Three-body orbital stability criteria for circular orbits

Orbital phasing of satellites on circular orbits

Chaining Periodic Three-Body Orbits

This paper studies how to construct orbit transfers, chains, and complex periodic orbits in the planar circular restricted three-body problem using the invariant manifolds of unstable three-body orbits. It is shown that the Poincaré map is a useful tool to identify and construct transfer trajectories from one orbit to another, i.e., homoclinic and heteroclinic orbit connections, with applicatio...

Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - Part II

We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem (PCR3BP) corresponding to the Sun-JupiterOterma system possesses an infinite number of symmetric periodic orbits and homoclinic orbits to the Lyapunov orbits. More...

Three classes of newtonian three-body planar periodic orbits.

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits' geome...

Oscillatory motions for the restricted planar circular three body problem

In this paper we consider the circular restricted three body problem which models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies, the primaries, which move along circular planar Keplerian orbits. In a suitable system of coordinates, this system has two degrees of freedom and the conserved energy is usually called the Jacobi cons...