Asymptotic solution to the restricted three‐body problem with a mass point moving near a small‐mass body

The motion of a mass point in the gravitational field of two bodies traveling along arbitrary orbits about their center of mass is considered. The mass ratio of the two bodies is equal to ε≪1. When the mass point passes close to the smaller mass, the character of its trajectory changes abruptly, and the trajectory asymptotics as ε→0 is complex. The uniform asymptotic expansion of the entire trajectory up to any power of ε is constructed and justified. In particular, an algorithm is presented for finding the limiting turning angle of the trajectory after the mass point passes a neighbourhood of the smaller mass. Copyright © 2010 John Wiley & Sons, Ltd.