Secular perturbations of third order in the motion of a satellite of an aspherical planet

Astronomy and Astrophysics – Astronomy

Scientific paper

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Asphericity, Geopotential, Natural Satellites, Satellite Rotation, Secular Variations, Differential Equations, Equations Of Motion, Sidereal Time

Scientific paper

The problem of constructing an analytic theory of satellite motion of third order relative to the flattening of an aspherical planet is considered. The theory is constructed on the basis of the intermediate orbit of the generalized problem of two fixed centers, and uses a method of successive approximations. The various families of perturbations arising in this problem are classified using a special group of indices. Secular terms are found to be present in the zeroth, first, third, and fifth families. The secular perturbations of the third and fifth families owe their appearance to the combined effect of the interaction with each other of harmonics of the geopotential higher than the second. The derivation of the relations defining these two families are derived in this paper.

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