Dependence of the probability of escape on the Jacobi constant in the N-body ring problem without central body

Abstract

In this work, we perform a numerical exploration of the escape in the N-body ring problem in absence of a central body, for 4≤N≤9 and ten values of the Jacobi constant. We show how the probability of escape per interval of time varies as a function of the Jacobi constant, finding that, for values of the Jacobi constant smaller than a certain limit value, the probability of escape from the system tends to decrease with time. However, if we consider values of the Jacobi constant larger than this limit value, the probability of escape grows with time, for times of escape smaller than 100 units of time.