An analytic solution for the orbital perturbations of the Venus Radar Mapper due to gravitational harmonics
Abstract
Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a nonspherical body. The rotation of the central planet about its spinaxis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the nonhomogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying wellknown results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.
 Publication:

Astrodynamics 1983
 Pub Date:
 August 1984
 Bibcode:
 1984asdy.conf.....V
 Keywords:

 EarthVenus Trajectories;
 Orbit Perturbation;
 Planetary Gravitation;
 Spacecraft Orbits;
 Spherical Harmonics;
 Venus Orbiting Imaging Radar (Spacecraft);
 Coordinate Transformations;
 Elliptical Orbits;
 Floquet Theorem;
 Gravity Anomalies;
 Hill Method;
 Orbit Calculation;
 Planetary Orbits;
 Planetocentric Coordinates;
 Astrodynamics