Study of lunar gravity assist orbits in the restricted four-body problem

In this paper, the lunar gravity assist (LGA) orbits starting from the Earth are investigated in the Sun–Earth–Moon–spacecraft restricted four-body problem (RFBP). First of all, the sphere of influence of the Earth–Moon system (SOIEM) is derived. Numerical calculation displays that inside the SOIEM, the effect of the Sun on the LGA orbits is quite small, but outside the SOIEM, the Sun perturbation can remarkably influence the trend of the LGA orbit. To analyze the effect of the Sun, the RFBP outside the SOIEM is approximately replaced by a planar circular restricted three-body problem, where, in the latter case, the Sun and the Earth–Moon barycenter act as primaries. The stable manifolds associated with the libration point orbit and their Poincaré sections on the SOIEM are applied to investigating the LGA orbit. According to our research, the patched LGA orbits on the Poincaré sections can efficiently distinguish the transit LGA orbits from the non-transit LGA orbits under the RFBP. The former orbits can pass through the region around libration point away from the SOIEM, but the latter orbits will bounce back to the SOIEM. Besides, the stable transit probability is defined and analyzed. According to the variant requirement of the space mission, the results obtained can help us select the LGA orbit and the launch window.

[1]  C. Ocampo.  Transfers to Earth centered orbits via lunar gravity assist , 2003 .

[2]  Shane D. Ross,et al.  Low Energy Transfer to the Moon , 2001 .

[3]  M. Dellnitz,et al.  Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario , 2012 .

[4]  K. C. Howell,et al.  Trajectory Design in the Sun- Earth- Moon System Using Lunar Gravity Assists , 1998 .

[5]  Shane D. Ross,et al.  Connecting orbits and invariant manifolds in the spatial restricted three-body problem , 2004 .

[6]  Junichiro Kawaguchi,et al.  On making use of lunar and solar gravity assists in LUNAR-A, PLANET-B missions , 1995 .

[7]  Victor Szebehely,et al.  Theory of Orbits. , 1967 .

[8]  J. Marsden,et al.  Dynamical Systems, the Three-Body Problem and Space Mission Design , 2009 .

[9]  Christian Circi,et al.  On the Dynamics of Weak Stability Boundary Lunar Transfers , 2001 .

[10]  Sidney A. Davis,et al.  Optimization of a multiple lunar-swingby trajectory sequence. , 1984 .

[11]  Shijie Xu,et al.  Earth-to-Moon Low Energy Transfer Using Time-dependent Invariant Manifolds , 2012 .

[12]  Kazuyuki Yagasaki,et al.  Sun-perturbed earth-to-moon transfers with low energy and moderate flight time , 2004 .

[13]  R. Castelli.  Regions of prevalence in the coupled restricted three-body problems approximation , 2012 .

[14]  Yi Qi,et al.  Mechanical analysis of lunar gravity assist in the Earth–Moon system , 2015 .

[15]  Paul A. Penzo.  A Survey and Recent Development of Lunar Gravity Assist , 2000 .

[16]  F. Topputo.  On optimal two-impulse Earth–Moon transfers in a four-body model , 2013 .

[17]  Daniel J. Scheeres,et al.  The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System , 1998 .

[18]  Shijie Xu,et al.  Gravitational lunar capture based on bicircular model in restricted four body problem , 2014 .

[19]  Michael Dellnitz,et al.  On target for Venus – set oriented computation of energy efficient low thrust trajectories , 2006 .