A theory for the shortperiodic motion due to the tesseral harmonic gravity field
Abstract
A model of the shortperiod motion of a satellite due to tesseral harmonic terms of the central gravity field is developed for inclusion in a semianalytical satellite theory for highaccuracy orbit prediction and determination problems. The generalized method of averaging is applied to the twophaseangle tesseral harmonic problem to obtain complete firstorder expressions for the shortperiod variations, which are then cast in the form of a double Fourier series in the mean meanlongitude and the Greenwich Sidereal Time, with coefficients that are slowly varying functions of time. The resulting model is general with respect to the geopotential coefficients and valid for fields of arbitrary degree and order. The Fourier coefficients are only evaluated with the theory a few times a day, with values at other times determined by interpolation. Results of numerical experiments with the model implemented as part of a semianalytical orbit generator are presented and compared with Cowell orbit determination results in order to verify model results for a range of satellite altitudes and eccentricities.
 Publication:

AIAA, Astrodynamics Specialist Conference
 Pub Date:
 August 1981
 Bibcode:
 1981aiaa.confU....P
 Keywords:

 Fourier Series;
 Gravitational Fields;
 Orbit Calculation;
 Orbital Mechanics;
 Satellite Orbits;
 Tesseral Harmonics;
 Algorithms;
 Coefficients;
 Computer Techniques;
 Equations Of Motion;
 Interpolation;
 Sidereal Time;
 Astrodynamics