Collinear solution to the three-body problem under a scalar-tensor gravity

Abstract

The three-body problem in the framework of a scalar-tensor theory of gravitation is considered. We find that the collinear solution to this problem exists in the presence of the scalar field. Through some numerical examples, we investigate the effects of the scalar field on this solution, the angular velocity of the system and the positions of Lagrange points. We find that while the scalar field's effects on the Lagrange points of the planets in the Solar System are practically beyond the limits of the current technology, a compact binary with comparable masses will be a good test bed.