An asymptotic solution to the bounded plane circular three body problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1606-1629
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The motion of a mass point in the gravitational field of two bodies traveling in circular orbits about their center of mass is considered. The mass ratio of the two bodies is equal to $\varepsilon\ll 1$. When the mass point passes close to the smaller mass, the character of its trajectory changes abruptly, and the trajectory asymptotics as $\varepsilon\to 0$ is complex. A uniform asymptotic expansion of the entire trajectory accurate to any power of $\varepsilon$ is constructed and validated. In particular, an algorithm is presented for finding the limiting turning angle of the trajectory after the mass point passes near the smaller mass.
@article{ZVMMF_2005_45_9_a8,
author = {A. E. El'bert},
title = {An asymptotic solution to the bounded plane circular three body problem},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1606--1629},
publisher = {mathdoc},
volume = {45},
number = {9},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a8/}
}
TY - JOUR AU - A. E. El'bert TI - An asymptotic solution to the bounded plane circular three body problem JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2005 SP - 1606 EP - 1629 VL - 45 IS - 9 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a8/ LA - ru ID - ZVMMF_2005_45_9_a8 ER -
A. E. El'bert. An asymptotic solution to the bounded plane circular three body problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1606-1629. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a8/