The family of Quasi-satellite periodic orbits in the circular co-planar RTBP

TL;DR

This paper investigates the family of quasi-satellite periodic orbits in the circular coplanar Restricted Three-body Problem, analyzing their properties, limitations of averaging methods, and bifurcation behaviors at high eccentricities.

Contribution

It characterizes the quasi-satellite orbit family, identifies the limits of the averaged problem, and explores bifurcations of periodic orbit families at high eccentricities.

Findings

Averaged problem fails for low-eccentricity QS orbits.

F L4 and F L5 merge with F L3 at high eccentricities.

F L3 bifurcates into a stable family.

Abstract

In the circular case of the coplanar Restricted Three-body Problem, we studied how the family of quasi-satellite (QS) periodic orbits allows to define an associated libration center. Using the averaged problem, we highlighted a validity limit of this one: for QS orbits with low eccentricities, the averaged problem does not correspond to the real problem. We do the same procedure to L 3 , L 4 and L 5 emerging periodic orbits families and remarked that for very high eccentricities F L4 and F L5 merge with F L3 which bifurcates to a stable family.