Integration theory for the elliptic restricted three-body problem

Details Integration theory for the elliptic restricted three-body problem Integration theory for the elliptic restricted three-body problem

Sep 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989a%26a...222..344h&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 222, no. 1-2, Sept. 1989, p. 344-352.

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Computation

3

Elliptic Functions, Jacobi Integral, Three Body Problem, Angular Momentum, Computational Astrophysics, Equations Of Motion, Partial Differential Equations

Scientific paper

The restricted elliptic three body problem is investigated analytically with respect to the problem of finding limits of space in which the infinitesimal body, under given circular initial condition, can move. Using synodic, rotating, and barycentric coordinates, approximate integrals are found which limit the region of nonnegative velocities. The analytic results are in good agreement with numerical experiments up to eccentricities of about 0.25. The dependence of these results with respect to the mass ratio of the primaries and the initial angle is discussed.

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