IV- A- 3. Orbit Considerations a. Perturbations V. R. Bond Mission Planning & Analysis Div. The tacit assumption is made in the discussion of a geosynchronous satellite that it is in orbit at a precise constant distance (42, 241 km) from the center of the earth and in the plane of the earth's equator. At this radius, the angular rate of the satellite is equal to the rotational rate of the earth. The satellite will therefore remain over the same point on the earth's equator, having the appearance of being fixed relative to this point. This is a rather idealized view and would be true if the earth were a homogeneous sphere and if the earth were the only gravitational body in the universe. Acutally, since the earth is not a homogeneous sphere and since it is perturbed by other gravity sources (mainly the sun and moon) and since the effects due to solar pressure are not negligible (on a satellite of substantial size), the motion is much more complicated than that described for the idealized situation above. But these perturbative effects* are fortunately for the most part uncoupled and may be analyzed somewhat independently. They are of approximately the same order of magnitude at the satellite radius and will be discussed in the order (1) luni-solar (moon and sun); (2) solar pressure; and (3) equatorial ellipticity {^22^’ (1) Luni-Solar (Sun and Moon Effects) The luni-solar perturbations have substantial effects only upon the node n and the inclination I of the orbit. These angles can be understood by referring to figure IV-A-3-1. The node Q is the angle measured from a fixed direction in space (a line from the center of the earth to the point where the sun crosses the earth's equator from south to north—the vernal equinox). The inclination I is the angle between the earth's equator and the satellite orbit. Table IV-A-3-1 shows some representative values of the inclination after two years and 26.5 years for different values of the initial inclination. The important point is that the inclination I has a period of 53 years and that the maximum value of I depends upon the initial values of I and q. For example, the first row of table IV-A-3-1 shows that an orbit initially in *For the solar power station there may be other forces which should be considered. For example, the induced thrust due to the emission of microwave energy from the antenna.
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