doi:10.1016/j.asr.2007.03.020
Copyright © 2007 COSPAR Published by Elsevier Ltd.
Alternative paths for insertion of probes into high inclination lunar orbits
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C.F. de Meloa, 
, 
, E.E.N. Macaua, O.C. Winterb and E. Vieira Netob
aInstituto Nacional de Pesquisas Espaciais, Av. dos Astronautas 1752, São José dos Campos, SP 12227-010, Brazil
bUNESP – Grupo de Dinâmica Orbital e Planetologia, CP 205, Guaratinguetá, SP 12516-410, Brazil
Received 1 November 2006;
revised 7 March 2007;
accepted 10 March 2007.
Available online 19 March 2007.
Abstract
The dynamics of the restricted three-body Earth–Moon-particle problem predicts the existence of direct periodic orbits around the Lagrangian equilibrium point L1. From these orbits, we derive a set of trajectories that form links between the Earth and the Moon and are capable of performing transfers between terrestrial and lunar orbits, in addition to defining an escape route from the Earth–Moon system. When we consider a more complex and realistic dynamical system – the four-body Sun–Earth–Moon-particle (probe) problem – the trajectories have an expressive gain of inclination when they penetrate in the lunar influence sphere, thus allowing the insertion of probes into low-altitude lunar orbits with high inclinations, including polar orbits. In this study, we present these links and investigate some possibilities for performing an Earth–Moon transfer based on these trajectories.
Keywords: Astrodynamics; Mission design; Earth–Moon transfer; Orbital maneuvers
Fig. 1. Synodic reference system and the relative location of the Lagrangian equilibrium points.
Fig. 2. Periodic orbits of Family G seen in the synodic coordinate system: (a) 
, (b) 
and (c) 
.
Fig. 3. Illustration of quantities involved in Earth–Moon transfer based on a trajectory derived from a Family G orbit seen in the synodic system (not to scale).
Fig. 4. Injection speed VI as a function of altitude of the initial circular terrestrial orbit HT, for collision trajectories with the Moon.
Fig. 5. Typical trajectory found for four-body problem, with HT = 240 km, VI = 10.9015 km/s, 
= −1.60 × 10−4 km/s, HL = 38.6 km, VL = 2.589 km/s, i = 41.7°, Ω = 117° and Tv = 13.913 days seen in a geocentric coordinate system. (a) Spatial view and (b) view in plane xz. (VL is the magnitude of the trajectory’s velocity at the periselenium and Tv is the flight time between the terrestrial orbit and the periselenium).
Fig. 6. Earth–Moon–Earth links seen in the synodic system extended to the Four-body problem. The area in dark grey contains only trajectories with 0 < HL 
100 km and the area in light grey contains trajectories with 100 < HL 20,000 km.
Fig. 7. Representation of the swing-by with the Moon for trajectories with periselenium in the anterior region to the Moon (not to scale).
Fig. 8. Typical escape trajectory from the Earth–Moon System. After the Swing-by with the Moon (not to scale).
Fig. 9. Projections in the xy plane of the synodic system: (a) escape route from the Earth–Moon System superimposed on the Earth–Moon link and (b) amplification showing the region between L1 and the Moon with trajectories crossing the xy plane in the ascending direction.
Fig. 10. Illustration of the basic geometry of the guided transfer in the geocentric coordinate system (not to scale).
Fig. 11. Diagrams (a) ΔVTotal × HL and (b) ΔVTotal × i. Leaving from a LEO (Low Earth Orbit) with HT = 240 km.
Table 1.
Relation between and HL for periselenium in the anterior region to the Moon
Table 2.
Relation between and HL for periselenium in the posterior region to the Moon
Table 3.
ΔVTotal of guided transfer for a path G with HT = 240 km and i 
90°
Corresponding author. Tel.: +55 32 3241 4744.
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