Regularization in the Restricted Four Body Problem

Abstract

The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian config- uration of the three-body problem, i,e,. they remain fixed at the apices of an equilateral triangle in a rotating coordinate system. A massless fourth body moves under the Newtonian gravitation law due to the three pri- maries; as in the restricted three-body problem the fourth mass does not affect the motion of the three primaries. In this paper we show a global regularization of binary collisions of the infinitesimal body with two of the primaries.