Collision Singularities in Gravitational Problems

Abstract

The rotating-pulsating coordinate system commonly used in the elliptic restricted problem of three bodies is modified to be useful also in the limit of rectilinear motion of the primaries. In these coordinates the homographic solutions of the problem of n bodies are equilibrium solutions, and so are, in particular, the homothetic solutions leading to a collision of n bodies. General collision solutions are thus obtained as solutions which asymptotically approach these equilibriums. In an example of a continuable triple collision the expansion valid at the singularity is given explicitely.