Satellite communication lecture3
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This document discusses various perturbations that can affect a satellite's orbit. It describes perturbations due to the non-spherical shape of the Earth, atmospheric drag, and solar radiation pressure. Perturbations from the Earth's oblateness and bulge at the equator cause mainly secular variations in the satellite's longitude of ascending node and argument of perigee. Atmospheric drag opposes the satellite's velocity and will cause its orbit to decay over time. Solar radiation pressure also produces periodic variations in the orbital elements, with its effect exceeding that of atmospheric drag for satellites above 800 km altitude.
Satellite communication lecture3
- 2. PERTURBATIONS • There are other forces acting on a satellite that perturb it away from the nominal orbit. These perturbations, or variations in the orbital elements, can be classified based on how they affect the Keplerian elements. • Forces which can be significant are the gravitational forces of the sun and moon and the atmospheric drag.
- 3. PERTURBATIONS DUE TO NON-SPHERICAL EARTH • we assumed the Earth was a spherically symmetrical, homogeneous mass. • In fact, the Earth is neither homogeneous nor spherical. The most dominant features are a bulge at the equator, a slight pear shape, and flattening at the poles. • For a potential function of the Earth, we can find a satellite's acceleration by taking the gradient of the potential function. • The most widely used form of the geopotential function depends on latitude and geopotential coefficients, Jn, called the zonal coefficients.
- 4. PERTURBATIONS DUE TO NON-SPHERICAL EARTH • The potential generated by the non-spherical Earth causes periodic variations in all the orbital elements. • The dominant effects, however, are secular variations in longitude of the ascending node and argument of perigee because of the Earth's oblateness, represented by the J2 term in the geopotential expansion. The rates of change of Ω and ω due to J2 are- • where n is the mean motion in degrees/day, J2 has the value 0.00108263, RE is the Earth's equatorial radius, a is the semi-major axis in kilometers, i is the inclination, e is the eccentricity, and Ω and ω are in degrees/day
- 5. PERTURBATIONS FROM ATMOSPHERIC DRAG • Drag is the resistance offered by a gas or liquid to a body moving through it. • A spacecraft is subjected to drag forces when moving through a planet's atmosphere. This drag is greatest during launch and reentry, however, even a space vehicle in low Earth orbit experiences some drag as it moves through the Earth's thin upper atmosphere. • In time, the action of drag on a space vehicle will cause it to spiral back into the atmosphere, eventually to disintegrate or burn up. If a space vehicle comes within 120 to 160 km of the Earth's surface, atmospheric drag will bring it down in a few days, with final disintegration occurring at an altitude of about 80 km.
- 6. PERTURBATIONS FROM ATMOSPHERIC DRAG • The drag force FD on a body acts in the opposite direction of the velocity vector and is given by the equation- • where CD is the drag coefficient, ρ is the air density, v is the body's velocity, and A is the area of the body normal to the flow. The drag coefficient is dependent on the geometric form of the body and is generally determined by experiment. Earth orbiting satellites typically have very high drag coefficients in the range of about 2 to 4.
- 7. PERTURBATIONS FROM ATMOSPHERIC DRAG • For circular orbits we can approximate the changes in semi-major axis, period, and velocity per revolution using the following equations: where a is the semi-major axis, P is the orbit period, and V, A and m are the satellite's velocity, area, and mass respectively.
- 8. PERTURBATIONS FROM SOLAR RADIATION • Solar radiation pressure causes periodic variations in all of the orbital elements. The magnitude of the acceleration in m/s2 arising from solar radiation pressure is where A is the cross-sectional area of the satellite exposed to the Sun and m is the mass of the satellite in kilograms. For satellites below 800 km altitude, acceleration from atmospheric drag is greater than that from solar radiation pressure; above 800 km, acceleration from solar radiation pressure is greater.