Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem

Abstract

Starting from 80 families of low-energy fast periodic transfer orbits in the Earth-Moon planar circular Restricted Three Body Problem (RTBP), we obtain by analytical continuation 11 periodic orbits and 25 periodic arcs with similar properties in the Sun-Earth-Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their stability parameters and minimal distances to the Earth and Moon. The periods of these orbits are between 2.5 and 5 synodic months, their energies are among the lowest possible to achieve an EarthMoon transfer, and they show a diversity of circumlunar trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close approaches to the last.

Invariant manifolds in Hamiltonian systems with applications to the Earth-Moon system

“…It is worth mentioning that calculating periodic orbits is generally a difficult task, specially in more complicated versions of the three-body problem which considers, for example, the influence of the Sun, the eccentricity of the lunar orbit, or the mass of the third particle [1]. With this, another relevance of studying periodic solutions in the circular restricted three-body problem, whose determination already relies on numerical or ad hoc mathematical methods [17], is that these solutions can be used as a basis for finding orbits in such complicated models [28,29].…”

Using space manifold dynamics to deploy a small satellite constellation around the Moon

“…SMD is today a very active research field with a considerable number of papers published on the subject in recent years, covering various aspects of the problem (Leiva and Briozzo 2008;Érdi et al 2009;Baig and McInnes 2009;Mingotti et al 2009; Barrabés et al 2009;Pergola et al 2009, just to name a few).…”

Quasi-bielliptic three-body problem

“…从QBCP的准周期Halo轨道出发, Andreu计算得到 了时间超过41年的真实地月星历(Real Ephemeris, REMS)下的L 2 附近的Halo轨道 [14] . 由地月平面CRTBP 模型下的80个低能快速周期转移轨道族出发, Leiva和 Briozzo [15] 利用关系式 7, 方程(6)简化为…”