Evolution with the mass parameter of families of asymmetric periodic solutions of the restricted three body problem

1983 ◽  
Vol 29 (1) ◽  
pp. 75-98 ◽  
Author(s):  
D. B. Taylor
Keyword(s):  
Periodic Solutions ◽  
Body Problem ◽  
Mass Parameter ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

Resonant Three-Dimensional Periodic Solutions About the Triangular Equilibrium Points in the Restricted Problem

1983 ◽  
Vol 74 ◽  
pp. 235-247 ◽  
Author(s):  
C.G. Zagouras ◽  
V.V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Special Values ◽  
Three Body

AbstractIn the three-dimensional restricted three-body problem, the existence of resonant periodic solutions about L4 is shown and expansions for them are constructed for special values of the mass parameter, by means of a perturbation method. These solutions form a second family of periodic orbits bifurcating from the triangular equilibrium point. This bifurcation is the evolution, as μ varies continuously, of a regular vertical bifurcation point on the corresponding family of planar periodic solutions emanating from L4.

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.

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