ABSTRACT
In the 19th century the American mathematician G. W. Hill devised a simple and useful approximation for the motion of the moon around the earth with perturbations by the sun. To most dynamical astronomers “Hill’s Problem” still means a model for motions in the solar system in which two nearby bodies move in nearly circular orbits about another much larger body at a great distance. These lectures have, however, been motivated by a problem in stellar dynamics. Stars gradually escape from star clusters. This chapter is devoted to the dynamics of escape and analyses the very definition of escape. It shows some ways in which the computation of the escape rate can be approached. In two star clusters there are stars whose radial velocity alone appears to exceed the escape velocity. Perhaps these are indeed stars permanently bound within the cluster at energies above the escape energy.
