Gravitational Perturbations of Equatorial Orbits

Details Gravitational Perturbations of Equatorial Orbits Gravitational Perturbations of Equatorial Orbits

Aug 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973cemec...8...85r&link_type=abstract

Celestial Mechanics, Volume 8, Issue 1, pp.85-98

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Scientific paper

Asymptotic solutions are developed for the motion of a geocentric satellite in the equatorial plane due to gravitational perturbations such as nonsphericity (especially oblateness) of the primary body. Axisymmetric potentials are considered. A class of transformations is developed and the equations of motion are solved by the method of generalized multiple scales. Further it is shown that the equations of motion can be transformed into the required form to within any specified degree of accuracy. The transformations form an Abelian group of infinite order which leaves the differential equations of motion invariant. Solutions are developed in terms of elementary functions instead of elliptic or other higher transcendental functions and are shown to agree with known results.

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