dong, S. Deng, H. Liu, G. Liu, B. Liu, D. Hu, and H. Liu.
2016., Astrobiology 16(12) DOI:10.1089/ast.2016.1477, https://www.re-
searchgate.net/publication/311362350_How_to_Establish_a_Bioregenera-
tive_Life_Support_System_for_Long-Term_Crewed_Mis-
sions_to_the_Moon_or_Mars
[García et al. 2016] Final Report: Starport, Enrique García and 37 individuals on the
Starport 1 team, 2016, Space Studies Program, International Space University,
https://isulibrary.isunet.edu/doc_num.php?explnum_id=1121
[Garrett 2019] A cinema, a pool, a bar: inside the post-apocalyptic underground fu-
ture, Bradley L Garrett, 16 December 2019, The Guardian, https://www.theguard-
ian.com/cities/2019/dec/16/a-cinema-a-pool-a-bar-inside-the-post-apocalyptic-un-
derground-future
[Globus 1991] The Design and Visualization of a Space Biosphere, Al Globus, May
1991, Space Manufacturing 8, Energy and Materials from Space, Space Studies
Institute, Princeton, NJ, pages 303-313. https://www.nas.nasa.gov/as-
sets/pdf/techreports/1991/rnr-91-018.pdf
[Globus 2006] Contest-Driven Development of Orbital Tourist Vehicles, Al Globus,
American Institute of Aeronautics and Astronautics Space 2006, San Jose, Califor-
nia, 19-21 September 2006. https://pdfs.seman-
ticscholar.org/4ca2/10f824b5c00c02b6a3f7ee8cef572f5bf649.pdf
[Globus and Hall 2017] Space Settlement Population Rotation Tolerance, Al Globus
and Theodore Hall, June 2017, NSS Space Settlement Journal,
https://space.nss.org/wp-content/uploads/NSS-JOURNAL-Space-Settlement-
Population-Rotation-Tolerance.pdf
[Globus et al. 2007] The Kalpana One Orbital Space Settlement Revised, Al Globus,
Nitin Arora, Ankur Bajoria, and Joe Strout,2007, American Institute of Aero-
nautics and Astronautics, http://alglobus.net/NASAwork/papers/2007Kalpa-
naOne.pdf
[Good 2017] A Clockwork Rover for Venus, Andrew Good, 25 August 2017, NASA,
Jet Propulsion Laboratory, California Institute of Technology, News, Technology,
https://www.jpl.nasa.gov/news/a-clockwork-rover-for-venus
[Hall 1991] The Architecture of Artificial Gravity: Mathematical Musings on Design-
ing for Life and Motion in a Centripetally Accelerated Environment, Theodore W.
Hall, November 1991, Space Manufacturing 8 Energy and Materials from Space,
Proceedings of the Tenth Princeton/AIAA/SSI Conference, 15-18 May 1991,
https://citeseerx.ist.psu.edu/viewdoc/down-
load?doi=10.1.1.551.3694&rep=rep1&type=pdf
[Hall 1993] The Architecture of Artificial Gravity: Archetypes and Transformations
of Terrestrial Design, Theodore W. Hall, 12-15 May 1993, Space Manufacturing
9, The High Frontier Accession, Development and Utilization, Proceedings of the
Eleventh SSI-Princeton Conference, p. 198-209, http://www.artificial-grav-
ity.com/SSI-1993-Hall.pdf
[Hall 1997] Artificial Gravity and the Architecture of Orbital Habitats, Theodore W.
Hall, 20 March 1997, Proceedings of 1st International Symposium on Space

Tourism, Daimler-Chrysler Aerospace GmbH., http://www.spacefuture.com/ar-
chive/artificial_gravity_and_the_architecture_of_orbital_habitats.shtml
[Hall 1999] Architectural considerations for self-replicating manufacturing systems.
J. Storrs Hall, 1 September 1999, Nanotechnology 10:323, c, http://www.autog-
eny.org/selfrepsys/
[Hall 2006] Artificial Gravity Visualization, Empathy, and Design, Theodore Hall,
19-21 September 2006, AIAA 2006-7321, Session: SAS-3: Space Architecture
Symposium: Gravity Regime Architecture and Construction,
https://doi.org/10.2514/6.2006-7321, http://www.artificial-gravity.com/AIAA-
2006-7321.pdf
[Hand and Finch 1998] Analytical Mechanics, Louis N. Hand and Janet D. Finch,
1998, Cambridge University Press. p. 267. ISBN 978-0-521-57572-0,
https://www.iaa.csic.es/~dani/ebooks/Mechanics/Analytical%20mechanics%20-
%20Hand,%20Finch.pdf
[Haskin 1992] Glass and Ceramics, Larry A. Haskin, 1992, NASA SP-509, Volume
3, Space Resources: Materials, pp.291-294, [McKay et al. 1992-v3],
https://ntrs.nasa.gov/citations/19930007686
[Honeybee 2019] The World Is Not Enough Demonstrates the Future of Space Explo-
ration, Honeybee Robotics, Inc., January 15, 2019, https://honeybeerobot-
ics.com/wine-the-world-is-not-enough/, Wayback Machine Access: https://web.ar-
chive.org/web/20190215050619/https://honeybeerobotics.com/wine-the-world-is-
not-enough/
[ICC 2009] International Building Code, International Code Council, February 2009,
http://www.co.washington.ne.us/media/ICC-
International_Building_Code_2009.pdf
[Janhunen 2018] Natural illumination solution for rotating space settlements, Pekka
Janhunen, 14 September 2018, NSS Space Settlement Journal, Issue 4,
https://arxiv.org/pdf/1806.09808.pdf
[JAXA MHU 2019]. The JAXA Mouse Habitat Unit (MHU), Japan Aerospace Ex-
ploration Agency (JAXA), Last Updated: July 26, 2019, https://iss.jaxa.jp/en/ki-
boexp/pm/mhu/
[Jensen 1993] Disk I/O in High Performance Computing System, David W. Jensen,
1993, University of Illinois at Champaign Urbana, Ph.D. Thesis, http://hdl.han-
dle.net/2142/72078
[Jensen 1996] Observations Regarding Threat Command Agents, David W. Jensen,
31 July 1996, Ed: Major David Payne, Command Decision Modeling Technology
Assessment, Compiled by The Us Army Artificial Intelligence Center for the Na-
tional Simulation Center, https://apps.dtic.mil/docs/citations/ADA334926
[Jensen 2008] Developing System-on-Chips with Moore, Amdahl, Pareto, and Ohm,
David W. Jensen, 2008, Proc. Int'l Conf. IEEE Electro/Information Technology,
IEEE Press, 2008, pp. 13-18, https://ieeexplore.ieee.org/document/4554260
[Johnson and Holbrow 1977] NASA SP-413: Space Settlements: A Design Study,
Eds: Richard D. Johnson and Charles Holbrow, 1977, Scientific and Technical In-
formation Office, https://ntrs.nasa.gov/ar-
[JPL SB Mission Design Tool] JPL Small-Body Mission-Design Tool, NASA Jet
Propulsion Laboratory, Solar System Dynamics,
https://ssd.jpl.nasa.gov/?mdesign_server
[JPL SBD Search Engine] JPL Small-Body Database Search Engine, NASA Jet Pro-
pulsion Laboratory, Solar System Dynamics,
https://ssd.jpl.nasa.gov/sbdb_query.cgi
[JPL SBD Small Body Lookup] JPL Small-Body Database Lookup, NASA Jet Pro-
pulsion Laboratory, Solar System Dynamics,
https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/
[Kayser 2011] Solar Sinter, Markus Kayser, 2011, Kayser Works, Royal College of
Art, London, https://kayserworks.com/798817030644
[Keeter 2020] Long-Term Challenges to Human Space Exploration, Bill Keeter, 4
September 2020, National Aeronautics and Space Administration,
https://www.nasa.gov/centers/hq/library/find/bibliographies/Long-Term_Chal-
lenges_to_Human_Space_Exploration
[Kersch 2015] Answer: How many people can you feed per square-kilometer of farm-
land?, Worldbuilding User: ckersch, 3 February 2015, https://worldbuild-
ing.stackexchange.com/questions/9582/how-many-people-can-you-feed-per-
square-kilometer-of-farmland
[Kesson 1975] Mare basalts - Melting experiments and petrogenetic interpretations,
S. E. Kesson, Lunar Science Conference, 6th, Houston, Tex., March 17-21, 1975,
Proceedings. Volume 1. (A78-46603 21-91) New York, Pergamon Press, Inc.,
1975, p. 921-944. SAO/NASA Astrophysics Data System (ADS), https://ad-
sabs.harvard.edu/full/1975LPSC....6..921K
[King 2002] Clockwork Prayer: A Sixteenth-Century Mechanical Monk, Elizabeth
King, Spring 2002, Blackbird Archive, Online Journal of Literature and the Arts,
https://blackbird.vcu.edu/v1n1/nonfiction/king_e/prayer_introduction.htm
[Koelle and Williams 1959] Project Horizon: Volume II, Technical Considerations &
Plans, H. H. Koelle and F. L. Williams, 9 June 1959, A U. S. Army Study For The
Establishment of a Lunar Outpost, United States Army, https://his-
tory.army.mil/faq/horizon/Horizon_V2.pdf
[Lackner and Wendt 1995] Exponential growth of large self-reproducing machine
systems, Klaus S. Lackner and Christopher H. Wendt, May 1995, Mathematical
and Computer Modelling, Volume 21, Issue 10, Pages 55-81,
https://doi.org/10.1016/0895-7177(95)00071-9, https://www.sciencedi-
rect.com/science/article/pii/0895717795000719
[Lesser and Corkill 2014] Comprehensive History of the Multi-Agent Systems Lab at
the University of Massachusetts Amherst, 1978-2014, Victor Lesser and Daniel
Corkill, https://mas.cs.umass.edu/Documents/LabHistory_Web-Article.pdf
[Lewis-Weber 2016] Lunar-Based Self-Replicating Solar Factory, Justin Lewis-We-
ber, 2016, New Space, vol. 4, issue 1, pp. 53-62, https://www.re-
searchgate.net/publication/297746685_Lunar-Based_Self-Replicating_Solar_Fac-
tory
[Liu et al. 2020] Computing Systems for Autonomous Driving: State-of-the-Art and
Challenges, Liangkai Liu, Sidi Lu, Ren Zhong, Baofu Wu, Yongtao Yao, Qing-
yang Zhang, and Weisong Shi, 7 December 2020, Accepted to IEEE Internet of
Things Journal, https://arxiv.org/abs/2009.14349
[Lucas 2019] What Are Centrifugal & Centripetal Forces?, Jim Lucas, 10 May 2019,
Live Science Contributor, https://www.livescience.com/52488-centrifugal-centrip-
etal-forces.html
[Maynard and Sevier 1966] General Mission Summary and Configuration Descrip-
tion, Owen E. Maynard and John R. Sevier, 25 June 1966, NASA Technical Mem-
orandum NASA TM X-58006, Apollo Lunar Landing Mission Symposium, p.49,
Fig. 2, https://www.hq.nasa.gov/alsj/LunarLandingMIssionSympo-
sium1966_1978075303.pdf
[Mazanek et al. 2014] Asteroid Redirect Mission Concept: A Bold Approach for Uti-
lizing Space Resources, Daniel D. Mazanek, Raymond G. Merrill, John R. Bro-
phy, and Robert P. Mueller, 29 September 2014, 65th International Astronautical
Congress, Toronto, Canada, IAC-14-D3.1.8, https://www.nasa.gov/sites/de-
fault/files/files/IAC-14-D3-Mazanek.pdf
[McKay et al. 1992-v3] NASA SP-509 Volume 3: Space Resources, Materials, 1992,
Eds: Mary Fae McKay, David S. McKay, and Michael B. Duke, Scientific and
Technical Information Office, https://ntrs.nasa.gov/citations/19930007686
[McKendree 1995] Implications of Molecular Nanotechnology Technical Perfor-
mance Parameters on Previously Defined Space System Architectures, Thomas
Lawrence McKendree, 9-11 November 1995, The Fourth Foresight Conference on
Molecular Nanotechnology, Palo Alto, California, http://www.zyvex.com/nano-
tech/nano4/mckendreePaper.html
[Metzger 2015] Resources for 3D Additive Construction on the Moon, Asteroids and
Mars, Philip Metzger, 24 August 2015. University of Central Florida, Keck Insti-
tute for Space Studies, https://kiss.caltech.edu/workshops/3d/presentations/Metz-
ger.pdf
[Metzger et al. 2012] Affordable, rapid bootstrapping of space industry and solar sys-
tem civilization, Philip T. Metzger, Anthony Muscatello, Robert P. Mueller, and
James Mantovani, January 2013, Journal of Aerospace Engineering, Vol 26, Issue
1, pp. 18-29, DOI: 10.1061/(ASCE)AS.1943-5525.0000236,
https://arxiv.org/ftp/arxiv/papers/1612/1612.03238.pdf
[Misra 2010] The "Tesla" Orbital Space Settlement, Gaurav Misra, 2010, Barcelona,
Spain, 40th International Conference on Environmental Systems, American Insti-
tute of Aeronautics and Astronautics, Inc, AIAA 2010-6133,
https://doi.org/10.2514/6.2010-6133, http://spacearchitect.org/pubs/AIAA-2010-
6133.pdf
[Moore 1962] Machine Models of Self- Reproduction, Edward F. Moore, 1962 Re-
printed 1965, Mathematical Problems in the Biological Sciences, Proceedings of
Symposia in Applied Mathematics, Volume 14, 1962, http://is.ifmo.ru/auto-
graph/moore-article.pdf
[Mordanicus 2014] Space Colonization: The Dumbbell Design, Mordanicus, 6 De-
cember 2014, Lagrangian Republican Association, https://republicoflagran-
gia.org/2014/12/06/the-dumbbell-design/
[Moses et al. 2014] An architecture for universal construction via modular robotic
components, Matthew S. Moses, Hans Ma, Kevin C. Wolfe, Gregory S. Chiri-
kjian, 2014, Robots and Autonomous Systems, 62, pp. 945–965,
https://rpk.lcsr.jhu.edu/wp-content/uploads/2014/08/Moses13_An-Architec-
ture.pdf
[Mueller 2017] Construction with Regolith, The Technology and Future of In-Situ
Resource Utilization (ISRU), Robert P. Mueller, 6 March 2017, A Capstone Grad-
uate Seminar, Orlando, FL March 6, 2017, http://ntrs.nasa.gov/ar-
[Mueller et al. 2009]. Lightweight Bulldozer Attachment for Construction and Exca-
vation on the Lunar Surface, Robert P. Mueller, Allen R. Wilkinson, Christopher
A. Gallo, Andrew J. Nick, Jason M. Schuler, and Robert H. King, 2009, Proc.,
AIAA Space 2009 Conference, Reston, VA. https://ntrs.nasa.gov/ar-
[Mueller et al. 2013] Regolith Advanced Surface Systems Operations Robot
(RASSOR), Robert P. Mueller, Rachel E. Cox, Tom Ebert, Jonathan D. Smith, Ja-
son M. Schuler, and Andrew J. Nick, March 2013, 2013 IEEE Aerospace Confer-
ence, 2-9 March 2013, https://ntrs.nasa.gov/ar-
[Myers 2022] CubeSat: The little satellite that could, Andrews Myers, 8 June 2022,
Stanford Engineering, Technology and Society, https://engineering.stan-
ford.edu/magazine/cubesat-little-satellite-could
[NASA 2004] Mars Mice, NASA, 20 January 2004, NASA Science – Share the Sci-
ence, science.nasa.gov, https://science.nasa.gov/science-news/science-at-
nasa/2004/20jan_marsmice/

[Nau et al. 2003] SHOP2: An HTN Planning Environment., Dana Nau, T. Au, O.
Ilghami, Ugur Kuter, J. William Murdock, D. Wu, and Fusun Yaman, 2003, Jour-
nal of Artificial Intelligence Research - JAIR., https://arxiv.org/pdf/1106.4869.pdf
[Nishioka et al. 1973] Feasibility of mining lunar resources for earth use: Circa 2000
AD. Volume 2: Technical discussion, K. Nishioka, R D. Arno, A. D. Alexander,
and R. E. Slye, 1 August 1973, NASA Ames Research Center Moffett Field, CA,
United States, NASA TM Document ID: 19730022067,
https://ntrs.nasa.gov/api/citations/19730022067/downloads/19730022067.pdf?at-
tachment=true
[Noordung 1929] The Problem of Space Travel - The Rocket Motor, Herman
Potočnik Noordung, Originally: Richard Carl Schmidt & Co., Berlin W62, 1929;
Digital edition of English translation, Tanja N. Zhelnina, December 2010,
https://history.nasa.gov/SP-4026.pdf
[O’Leary et al. 1979] Retrieval of Asteroidal Materials, Brian O'Leary, Michael
Gaffey, David Ross, and Robert Salkeld, 1979, NASA SP-428 Space Resources
and Space Settlements, pp.173-189, [O’Neill et al. 1979],
https://ntrs.nasa.gov/api/citations/19790024054/downloads/19790024054.pdf
[O’Neill 1974] The Colonization of Space, Gerard K. O’Neill, September 1974,
Physics Today. 27 (9): 32-40. Bibcode:1974PhT....27i..32O.
doi:10.1063/1.3128863, https://physicstoday.scita-
tion.org/doi/pdf/10.1063/1.3128863
[O’Neill 1976] The High Frontier: Human Colonies in Space, Gerard K. O’Neill,
Morrow New York 1976, ISBN-13:978-1896522678; https://archive.org/de-
tails/highfrontierhuma0000onei_y9i8/mode/1up
[O’Neill and Driggers 1976] Observable Effects In and Human Adaptation To Rotat-
ing Environments, Gerard K. O’Neill and Gerald W. Driggers, Space-Based Man-
ufacturing From Nonterrestrial Materials, p. 173–176. Edited by Gerard K.
O’Neill and Brian O’Leary, AIAA, August 1977. Volume 57, Progress in Astro-
nautics and Aeronautics: technical papers derived from the 1976 Summer Study at
NASA Ames Research Center, ISBN (print): 978-0-915928-21-7,
https://arc.aiaa.org/doi/10.2514/5.9781600865312.0173.0176
[O’Neill et al. 1979] NASA SP-428, Space Resources and Space Settlements, Gerard
O’Neill, Eds: John Billingham, William Gilbreath, and Brian O'Leary, 1 January
1979, NASA, Technical papers derived from the 1977 Summer Study at NASA
Ames Research Center, Moffett Field, California, https://ntrs.nasa.gov/api/cita-
tions/19790024054/downloads/19790024054.pdf
[Oberth 1923] Die Rakete zu den Planetenräumen, Hermann Oberth, 1923, The
Rocket into Interplanetary Space, Verlag R. Oldenbourg, München und Berlin,
https://vdoc.pub/documents/the-rocket-into-planetary-space-442l1h2fh480
[Poljak, Klindzic and Kruljac 2018] Effects of exoplanetary gravity on human loco-
motor ability, Nikola Poljak, Dora Klindzic and Mateo Kruljac, Department of
Physics, Faculty of Science, University of Zagreb, Croatia, Dated: August 23,
2018, https://arxiv.org/pdf/1808.07417.pdf
[Prado and Fraser 2018] Construction Materials from Minimally Processed Bulk Lu-
nar and Asteroidal Soils, Mark Prado and Sam Fraser, 2018, The Permanent Space
Development Foundation, Inc, https://www.permanent.com/space-industry-bulk-
construction.html
[Queijo et al. 1988] Some Operational Aspects of a Rotating Advanced-Technology
Space Station for the Year 2025, M.J. Queijo, A.J. Butterfield, W.F. Cuddihy,
C.B. King, R.W. Stone, J.R. Wrobel, and P.A. Garn, June 1988, The Bionetics
Corporation, NASA Contractor Report 181617, Report 19880017013, National
Aeronautics and Space Administration, Langley Research Center,
https://ntrs.nasa.gov/api/citations/19880017013/downloads/19880017013.pdf
[Rivera-Valentin et al. 2017] Discovery Announcement of Binary System (163693)
Atira, E. G. Rivera-Valentin, P. A. Taylor, A. Virkki, and B. Aponte-Hernandez,
20 January 2017, Planetary, Arecibo Observatory, http://out-
reach.naic.edu/ao/blog/discovery-announcement-binary-system-163693-atira
[Ross 2001] Near-Earth Asteroid Mining, Shane D. Ross, Control and Dynamical
Systems Caltech 107-81, Pasadena, CA, December 14, 2001 Space Industry Re-
port, https://space.nss.org/media/Near-Earth-Asteroid-Mining-Ross-2001.pdf
[Ruess, Schaenzlin, and Benaroya 2006] Structural Design of a Lunar Habitat, F.
Ruess, J. Schaenzlin, and H. Benaroya, July 2006, Journal of Aerospace Engineer-
ing. American Society of Civil Engineers. 19 (3): 138. doi:10.1061/(ASCE)0893-
1321(2006)19:3(133), http://coewww.rutgers.edu/~benaroya/publica-
tions/Ruess%20et%20al%20ASCE%20JAE.pdf
[Sanders and Larson 2012] Progress made in lunar in situ resource utilization under
NASA’s exploration technology and development program, G.B. Sanders and
W.E. Larson, 2012, Journal of Aerospace Engineering. 26.1, 5-17.
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20120006109.pdf
[Sauder 2017] Automaton Rover for Extreme Environments, Jonathan Sauder, 2017,
NASA Innovative Advanced Concepts (NIAC) Phase I Final Report, California
Institute of Technology, https://www.nasa.gov/sites/default/files/at-
oms/files/niac_2016_phasei_saunder_aree_tagged.pdf
[Savard 2012] A Space Habitat Design, John J. G. Savard, quadibloc web page,
http://www.quadibloc.com/science/spaint.htm
[Schrunk et al. 2008] The Moon: Resources, Future Development and Settlement,
Second Edition, David Schrunk, Burton Sharpe, Bonnie L. Cooper, and Madhu
Thangavelu, Published: 4 October 2007, Springer Science & Business Media,
https://epdf.pub/queue/moon-resources-future-development-and-settlement.html
[Sifakis 2018] Autonomous Systems – An Architectural Characterization, Joseph Si-
fakis, November 2018, arXiv:1811.10277, https://arxiv.org/ftp/arxiv/pa-
pers/1811/1811.10277.pdf
[Soilleux 2019] Orbital Civil Engineering: Waste Silicates Reformed into Radiation-
shielded Pressure Hulls, Richard Soilleux, July 2019, Journal of the British Inter-
planetary Society (JBIS), Volume 72, No 7, https://www.bis-space.com/member-
ship/jbis/2019/JBIS-v72-no07-July-2019%20-%20Subscription%20Copy.pdf
[Soilleux and Gunn 2018] Environmental Control and Life Support (ECLSS) for
Large Orbital Habitats: Ventilation for Heat and Water Transport and Manage-
ment, Richard J. Soilleux and Stephen D. Gunn, January 2018, NSS Space Settle-
ment Journal, Issue 3, November 2017-September 2018, https://space.nss.org/wp-
content/uploads/NSS-JOURNAL-ECLSS-for-Large-Orbital-Habitats-Ventilation-
and-Heat-Transport.pdf
[SpaceX 2018] SpaceX, Space Exploration Technologies Corp, 2018,
https://www.spacex.com/
[Stanley 2018] Biosphere 2 and Closed Ecological Systems, Systems Biology for
Sustainable Life Outside Earth, Greg Stanley, 12 May 2018, Presentation to Na-
tional Space Society North Houston, Nhttps://gregstanleyandassociates.com/suc-
cessstories/Biosphere2/Bio2-r1.pdf
[Sterritt and Hinchey 2005] SPAACE:: Self-Properties for an Autonomous & Auto-
nomic Computing Environment, Roy Sterritt and Michael G. Hinchey, June 2005,
Proceedings of the International Conference on Software Engineering Research
and Practice, SERP 2005, Las Vegas, Nevada, USA, https://www.re-
searchgate.net/publication/221610408_SPAACE_Self-
Properties_for_an_Autonomous_Autonomic_Computing_Environment
[Stryk 2008] Šteins Asteroid Image Credit, Ted Stryk, September 2008, Processing
European Space Agency data, ESA 2008 MPS for OSIRIS Team,
MPS/UPD/LAM/IAA/RSSD/INTA/UPM/DASP/IDA; https://commons.wiki-
media.org/wiki/File:2867_%C5%A0teins_by_Rosetta_(reprocessed).png
[Tosaka 2008] Continuous Casting (Tundish and Mold), Wikipedia User: Tosaka, 25
July 2008, Kontinuerlig gjutning, Creative Commons Attribution 3.0 Unported
(CC BY 3.0), Artwork Changes: Labels Added, https://en.wikipe-
dia.org/wiki/Continuous_casting#/media/File:Continuous_casting_(Tun-
dish_and_Mold)-2_NT.PNG
[Tsiolkovsky 1883] First space ship draft, Konstantin Tsiolkovsky, 1883, Manuscript
“Free space” (Свободное пространство), https://en.wikipe-
dia.org/wiki/File:Chertrg_Tsiolkovsky.jpg
[Tsiolkovsky 1920] Beyond the Planet Earth, Konstantin Tsiolkovsky, 1920, origi-
nally published under the title Вне Земли by the Kaluga Society for Natural His-
tory and Local Studies, Translated by Kenneth Syers, Foreword by B. N. Voro-
byev, 1960, New York, Pergamon Press, https://archive.org/details/beyondplane-
teart00tsio
[Vandenbos 2006] Asteroid mining, Jan Vandenbos, 2006, Slideshare, Published on
Apr 26, 2012, https://www.slideshare.net/jvandenbos/asteroid-mining-2006
[Volpe 2018] 2018 Robotics Activities at JPL, Richard Volpe, Jet Propulsion Labora-
tory, 2018, California Institute of Technology, https://www-robot-
ics.jpl.nasa.gov/media/documents/volpe%20paper,%20iSAIRAS%202018.pdf
[Volpe 2018a] The LEMUR Robots, Jet Propulsion Laboratory, Retrieved 2018-04-
11, Curator: Richard Volpe, Webmaster: David Martin, https://www-robot-
ics.jpl.nasa.gov/how-we-do-it/systems/the-lemur-robots/
[Volpe 2018b] The ATHLETE Rover. Jet Propulsion Laboratory, Retrieved 2018-04-
11, Curator: Richard Volpe, Webmaster: Kristy Kawasaki, https://www-robot-
ics.jpl.nasa.gov/systems/system.cfm?System=11
[von Neumann 1966] The Theory of Self-reproducing Automata, von Neumann,
John, A. Burks (ed.). Urbana, IL: Univ. of Illinois Press. ISBN 978-0-598-37798-
2, 1966, https://archive.org/details/theoryofselfrepr00vonn_0
[Wall 2017] Building Huge Structures in Space: 'Archinaut' Takes Another Step,
Mike Wall, Posted August 14, 2017, Retrieved April 18, 2018, Space.com,
https://www.space.com/37767-made-in-space-archinaut-vacuum-chamber-
test.html
[Webster 2020] Asterank, Ian Webster, 2020, Asterank Database and Website,
http://www.asterank.com/
[Wheeler 2017] Agriculture for Space: People and Places Paving the Way, Raymond
M. Wheeler, 15 January 2017, Open Agriculture, 2017, Volume 2, pp. 14-32,
10.1515/opag-2017-0002, https://www.researchgate.net/publica-
tion/313732842_Agriculture_for_Space_People_and_Places_Pav-
ing_the_Way/fulltext/58a68b7a4585150402ee09ce/Agriculture-for-Space-People-
and-Places-Paving-the-Way.pdf
[Williams 2016] Tools used by the pioneers to tame the wilderness, Doug Williams,
12 Sept 2016, Outdoor Revival, https://m.outdoorrevival.com/instant-arti-
cles/tools-used-by-the-pioneers-to-tame-the-wilderness.html
[Williams et al. 1979] Mining and Beneficiation of Lunar Ores, Richard J. Williams,
David S. Mckay, David Giles, and Theodore E. Bunch, 1979, 1979, NASA SP-
428 Space Resources and Space Settlements, pp.275-288, [O’Neill et al. 1979],
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19790024054.pdf
[Yale 2013] Non-brittle glass possible: In probing mysteries of glass, researchers find
a key to toughness, Yale University, 26 February 2013, Science Daily,
https://www.sciencedaily.com/releases/2013/02/130226114023.htm

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9 Contents
1 Asteroid Restructuring - Introduction _____________________________________________________ 1
2 Asteroid Restructuring – Asteroids_______________________________________________________ 2
2.1 Asteroids – Background____________________________________________________________________________________________________ 2
2.1.1 Asteroid – Background Credit_____________________________________________________________________________________________ 2
2.1.2 Asteroid Examples _____________________________________________________________________________________________________ 3
2.1.3 Asteroid Spectral Classification ___________________________________________________________________________________________ 4
2.1.4 Asteroid Mining _______________________________________________________________________________________________________ 5
2.1.5 Asteroids Surface Characteristics __________________________________________________________________________________________ 5
2.1.6 Asteroids Resources and Applications ______________________________________________________________________________________ 5
2.2 Asteroids – Analysis_______________________________________________________________________________________________________ 6
2.2.1 Asteroid Materials _____________________________________________________________________________________________________ 6
2.2.2 Construction Material___________________________________________________________________________________________________ 6
2.2.3 Construction Material Production _________________________________________________________________________________________ 7
2.2.4 Mission Cost __________________________________________________________________________________________________________ 7
2.2.5 Return on Investment___________________________________________________________________________________________________ 8
2.3 Asteroids – Results________________________________________________________________________________________________________ 8
2.3.1 Asteroid Selection______________________________________________________________________________________________________ 8
2.3.2 Harvested Material_____________________________________________________________________________________________________ 9
2.4 Asteroids – Summary______________________________________________________________________________________________________ 9
3 Asteroid Restructuring – Space Stations ___________________________________________________ 9
3.1 Space Stations – Background ______________________________________________________________________________________________ 10
3.1.1 Space Stations – Background Credit_______________________________________________________________________________________ 10
3.1.2 Space Station Geometries ______________________________________________________________________________________________ 10
3.1.3 Artificial Gravity ______________________________________________________________________________________________________ 11
3.2 Space Stations – Analysis _________________________________________________________________________________________________ 14
3.2.1 Station Characteristics _________________________________________________________________________________________________ 14
3.2.2 Geometry Rotational Stability ___________________________________________________________________________________________ 20
3.2.3 Station Gravity Ranges _________________________________________________________________________________________________ 21
3.2.4 Geometry Adaptations _________________________________________________________________________________________________ 24
3.2.5 Station Mass _________________________________________________________________________________________________________ 26
3.3 Space Stations – Results __________________________________________________________________________________________________ 29
3.3.1 Specific Space Station__________________________________________________________________________________________________ 29
3.3.2 Station Characteristics _________________________________________________________________________________________________ 29
3.3.3 Station Construction___________________________________________________________________________________________________ 30
3.3.4 Station Materials _____________________________________________________________________________________________________ 30
3.3.5 Station Building Materials ______________________________________________________________________________________________ 31
3.3.6 Station Population ____________________________________________________________________________________________________ 32
3.4 Space Stations – Summary ________________________________________________________________________________________________ 32
4 Asteroid Restructuring – Robotics ______________________________________________________ 32
4.1 Robotics – Introduction___________________________________________________________________________________________________ 32
4.2 Robotics – Background ___________________________________________________________________________________________________ 33
4.2.1 Robotics – Background Credit ___________________________________________________________________________________________ 33
4.2.2 Robotic Examples _____________________________________________________________________________________________________ 34
4.2.3 Robotics and Autonomous Systems_______________________________________________________________________________________ 34
4.2.4 Robotics and Self-Replication____________________________________________________________________________________________ 35
4.3 Robotics – Analysis ______________________________________________________________________________________________________ 38
4.3.1 Mathematical Analysis _________________________________________________________________________________________________ 38
4.3.2 Replicator, Helper, and Product Example __________________________________________________________________________________ 39
4.3.3 Production Rate Analysis Results _________________________________________________________________________________________ 40
4.3.4 Analysis Approach Using Simulations______________________________________________________________________________________ 43
4.3.5 Technology Advancements______________________________________________________________________________________________ 45
4.3.6 Analysis Summary_____________________________________________________________________________________________________ 45
4.4 Robots – Results_________________________________________________________________________________________________________ 46
4.4.1 Introduction _________________________________________________________________________________________________________ 46
4.4.2 Tool Construction _____________________________________________________________________________________________________ 46
4.4.3 High Level Schedule ___________________________________________________________________________________________________ 47
4.4.4 Total Equipment Built__________________________________________________________________________________________________ 48
4.4.5 Total Equipment over Time _____________________________________________________________________________________________ 48
4.4.6 Equipment Working on Station Structures _________________________________________________________________________________ 50
4.4.7 Productivity Measure of Self Replication ___________________________________________________________________________________ 50
4.5 Robotics – Summary _____________________________________________________________________________________________________ 52
5 Asteroid Restructuring – System _______________________________________________________ 52
5.1 Asteroids and Station Size_________________________________________________________________________________________________ 52
5.2 Build Time and Population ________________________________________________________________________________________________ 53
5.3 Restructuring Cost _______________________________________________________________________________________________________ 53
5.4 Station Quantitative Design Accuracy _______________________________________________________________________________________ 55
5.5 Station Qualitative Design Evaluation _______________________________________________________________________________________ 55
6 Asteroid Restructuring – Future________________________________________________________ 55
6.1 Geometry Alternative ____________________________________________________________________________________________________ 55
6.2 Landing on Runways _____________________________________________________________________________________________________ 57
6.3 Early Colonists __________________________________________________________________________________________________________ 58
6.4 Atira Moon_____________________________________________________________________________________________________________ 59
6.5 Restructuring Future _____________________________________________________________________________________________________ 60
6.6 Conclusions ____________________________________________________________________________________________________________ 60
7 Asteroid Restructuring – References_____________________________________________________ 60
8 License Types____________________________________________________________________ 64

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