Thirdorder solution of an artificialsatellite theory
Abstract
A thirdorder solution was developed for the motions of artificial satellites moving in the gravitational field of the earth, whose potential includes the second, third, and fourthorder zonal harmonics. Thirdorder periodic perturbations with fourthorder secular perturbations were derived by the Hori perturbation method. All quantities were expanded into power series of the eccentricity, but the solution was obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a closeearth, smalleccentricity satellite with an accuracy of better than one cm over a period of one month.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1977
 Bibcode:
 1977STIN...7810184K
 Keywords:

 Artificial Satellites;
 Harmonic Motion;
 Problem Solving;
 Equations Of Motion;
 Gravitational Fields;
 Numerical Integration;
 Perturbation Theory;
 Astrodynamics