J2 EFFECT AND ELLIPTIC INCLINED PERIODIC ORBITS IN THE COLLISION RESTRICTED THREE–BODY PROBLEM

Abstract. The existence of a new class of inclined periodic orbits of the collision restricted three–body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet. Key words. Collision restricted three-body problem, periodic orbits, symmetric orbits, critical inclination, continuation method. AMS subject classifications. 70F07, 70F15, 70H09, 70H12, 70M20. 1. Introduction. The launch of the Sputnik in October 1957 opened the space age. The use of circular, elliptic, and synchronous orbits, combined with dynamical effects due to the Earths equatorial bulge gives rise to an array of orbits with specific properties to support various mission constraints. One example is the Molniya orbit: a highly elliptic 12-hour-period orbit the former USSR originally designed to observ