Networks and Bifurcations of Eccentric Orbits in Exoplanetary Systems

Abstract

A systematic study of families of planar symmetric periodic orbits of the elliptic restricted three-body problem is presented, in exoplanetary systems. We find families of periodic orbits that surround only one of the primaries (Satellite-Type), that are moving around both primaries (Planet-Type), and also moving about the collinear Lagrange points. The linear stability of every periodic orbit is calculated, and the families are interpreted through stability diagrams. We focus on quasi-satellite motions of test particles that are associated with the known family [Formula: see text] that consists of 1:1 resonant retrograde Satellite-Type orbits. Over the last years, quasi-satellite orbits are of special interest due to the many applications in the design of spacecraft missions around moons and asteroids. We find the critical simple (1:1 resonant) periodic orbits of the basic families of the circular problem from which we calculate new families of the elliptic problem. Additionally, families of the elliptic problem which bifurcate from the main family [Formula: see text], for various resonances, are also presented and discussed. Hundreds of critical orbits (bifurcation points), from which families of the elliptic problem of higher multiplicity emerge, are found and the corresponding resonances are identified.