Asymptotic Orbits at the Triangular Equilibria in the Photogravitational Restricted Three-Body Problem

Author: Papadakis, K.

Source: Astrophysics and Space Science, Volume 305, Number 1, September 2006 , pp. 57-66(10)

Publisher: Springer

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Abstract:

We study numerically the asymptotic homoclinic and heteroclinic orbits associated with the triangular equilibrium points L 4 and L 5, in the gravitational and the photogravitational restricted plane circular three-body problem. The invariant stable-unstable manifolds associated to these critical points, are also presented. Hundreds of asymptotic orbits for equal mass of the primaries and for various values of the radiation pressure are computed and the most interesting of them are illustrated. In the Copenhagen case, which the problem is symmetric with respect to the x- and y-axis, we found and present non-symmetric heteroclinic asymptotic orbits. So pairs of heteroclinic connections (from L 4 to L 5 and vice versa) form non-symmetric heteroclinic cycles. The termination orbits (a combination of two asymptotic orbits) of all the simple families of symmetric periodic orbits, in the Copenhagen case, are illustrated.

Keywords: Asymptotic orbit; Cut of Poincaré; Heteroclinic orbit; Homoclinic orbit; Periodic orbit; Photogravitational restricted three-body problem; Triangular points; surface of section

Document Type: Research Article

DOI: http://dx.doi.org/10.1007/s10509-006-9043-x

Affiliations: Email: k.papadakis@des.upatras.gr

Publication date: September 1, 2006

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