New periodic orbits in the solar sail restricted three body problem

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

Research output: Contribution to conferencePaper

Abstract

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.
LanguageEnglish
Number of pages11
Publication statusPublished - Jul 2008
Event2nd Conference on Nonlinear Science and Complexity - Porto, Portugal
Duration: 28 Jul 200831 Jul 2008

Conference

Conference2nd Conference on Nonlinear Science and Complexity
CityPorto, Portugal
Period28/07/0831/07/08

Fingerprint

Orbits
Nonlinear equations
Sun
Equations of motion
Earth (planet)

Keywords

  • periodic orbits
  • solar sail
  • elliptic three body problem

Cite this

Biggs, J. D., McInnes, C., & Waters, T. (2008). New periodic orbits in the solar sail restricted three body problem. Paper presented at 2nd Conference on Nonlinear Science and Complexity, Porto, Portugal, .
Biggs, J.D. ; McInnes, C. ; Waters, Thomas. / New periodic orbits in the solar sail restricted three body problem. Paper presented at 2nd Conference on Nonlinear Science and Complexity, Porto, Portugal, .11 p.
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Biggs, JD, McInnes, C & Waters, T 2008, 'New periodic orbits in the solar sail restricted three body problem' Paper presented at 2nd Conference on Nonlinear Science and Complexity, Porto, Portugal, 28/07/08 - 31/07/08, .

New periodic orbits in the solar sail restricted three body problem. / Biggs, J.D.; McInnes, C.; Waters, Thomas.

2008. Paper presented at 2nd Conference on Nonlinear Science and Complexity, Porto, Portugal, .

Research output: Contribution to conferencePaper

TY - CONF

T1 - New periodic orbits in the solar sail restricted three body problem

AU - Biggs, J.D.

AU - McInnes, C.

AU - Waters, Thomas

PY - 2008/7

Y1 - 2008/7

N2 - 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.

AB - 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.

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Biggs JD, McInnes C, Waters T. New periodic orbits in the solar sail restricted three body problem. 2008. Paper presented at 2nd Conference on Nonlinear Science and Complexity, Porto, Portugal, .