Periodic solutions of the restricted three-body problem for a small mass ratio

2007 ◽  
Vol 71 (6) ◽  
pp. 933-960 ◽  
Author(s):  
A.D. Bruno ◽  
V.P. Varin
Keyword(s):  
Periodic Solutions ◽  
Body Problem ◽  
Small Mass ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Three Body

scholarly journals Progression of bifurcated family f type periodic orbits in the circular restricted three-body problem

2017 ◽  
Vol 5 (2) ◽  
pp. 69
Author(s):  
Nishanth Pushparaj ◽  
Ram Krishan Sharma
Keyword(s):  
Solar Radiation ◽  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Solar Radiation Pressure ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Three Body

Progression of f-type family of periodic orbits, their nature, stability and location nearer the smaller primary for different mass ratios in the framework of circular restricted three-body problem is studied using Poincaré surfaces of section. The orbits around the smaller primary are found to decrease in size with increase in Jacobian Constant C, and move very close towards the smaller primary. The orbit bifurcates into two orbits with the increase in C to 4.2. The two orbits that appear for this value of C belong to two adjacent separate families: one as direct orbit belonging to family g of periodic orbits and other one as retrograde orbit belonging to family f of periodic orbits. This bifurcation is interesting. These orbits increase in size with increase in mass ratio. The elliptic orbits found within the mass ratio 0 < µ ≤ 0.1 have eccentricity less than 0.2 and the orbits found above the mass ratio µ > 0.1 are elliptical orbits with eccentricity above 0.2. Deviations in the parameters: eccentricity, semi-major axis and time period of these orbits with solar radiation pressure q are computed in the frame work of photogravitational restricted Three-body problem in addition to the restricted three-body problem. These parameters are found to decrease with increase in the solar radiation pressure.

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].

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