Poisson series solution of geosynchronous drift
Abstract
The motion of an uncontrolled satellite in a nearly equatorial, synchronous orbit is analyzed by use of spherical coordinates. For such a satellite the longitude motion is governed by a nonlinear oscillator equation. Eightytwo of the GEM9 equatorial tesseral coefficients are used to construct the longitude potential energy which has two minima. The longitudes of the minima correspond to the minor axes of the nearly elliptical, equatorial cross section of the geopotential at synchronous radius. A power series in the longitude variation is developed about each of the minima. The author's Poisson series method is then used to generate the Type I solution coefficients to the sixteenth order. From these coefficients the large amplitude, periodic longitude drift solutions are constructed for each potential well.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1983
 Bibcode:
 1983aiaa.meetS....M
 Keywords:

 Drift Rate;
 Equatorial Orbits;
 Geosynchronous Orbits;
 Orbit Perturbation;
 Poisson Equation;
 Satellite Perturbation;
 Equations Of Motion;
 Geopotential;
 Nonlinear Systems;
 Orbit Decay;
 Spherical Coordinates;
 Tesseral Harmonics;
 Astrodynamics