Equilibria Bifurcations of Satellite Orbits

Abstract

Equilibria of circular satellite orbits around an oblate central body exist in three planes, as long as the perturbing influence of a third body is comparatively small. In terms of inclination and longitude of node, two of these equilibria are stable and one unstable; for small eccentricities all three equilibria are stable. If the influence of a third body is in the range of 1/4 to 1/2 of the perturbations caused by the oblateness, all three equilibria become unstable in eccentricity. At all these boundary lines of stability a bifurcation into two equilibria of elliptic orbits originates. Even more complex configurations of these equilibria can be observed in the Laplacian plane for inclinations of the third body between 68.87 ° and 111.13°, and in the orthogonal Laplacian plane for inclinations of the third body between 84.09° and 95.91°. The lines of apsides of these “balanced” elliptic orbits lie either in the plane of the disturbing third body or in the plane orthogonal to the line of intersection of the plane of the disturbing third body and the equatorial plane of the oblate central body.