Escape Distribution for an Inclined Billiard

Hénon [8] used an inclined billiard to investigate aspects of chaotic scattering which occur in satellite encounters and in other situations. His model consisted of a piecewise mapping which described the motion of a point particle bouncing elastically on two disks. A one parameter family of orbits, named $h$-orbits, was obtained by starting the particle at rest from a given height. We obtain an analytical expression for the escape distribution of the $h$-orbits, which is also compared with results from numerical simulations. Finally, some discussion is made about possible applications of the $h$-orbits in connection with Hill’s problem.