New periodic orbits in the solar sail restricted three body problem

J.D. Biggs, C. McInnes, Thomas Waters

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In this paper we consider periodic orbits of a solar sail in the Earth-Sun restricted three-body problem. In particular, we consider orbits which are high above the ecliptic plane, in contrast to the classical Halo orbits about the collinear equilibria. We begin with the Circular Restricted Three-Body Problem (CRTBP) where periodic orbits about 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 Elliptic Restricted Three Body Problem (ERTBP). 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
Number of pages11
Publication statusPublished - Jul 2008
Event2nd Conference on Nonlinear Science and Complexity - Porto, Portugal
Duration: 28 Jul 200831 Jul 2008


Conference2nd Conference on Nonlinear Science and Complexity
CityPorto, Portugal


  • periodic orbits
  • solar sail
  • elliptic three body problem


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