New periodic orbits in the solar sail three-body problem

J. D. Biggs*, T. Waters, C. McInnes

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


We identify displaced periodic orbits in the circular restricted three-body problem, where 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 ecliptic plane. It is shown that periodic orbits about surfaces of artificial equilibria are naturally present at linear order. Using the method of Lindstedt-Poincaré, 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 required eccentricity of e=0.0167. The stability of these periodic orbits is investigated.

Original languageEnglish
Title of host publicationNonlinear Science and Complexity
EditorsJ. A. Tenreiro Machado, Alberto C. J. Luo, Ramiro S. Barbosa, Manuel F. Silva, Lino B. Figueiredo
PublisherSpringer Netherlands
Number of pages8
ISBN (Electronic)9789048198849
ISBN (Print)9789048198832
Publication statusPublished - 2011


  • Displaced periodic orbits
  • Restricted three body problem
  • Solar sail


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