Motion of Orbit, Earth and Sun

Abstract

In the last chapter, we calculated the motion of the orbital plane of a satel- lite with respect to a Galilean frame, via the rate of nodal precession, and the motion of the orbit in this plane. At the beginning of this chapter, we shall review the way the Earth moves with respect to a Galilean frame. By composing the two motions, we will then be able to follow the motion of the satellite relative to the Earth, which was indeed our original aim. We shall then study the apparent motion of the Sun relative to the Earth, so that we may subsequently study the cycles of the satellite in relation to the Sun. The aim here will ultimately be to specify the geometry of the satel- lite, its target, and the Sun: we consider a point on the Earth’s surface and determine how this point is seen by the satellite and under what conditions of solar illumination.