Newtonian restricted three-body gravitational problem with positive and negative point masses

Abstract

The Newtonian restricted three-body problem involving a positive primary point mass, m+, and a negative secondary point mass, m-, in a circular orbit, and a positive or negative tertiary point mass, m3, with m+>|m-|≫|m3|, is solved. Five Lagrange points are found for m3, three of which are coplanar with m+ and m-, and two of which are not, a subtle consequence of the gravitational repulsion from m-. All Lagrange points are linearly unstable, except for one point in the regime m+≳8.4|m-|, which is linearly stable and collinear with m+ and m-.