Procedure for integrating equations for elements of intermediate satellite orbit
Abstract
One of the most perfect models of intermediate motion of a satellite is the orbit of the generalized problem of two fixed centers which takes into account the second and third zonal harmonics in the expansion of planetary gravitational potential. However, until now the equations for the elements of such an intermediate orbit have been solved only in the first approximation and there has been no clearly defined scheme for their integration in subsequent approximations. Since for an intermediate orbit, taking the Earth's oblateness into account, the perturbing actor is 1,000 times less than for a Keplerian orbit, the solution is simpler. The coefficients of the equations for such an intermediate orbit and the perturbing function are represented in the form of expansions in powers of the Earth's oblateness and it is an unwieldy problem to write these expansions. Operations which must be performed are clarified. Expansion terms that must be taken into account in order to obtain perturbations of the elements of an intermediate orbit with accuracy are discussed. The problem is solved on the assumption that secular and shortperiod perturbations must be determined with an accuracy to the third power of the Earth's oblateness and longperiod perturbations with an accuracy to the second power of oblateness.
 Publication:

USSR Report Space
 Pub Date:
 January 1986
 Bibcode:
 1986RpSpR.......84Y
 Keywords:

 Approximation;
 Harmonics;
 Orbital Mechanics;
 Planetary Gravitation;
 Satellite Orbits;
 Satellite Perturbation;
 Accuracy;
 Coefficients;
 Mathematical Models;
 Problem Solving;
 Astrodynamics