Relative equilibria and periodic orbits in a Circular Planar (2+2)-Body Problem, Equilibria in an accelerated three-body problem

Abstract

Relative equilibria and periodic orbits in a Circular Planar (2+2)-Body Problem Authors: Lennard F. Bakker, Nicholas J. Freeman We present a planar four-body model, the Circular Planar (2+2)-Body Problem, for the motion of two asteroids (having small but positive masses) moving under the gravitational attraction of each other and under the gravitational attraction of two primaries (with masses much larger than the two smaller mass bodies) moving in uniform circular motion about their center of mass. Equilibria in an accelerated three-body problem The general three-body problem is investigated with the addition of an external force applied to one of the masses. It is firstly demonstrated that the centre-of-mass of the three-body system accelerates. Then, it is demonstrated that only a single, unstable, collinear equilibrium solution exits in the accelerating frame. While unstable, it is also demonstrated that this single equilibrium configuration is in principle controllable using additional control accelerations distributed between the masses. Potential applications of such an accelerated collinear equilibrium configuration are discussed for the active manoeuvring of chains of small asteroids for space resource utilisation.