Evolution of the L1 halo family in the radial solar sail CRTBP

Patricia Verrier, Thomas Waters, Jan Sieber

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We present a detailed investigation of the dramatic changes that occur in the L1 halo family when radiation pressure is introduced into the Sun-Earth circular restricted three-body problem (CRTBP). This photo-gravitational CRTBP can be used to model the motion of a solar sail orientated perpendicular to the Sun-line. The problem is then parameterized by the sail lightness number, the ratio of solar radiation pressure acceleration to solar gravitational acceleration. Using boundary-value problem numerical continuation methods and the AUTO software package (Doedel et al. 1991) the families can be fully mapped out as the parameter ß is increased. Interestingly, the emergence of a branch point in the retrograde satellite family around the Earth at  ß ~ 0:0387 acts to split the halo family into two new families. As radiation pressure is further increased one of these new families subsequently merges with another non-planar family at ß ~ 0:289, resulting in a third new family. The linear stability of the families changes rapidly at low values of ß, with several small regions of neutral stability appearing and disappearing. By using existing methods within AUTO to continue branch points and period-doubling bifurcations, and deriving a new boundary-value problem formulation to continue the folds and Krein collisions, we track bifurcations and changes in the linear stability of the families in the parameter ß and provide a comprehensive overview of the halo family in the presence of radiation pressure. The results demonstrate that even at small values of ß there is significant difference to the classical CRTBP, providing opportunity for novel solar sail trajectories. Further, we also find that the branch points between families in the solar sail CRTBP provide a simple means of generating certain families in the classical case.
LanguageEnglish
Pages373-400
Number of pages27
JournalCelestial Mechanics and Dynamical Astronomy
Volume120
Issue number4
Early online date31 Aug 2014
DOIs
Publication statusPublished - Dec 2014

Fingerprint

Restricted Three-body Problem
ice ridge
three body problem
radiation pressure
halos
Radiation
boundary value problems
Sun
Boundary value problems
sun
Earth (planet)
Bifurcation (mathematics)
period doubling
Branch Point
solar radiation
Solar radiation
Software packages
Numerical methods
Trajectories
trajectories

Keywords

  • circular restricted three-body problem
  • solar sails
  • periodic orbits
  • halo orbits
  • numerical continuation

Cite this

Verrier, Patricia ; Waters, Thomas ; Sieber, Jan. / Evolution of the L1 halo family in the radial solar sail CRTBP. In: Celestial Mechanics and Dynamical Astronomy. 2014 ; Vol. 120, No. 4. pp. 373-400.
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Evolution of the L1 halo family in the radial solar sail CRTBP. / Verrier, Patricia; Waters, Thomas; Sieber, Jan.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 120, No. 4, 12.2014, p. 373-400.

Research output: Contribution to journalArticle

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AU - Waters, Thomas

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AB - We present a detailed investigation of the dramatic changes that occur in the L1 halo family when radiation pressure is introduced into the Sun-Earth circular restricted three-body problem (CRTBP). This photo-gravitational CRTBP can be used to model the motion of a solar sail orientated perpendicular to the Sun-line. The problem is then parameterized by the sail lightness number, the ratio of solar radiation pressure acceleration to solar gravitational acceleration. Using boundary-value problem numerical continuation methods and the AUTO software package (Doedel et al. 1991) the families can be fully mapped out as the parameter ß is increased. Interestingly, the emergence of a branch point in the retrograde satellite family around the Earth at  ß ~ 0:0387 acts to split the halo family into two new families. As radiation pressure is further increased one of these new families subsequently merges with another non-planar family at ß ~ 0:289, resulting in a third new family. The linear stability of the families changes rapidly at low values of ß, with several small regions of neutral stability appearing and disappearing. By using existing methods within AUTO to continue branch points and period-doubling bifurcations, and deriving a new boundary-value problem formulation to continue the folds and Krein collisions, we track bifurcations and changes in the linear stability of the families in the parameter ß and provide a comprehensive overview of the halo family in the presence of radiation pressure. The results demonstrate that even at small values of ß there is significant difference to the classical CRTBP, providing opportunity for novel solar sail trajectories. Further, we also find that the branch points between families in the solar sail CRTBP provide a simple means of generating certain families in the classical case.

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