Homoclinic and heteroclinic orbits in the photogravitational restricted three-body problem

Details Homoclinic and heteroclinic orbits in the photogravitational restricted three-body problem Homoclinic and heteroclinic orbits in the photogravitational restricted three-body problem

Apr 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006ap%26ss.302...67p&link_type=abstract

Astrophysics and Space Science, Volume 302, Issue 1-4, pp. 67-82

Astronomy and Astrophysics

Astrophysics

4

Photogravitational Restricted Three-Body Problem, Asymptotic Orbit, Homoclinic Orbit, Heteroclinic Orbit, Cut Of Poincar&Eacute, Surface Of Section, Periodic Orbit, Lyapunov Orbit

Scientific paper

We study numerically the asymptotic homoclinic and heteroclinic orbits around the hyperbolic Lyapunov periodic orbits which emanate from Euler's critical points L 1 and L 2, in the photogravitational restricted plane circular three-body problem. The invariant stable-unstable manifolds associated to these Lyapunov orbits, are also presented. Poincaré surface of sections of these manifolds on appropriate planes and several homoclinic and heteroclinic orbits for the gravitational case as well as for varying radiation factor q 1, are displayed. Homoclinic-homoclinic and homoclinic-heteroclinic-homoclinic chains which link the interior with the exterior Hill's regions, are illustrated. We adopt the Sun-Jupiter system and assume that only the larger primary radiates. It is found that for small deviations of its value from the gravitational case ( q 1 = 1), the radiation pressure exerts a significant impact on the Hill's regions and on these asymptotic orbits.

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