Stability of the triangular points in the elliptic restricted problem of three bodies

Abstract

In the elliptic restricted problem of three bodies, the relative orbit of two bodies with mass ratio ,s/(1 - ) is an ellipse of eccentricity e, and a third body, of negligible mass, moves in their field. Possible positions of equilibrium occur when the three bodies form equilateral triangles. The stability of these configurations is investigated for general and e, and the region in the -e plane in which there is stability is found. Here "stability" is investigated using only the first-order, linear equations for displacements from the points of equilibrium.