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New periodic orbits in the solar sail three-body problem

Biggs, J.D. and Waters, T. and McInnes, C.R. (2011) New periodic orbits in the solar sail three-body problem. In: Nonlinear Science and Complexity. Springer, pp. 131-138. ISBN 9789048198832

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Abstract

We identify displaced periodic orbits in the circular restricted three-body problem, wher the third (small) body is a solar sail. In particular, we consider solar sail orbits in the earth-sun system which are high above the exliptic plane. It is shown that periodic orbits about surfaces of artificial equilibria are naturally present at linear order. Using the method of Lindstedt-Poincare, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the solar sail elliptical restricted three-body problem. A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e=0 and continuing to the requied eccentricity of e=0.0167. The stability of these periodic orbits is investigated.