Premium
Asymptotic solution to the restricted three‐body problem with a mass point moving near a small‐mass body
Author(s) -
El'bert Alexander
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1293
Subject(s) - trajectory , center of mass (relativistic) , limiting , mathematics , three body problem , point (geometry) , reduced mass , point particle , mathematical analysis , classical mechanics , geometry , physics , mechanical engineering , energy–momentum relation , astronomy , engineering
Abstract 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.