The motion of a geosynchronous satellite

Abstract

The motion of a geosynchronous satellite has been studied under the combined gravitational effects of the oblate Earth (including its equatorial ellipticity), the Sun, the Moon and the solar-radiation pressure. It is observed that the orbital plane rotates with an angular velocity the maximum value of which is 0.058°/yr. and regresses with a period which increases both as the orbital inclination and the altitude increase. The effect of earth's equatorial ellipticity on the regression period is oscillatory whereas that of Solar-radiation pressure is to decrease it.

The synchronism is achieved when the angular velocity of the satellite is equal to the difference between the spin-rate of the Earth and the regression rate of the orbital plane. With this angular velocity of the satellite, the ground trace is in the shape of figure eight, though its size and position relative to the Earth change as the time elapses. The major effect of earth's equatorial ellipticity is to produce a change in the relative angular position of the satellite as seen from the Earth. If the satellite is allowed to execute large angle oscillations the mid-point of oscillation would be at the position of the minor axis of the earth's equatorial section. The oscillatory period T has been determined in terms of the amplitude Γ and the tesseral harmonic J₂⁽²⁾. From this result we can determine the value of J₂⁽²⁾ as T and Γ can be observed accurately.