Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {An asymptotic solution to the bounded plane circular three body problem},
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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/

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