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.