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Title of Journal: Astrophys Space Sci

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Abbravation: Astrophysics and Space Science

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Springer Netherlands

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DOI

10.1002/nme.1620261105

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1572-946X

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Doublysymmetric horseshoe orbits in the general p

Authors: Abimael Bengochea Jorge Galán Ernesto PérezChavela
Publish Date: 2013/08/23
Volume: 348, Issue: 2, Pages: 403-415
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Abstract

We present some results about the continuation of doublysymmetric horseshoe orbits in the general planar threebody problem This is done by means of solving a boundary value problem with one free parameter which is the quotient of the masses of two bodies μ 3=m 3/m 1 keeping constant μ 2=m 2/m 1 m 1 represents the mass of a big planet whereas m 2 and m 3 of minor bodies For the numerical continuation of the horseshoe orbits we have considered m 2/m 1=35×10−4 and the variation of μ 3 from 35×10−4 to 97×10−5 or vice versa depending on the orbit selected as “seed” We discuss some issues related to the periodicity and symmetry of the orbits We study the stability of some of them taking the limit μ 3→0 The numerical continuation was done using the software AUTOThe first author is pleased to acknowledge the financial support from CONACYTMéxico which allows him a postdoctoral stay in the Departamento de Matemática Aplicada II of the Universidad de Sevilla and the facilities given by the Universidad de Sevilla The second author wishes to acknowledge financial support from the Spanish government through grants MTM200907849 and MTM201231821 The first and third authors have been partially supported by CONACYT Grant 128790

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