Parabolic solutions for the planar \(N\)-centre problem: multiplicity and scattering (Q1647876)

This paper deals with the planar \(N\)-centre problem and proves the existence of parabolic solutions. The \(N\)-centre system can be seen as a central problem of celestial mechanics where \(N\) fixed heavy objects provide an attracting potential for a test particle. In this paper, two theorems are presented and proven. They deal with self-interaction free parabolic solutions of the corresponding \(N\)-centre Hamiltonian for certain asymptotic directions. Furthermore, entire parabolic solutions, the virial identity and a generalized solution are discussed. In the single-body limit, the Kepler problem is recovered.