Effect of three-body interaction on the number and location of equilibrium points of the restricted three-body problem

In this paper we deal with a modified version of the classical restricted three-body problem in which the additional effect of a three-body interaction is considered. This new force component appears in the potential of the classical problem as a new additional term. Our aim is to study the existence of all equilibrium points of this new model-problem as well as to determine their number and location, in the full range of the parameters of the problem, using analytical techniques. It is found that, depending on the sign and magnitude of the three-body interaction, the number of collinear and triangular equilibrium points may vary from 1 to 7 and 0 to 4, respectively, contrary to the classical case where the number of these equilibria is fixed to 3 and 2, correspondingly. Also, another remarkable result is that out of the orbital plane equilibria may exist.