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−. Published by the American Physical Society 2024