There exist families of periodic orbits around relative equilibrium points 
in the circular restricted three body problem (CR3BP). There also exist 
homoclinic connections to some of these periodic orbits, and heteroclinic 
connections between them. An existing algorithm that finds, using homotopy 
techniques, and continues connecting orbits in three-dimensional systems 
of ordinary differential equations is adapted to apply to this six 
dimensional Hamiltonian system. We then use this algorithm to find 
homoclinic and heteroclinic connections and continue them as the mass 
ratio between the two heavy bodies in the CR3BP is varied.

The algorithm is now partially, for homoclinic connections only, 
implemented using AUTO-07p, an updated version of the well-known
continuation package AUTO. Using this software we show a demo that 
computes and continues a homoclinic connection.