Periodic Orbits of Third Kind in the Zonal J2 + J3 Problem

Abstract

In this work, the periodic orbits’ phase portrait of the zonal J 2 + J 3 problem is studied. In particular, we center our attention on the periodic orbits of the third kind in the Poincaré sense using the averaging theory of dynamical systems. We find three families of polar periodic orbits and four families of inclined periodic orbits for which we are able to state their explicit expressions.

Keywords

• periodic orbits
• perturbed Kepler problem
• frozen orbits
• zonal problem
• averaging theory