The firstorder shortperiodic motion of an artificial satellite due to third body perturbations
Abstract
Analytical formulas are developed for the construction of the firstorder shortperiodic motion of a satellite caused by a disturbing point mass. Expressions for the six partial derivatives of the firstorder shortperiod generating function are developed in the nonsingular equinoctial elements as Fourier sums in the mean eccentriclongitude. The coefficients are of closed form in the eccentricity and are expressed in terms of special functions which provide a recurrent scheme for direct evaluation. The coefficients are a function of the five slowly varying mean elements, and are thus amenable to evaluation with loworder interpolation algorithms. The formulas are valid for disturbing potential expansions of arbitrary degree in the Legendre polynomials; however, they are readily truncated on powers of the parallax factor and/or on the eccentricity. The theory is applicable to satellites with altitudes ranging up to the geosynchronous regime, with the inclusion of weak timedependent effects.
 Publication:

AIAA, Astrodynamics Specialist Conference
 Pub Date:
 August 1981
 Bibcode:
 1981aiaa.confZ....S
 Keywords:

 Artificial Satellites;
 Astrodynamics;
 Satellite Orbits;
 Satellite Perturbation;
 Spacecraft Motion;
 Three Body Problem;
 Eccentric Orbits;
 Fourier Series;
 Legendre Functions;
 Orbit Calculation;
 Synchronous Satellites;
 Astrodynamics