On the restricted circular three-charged-body problem

Abstract

Two-charged bodiesM ₁ andM ₂ revolve round their centre of mass in circular orbits under Newton's inverse-square law and the so similar Coulomb's law. A third-charged-bodyM, without mass and charge (i.e., such that it is attracted or repulsed byM ₁ andM ₂, but does not influence their motion), moves in a field with a force function, namely

$$U = {\text{ }}\frac{{q - \mu }}{{r_1 }}{\text{ }} + {\text{ }}\frac{{\mu - q}}{{r_2 }}$$

,

which is created byM ₁ andM ₂.

In what follows, the existence and location of the collinear and equilateral Lagrangian points or solutions with be discussed and the interpretation of them will be given. This work is a generalization of the classical restricted circular three-body problem.