scholarly journals Transfers from the Earth to $$L_2$$ Halo orbits in the Earth–Moon bicircular problem

2021 ◽  
Vol 133 (11-12) ◽  
Author(s):  
José J. Rosales ◽  
Àngel Jorba ◽  
Marc Jorba-Cuscó
Keyword(s):  
Direct Effect ◽  
Body Problem ◽  
Time Dependent ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Halo Orbits ◽  
The Earth ◽  
Gravitational Influence ◽  
Three Body

AbstractThis paper deals with direct transfers from the Earth to Halo orbits related to the translunar point. The gravitational influence of the Sun as a fourth body is taken under consideration by means of the Bicircular Problem (BCP), which is a periodic time dependent perturbation of the Restricted Three Body Problem (RTBP) that includes the direct effect of the Sun on the spacecraft. In this model, the Halo family is quasi-periodic. Here we show how the effect of the Sun bends the stable manifolds of the quasi-periodic Halo orbits in a way that allows for direct transfers.

scholarly journals New relativistic effects in the motion of the Moon

1986 ◽  
Vol 114 ◽  
pp. 407-410
Author(s):  
Bahram Mashhoon
Keyword(s):  
Body Problem ◽  
Gravitational Constant ◽  
Relativistic Effects ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
The Moon ◽  
Three Body Problem ◽  
Novel Approach ◽  
Lunar Motion ◽  
Three Body

A summary of the main relativistic effects in the motion of the Moon is presented. The results are based on the application of a novel approach to the restricted three-body problem in general relativity to the lunar motion. It is shown that the rotation of the Sun causes a secular acceleration in the relative Earth-Moon motion. This might appear to be due to a temporal “variation” of the gravitational constant.

A Framework for Constructing Transfers Linking Periodic Libration Point Orbits in the Spatial Circular Restricted Three-Body Problem

2016 ◽  
Vol 26 (05) ◽  
pp. 1630013 ◽  
Author(s):  
Amanda F. Haapala ◽  
Kathleen C. Howell
Keyword(s):  
Body Problem ◽  
Libration Point ◽  
Mass Parameter ◽  
Solar Radiation Pressure ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Libration Point Orbits ◽  
The Earth ◽  
Three Body ◽  
Fidelity Model

The Earth–Moon libration points are of interest for future missions and have been proposed for both storage of propellant and supplies for lunar missions and as locations to establish space-based facilities for human missions. Thus, further development of an available transport network in the vicinity of the Moon is valuable. In this investigation, a methodology to search for transfers between periodic lunar libration point orbits is developed, and a catalog of these transfers is established, assuming the dynamics associated with the Earth–Moon circular restricted three-body problem. Maneuver-free transfers, i.e. heteroclinic and homoclinic connections, are considered, as well as transfers that require relatively small levels of [Formula: see text]. Considering the evolution of Earth–Moon transfers as the mass parameter is reduced, a relationship emerges between the available transfers in the Earth–Moon system and maneuver-free transfers that exist within the Hill three-body problem. The correlation between transfers in these systems is examined and offers insight into the existence of solutions within the catalog. To demonstrate the persistence of the catalog transfers in a higher-fidelity model, several solutions are transitioned to a Sun–Earth–Moon ephemeris model with the inclusion of solar radiation pressure and lunar gravity harmonics. The defining characteristics are preserved in the high-fidelity model, validating both the techniques employed for this investigation and the solutions computed within the catalog.

scholarly journals Qualitative Dynamics of the Sun-Jupiter-Saturn System

1978 ◽  
Vol 41 ◽  
pp. 53-55
Author(s):  
V. Szebehely
Keyword(s):  
Body Problem ◽  
Stellar Systems ◽  
The Sun ◽  
Three Body Problem ◽  
Moon System ◽  
The Earth ◽  
Qualitative Dynamics ◽  
Binary Orbit ◽  
The Stability ◽  
Three Body

AbstractThe stability of the three-body problem formed by the Sun, Jupiter and Saturn is investigated using surfaces of zero velocity. The results obtained with the models of the restricted and general problems of three bodies are compared with numerical integration. The system is found to be stable in the sense that Saturn will neither interrupt the (perturbed) binary orbit of Jupiter around the Sun, nor will it escape from the system. It is shown that the known classical triple stellar systems are “more stable” than the solar system, which in turn is “more stable” than the Earth-Moon system.

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