Formulation of the restricted three-body problem with two-center problem orbits as intermediate orbits

Langebartel, R.G.

Astrophysics and Space Science 75(2): 437-454


ISSN/ISBN: 0004-640X
Accession: 084132921

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The restricted three-body Hamiltonian is partitioned into a two-center type principal part and its accompanying perturbational part. The mathematical analysis, involving the Jacobian elliptic functions, is adapted for the case of figure-eight orbits winding around the two given mass points. For many such orbits the elliptic function modulusk is small and can serve as a small parameter. Fourier expansions in terms of a parameter related tot are obtained for the intermediate orbit functions which provide representations in terms of elementary functions.