Libration Points in Schwarzschild's Circular Restricted Three-Body Problem

Abstract

The restricted three-body problem in Schwarzschild’s gravitational field is analyzed. The existence of the equilibrium points in the orbital plane is discussed and the corresponding positions are established. There are three collinear libration points, and, if they exist, two triangular libration points (situated in the orbital plane of the primaries). If triangular points exist, they may not form equilateral triangles; the triangles are isosceles for equal masses of the primaries, and scalene else.