On the Periodic Orbits of the Perturbed Two- and Three-Body Problems

Abstract

In this work, a perturbed system of the restricted three-body problem is derived when the perturbation forces are conservative alongside the corresponding mean motion of two primaries bodies. Thus, we have proved that the first and second types of periodic orbits of the rotating Kepler problem can persist for all perturbed two-body and circular restricted three-body problems when the perturbation forces are conservative or the perturbed motion has its own extended Jacobian integral.

Keywords

• restricted 3–body problem
• first- (second)-type periodic orbits
• conservative forces
• first integral of motion