NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
An analytic solution for the orbital perturbations of the Venus Radar Mapper due to gravitational harmonicsHill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis 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 non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.
Document ID
19840061425
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Vijayaraghavan, A.
(California Institute of Technology, Jet Propulsion Laboratory, Navigation Systems Section, Pasadena CA, United States)
Date Acquired
August 12, 2013
Publication Date
August 1, 1984
Subject Category
Astrodynamics
Report/Patent Number
AIAA PAPER 84-1995
Accession Number
84A44212
Distribution Limits
Public
Copyright
Other

Available Downloads

There are no available downloads for this record.
No Preview Available