Horseshoe Periodic Orbits in the Restricted Three Body Problem

Abstract

We consider the circular restricted three-body problem (CRTBP) in the synodical system of coordinates for values of the Jacobi constant C in the interval (3, C1) (where C1 is the value of C at the collinear equilibrium point L 1). We describe the existence of families of horseshoe periodic orbits when varying the mass parameter and the Jacobi constant. The relation between such orbits and the invariant manifolds of the Lyapunov families of periodic orbits around the collinear equilibrium point L 3 is also analysed.