Frequencies and resonances around L4 in the elliptic restricted three-body problem

Pintérné Rajnai, Renáta and Nagy, Imre and Érdi, Bálint (2014) Frequencies and resonances around L4 in the elliptic restricted three-body problem. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 443 (3). pp. 1988-1998. ISSN 0035-8711

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Abstract

The stability of the Lagrangian point L4 is investigated in the elliptic restricted three-body problem by using Floquet’s theory. Stable and unstable domains are deter- mined in the parameter plane of the mass parameter and the eccentricity by computing the characteristic exponents. Frequencies of motion around L4 have been determined both in the stable and unstable domains and fitting functions for the frequencies are derived depending on the mass parameter and the eccentricity. Resonances between the frequencies are studied in the whole parameter plane. It is shown that the 1:1 resonances are not restricted only to single curves but extend to the whole unstable domain. In the unstable domains longer escape times of the test particle from the neighbourhood of L4 are related to certain resonances, but changing the parameters the same resonances may lead to faster escape.

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