The phenomenon of chaotic scattering is described in the context of satellite encounters. We consider a one-parameter family of orbits obtained by starting with two satellites on circular, coplanar and close orbits. We numerically find that this family exhibits a large number of discontinuities, probably an infinite number. This phenomenon seems to be due to the existence of homoclinic and heteroclinic points of unstable periodic orbits. We model the chaotic scattering by a simple billiard: a point particle bounces on two disks and in addition is subjected to a constant acceleration. This leads to a one-parameter family with chaotic scattering. With the help of symbolic dynamics, the structure of the family can be completely elucidated.