Systems of time measurement (Lecture5)
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This document discusses various systems of time measurement. It describes: 1. Solar time, which is based on the sun's apparent daily motion, and mean solar time, which averages small variations. 2. Sidereal time, which is based on fixed stars' daily motions rather than the sun. 3. Universal Time (UT) and its variants, which are based on mean solar time at the Greenwich meridian. 4. International Atomic Time (TAI) and Coordinated Universal Time (UTC), which are atomic clock-based time standards. 5. Time scales used in global navigation satellite systems like GPS, GLONASS, Galileo, and BeiDou.
Systems of time measurement (Lecture5)
- 1. Lecture 5. Systems of time measurement
- 2. Time measurement (timing) is based on periodically repeated processes. Such as change of the moon phases, alternation of seasons, alternations of day and night, sunrise and sunset, mechanical oscillations. Scales of time measurement Time is the measure of durations of events and the intervals between them. The main requirement to the units of time measurement is stability. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum.
- 3. Solar time Solar time follows the apparent revolution of the Sun around the Earth. A solar day is the interval between two successive passages of the Sun through the meridian. Of course, this apparent revolution only reflects the true rotation of the Earth. Complete turnover of the Earth around its axis relative to the direction of the Sun is called true solar day. The duration of the true solar day varies with the seasons. This is a consequence both of the eccentricity of the Earth's orbit and the obliquity of the ecliptic (the tilt of Earth's rotation axis).
- 4. Mean solar time Firstly, the Earth moves at different speeds in different parts of its elliptical orbit, according to Kepler's second law, hence the sun seems to move at different speeds among the stars. Secondly, even with a perfectly circular Earth orbit, the Sun would move evenly along the ecliptic but its projection onto the celestial equator would move at varying speeds. To obtain a more even time scale, one defines a fictitious ``Mean Sun''. This Mean Sun takes the same time from one vernal equinox to the next as the true Sun, but it is supposed to move with constant velocity along the celestial equator. The difference between True and Mean Solar Time is called the equation of time.
- 5. Because two different effects with different time scales overlap (the eccentricity causes a period of one year, the obliquity of the ecliptic one of half a year), the equation of time has two minima and two maxima per year: Equation of time ~ 11.Feb ~ -14.5 min ~ 14.Mai ~ +4 min ~ 26.Jul ~ -6.4 min ~ 3.Nov ~ +16.3 min
- 6. Sidereal time The sidereal time is deduced from the revolution of the Earth with respect to the distant stars. A sidereal day can be defined in a first approximation as the time interval between two successive passages of the same star through the meridian.
- 7. Left: a distant star (the small red circle) and the Sun are at culmination, on the local meridian. Centre: only the distant star is at culmination (a mean sidereal day). Right: a few minutes later the Sun is on the local meridian again. A solar day is complete. Sidereal time vs solar time
- 8. Universal Time Universal Time (UT) is time scale based on the rotation of the Earth. It is the mean solar time on the Prime Meridian at Greenwich. This time includes year, month, day, hour, minute and second. The first three values measured by Gregorian calendar, others – local mean time at Greenwich. UT is the same everywhere on Earth. There are several versions of Universal Time: UT0 – determined at an observatory by observing the motion of stars, Moon and artificial Earth satellites. UT1 – calculated in accordance with movements of the poles. UT2 – time UT1 with seasonal corrections.
- 9. Terrestrial Dynamical Time (TDT) Due to irregularity of the daily rotation of the Earth sidereal and solar days slightly vary. For accurate astronomic calculations is used ephemeris second calculated as 1/86400 share of the average day on Jan. 1 1900 . The ephemeris second is unit of Terrestrial Dynamical Time (TDT), which is used in astronomical tables of positions (ephemerides) of the Sun, Moon and planets as seen from the Earth. Dynamic time also is used for determination satellite ephemerides.
- 10. International Atomic Time (TAI) Introduced in 1971, and based on a line in spectrum of cesium (Cs). TAI is based on SI second which = 9,192,631,770 periods of radiation emitted by Cs133. TAI is a time scale is a weighted average of the time kept by over 200 atomic clocks in about 70 national laboratories worldwide. The clocks are compared using satellites. Due to averaging it is far more stable than any clock would be alone. TAI is currently the best realization of a timescale based on the SI-second, with a relative accuracy of +/- 2 ∙ 10−14
- 11. Coordinated Universal Time(UTC) Coordinated Universal Time (abbreviated UTC) is the time standard by which the world regulates clocks and time. It is a time standard based on International Atomic Time (TAI) with leap seconds added at irregular intervals to compensate for the Earth’s slowing rotation. Time zones around the world are expressed using positive or negative offsets from UTC.
- 12. Time scales of GNSS GPS Time (GPST) GPS Time (GPST) is a continuous time scale (no leap seconds) defined by the GPS Control segment on the basis of a set of atomic clocks at the Monitor Stations and onboard the satellites. It starts at 0h UTC (midnight) of January 5th to 6th 1980. At that epoch, the difference TAI−UTC was 19 seconds, thence GPS−UTC=n − 19s. GPS time is synchronized with the UTC at 1 microsecond level (modulo one second), but actually is kept within 25 ns.
- 13. GLONASS Time (GLONASST) GLONASS Time (GLONASST) is generated by the GLONASS Central Synchronizer and the difference between the UTC(SU) and GLONASST should not exceed 1 millisecond plus three hours (i.e., GLONASST=UTC+3h - τ, where 𝜏 < 1𝑚𝑖𝑙𝑖𝑠𝑒𝑐), but τ is typically better than 1 microsecond. Unlike GPS, Galileo or BeiDou, GLONASS time scale implements leap seconds, like UTC. Galileo System Time (GST) Galileo System Time (GST) is a continuous time scale maintained by the Galileo Central Segment and synchronised with TAI with a nominal offset below 50 ns. The GST start epoch is 0h UTC on Sunday, 22 August 1999 (midnight between 21 and 22 August). BeiDou (BDT) BeiDou Time (BDT) is a continuous time scale starting at 0h UTC on January 1st, 2006 and is synchronised with UTC within 100 ns< (modulo one second).