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On the quasi-equilibria of the BiElliptic four-body problem with non-coplanar motion of primaries

Assadian, N ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1016/j.actaastro.2009.05.014
  3. Publisher: 2010
  4. Abstract:
  5. In this study the effect of the Sun on the Lagrange points of the Earth-Moon system is investigated. A restricted four-body problem (R4BP) is introduced to take into account the effect of the Sun, Earth and Moon on the motion of an infinitesimal particle. The motion of the Earth-Moon-barycenter (EMB) around the Sun is considered to be elliptic in the ecliptic plane. Similarly, the motion of the Moon around the Earth is presumed to be elliptic, but out of the ecliptic plane. In this way, a spatial R4BP with non-coplanar motion of primaries is derived, which is named as BiElliptic problem (BEP). Transforming the equations of motion to a coordinate system originated at the EMB that rotates with the variable angular velocity of the Moon around the Earth, allows for the investigation of the effect of the Sun on the Lagrange points of the Earth-Moon circular restricted three-body system. The results reveal that the L1 and L2 points are replaced with nearby complex quasi-periodic orbits with considerable deviation from the Earth-Moon line of axes. These orbits are highly unstable and were found with the aid of a new algorithm developed for this purpose. The L3 quasi-equilibrium is greatly displaced, such that its trace approaches those of L4 and L5 with considerable overlaps. Also, for some specific time intervals two additional quasi-equilibrium points are detected for the real Sun-Earth-Moon BEP. In addition, a parametric study is also performed to detect the conditions for which the structure of the quasi-equilibria changes. © 2009 Elsevier Ltd. All rights reserved
  6. Keywords:
  7. BiElliptic problem (BEP) ; Lagrange points ; Non-coplanar motion of primaries ; Quasi-equilibria ; Quasi-periodic orbits ; Restricted four-body problem (R4BP) ; BiElliptic problem (BEP) ; Lagrange points ; Non-coplanar motion of primaries ; Quasi-equilibria ; Quasi-periodic orbits ; Restricted four-body problem (R4BP) ; Equations of motion ; Lagrange multipliers ; Orbits ; Space flight ; Sun ; Time varying systems ; Moon
  8. Source: Acta Astronautica ; Volume 66, Issue 1-2 , 2010 , Pages 45-58 ; 00945765 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0094576509003270