Asymptotic solution to the restricted three-body problem with a mass point moving near a small-mass body

2010 ◽  
Vol 33 (15) ◽  
pp. 1807-1849
Author(s):  
Alexander El'bert
Keyword(s):  
Asymptotic Solution ◽  
Body Problem ◽  
Small Mass ◽  
Mass Point ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals A note on the existence of invariant punctured tori in the planar circular restricted three-body problem

1988 ◽  
Vol 8 (8) ◽  
pp. 63-72 ◽  
Keyword(s):  
Body Problem ◽  
Small Mass ◽  
Connected Components ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Jacobi Constant ◽  
Hill Region ◽  
The Masses ◽  
Three Body ◽  
Collision Orbits

AbstractThe existence of transversal ejection—collision orbits in the restricted three-body problem is shown to imply, via the KAM theorem, the existence, for certain intervals of (large) values of the Jacobi constant, of an uncountable number of invariant punctured tori in the corresponding (non-compact) energy surface. The proof is based on a comparison between Levi-Civita and McGehee regularizing variables. That these transversal ejection-collision orbits do actually exist was proved in [5] in the case where one of the primaries has a small mass and the zero-mass body revolves around the other (and for all values of the Jacobi constant compatible with the existence of three connected components for the Hill region); it is proved here without any restriction on the masses, well in the spirit of Conley's thesis [3].

scholarly journals Is Jacobi theorem valid in the singly averaged restricted circular Three-Body-Problem?

2021 ◽  
Vol 8 (1) ◽  
pp. 179-184
Author(s):  
Konstantin V. Kholshevnikov ◽  
◽  
Keyword(s):  
Total Energy ◽  
Body Problem ◽  
Negative Energy ◽  
Mass Point ◽  
Restricted Three Body Problem ◽  
Energy Integral ◽  
Three Body Problem ◽  
Zero Mass ◽  
N Body Problem ◽  
Three Body

C. Jacobi found that in the General N-Body-Problem (including N = 3) for the Lagrangian stability of any solution necessary is the negativity of the total energy of the system. For the restricted three-body-problem, this statement is trivial, since a zero-mass body introduces zero contribution to the energy of the system. If we consider only the equations describing the movement of the zero mass point, then the energy integral disappears. However, if we average the equations over the longitudes of the main bodies, the energy integral appears again. Is the Jacobi theorem valid in this case? It turned out not. For arbutrary large values of total energy, there exist bounded periodic orbits. At the same time the negative energy is sufficient for the boundedness of an orbit in the configuration space.

On the modified circular restricted three-body problem with variable mass

New Astronomy ◽  
2021 ◽  
Vol 84 ◽  
pp. 101510
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Md Chand Asique ◽  
Amit Mittal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body
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