Triple collisions in the isosceles three body problem with small mass ratio

1989 ◽  
Vol 40 (5) ◽  
pp. 645-664 ◽  
Author(s):  
Mohamed Sami ElBialy
Keyword(s):  
Body Problem ◽  
Small Mass ◽  
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].

scholarly journals Retrograde Satellites in the Circular Plane Restricted Three-Body Problem

1974 ◽  
Vol 62 ◽  
pp. 129-129
Author(s):  
D. Benest
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Three Body ◽  
Circular Plane

Characteristics and stability of simple-periodic retrograde satellites of the lighter body are presented for Hill's case and for all values of the mass ratio m2/(m1+m2) between 0 and 0.5.

Perturbed Location of L1 point in the photogravitational relativistic restricted three-body problem (R3BP) with oblate primaries

2015 ◽  
Vol 93 (3) ◽  
pp. 300-311 ◽  
Author(s):  
S.E. Abd El-Bar ◽  
F.A. Abd El-Salam ◽  
M. Rassem
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Series Form ◽  
Analytical Result ◽  
Three Body

The restricted three-body problem is studied in the post-Newtonian framework. The primaries are assumed oblate radiant sources. The perturbed location of the L1 point is computed, and a series form of the location of this point is obtained as a new analytical result. To introduce a semianalytical view, a Mathematica 9 program is constructed so as to draw the location of L1 versus the mass ratio μ ∈ (0, 0.5) taking into account one or more of the considered perturbations. All the obtained illustrations are analyzed.

scholarly journals On stability of triangular points of the restricted relativistic elliptic three-body problem with triaxial and oblate primaries

2017 ◽  
pp. 47-52
Author(s):  
K. Zahra ◽  
Z. Awad ◽  
H.R. Dwidar ◽  
M. Radwan
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Critical Mass ◽  
Combined Effects ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Triangular Points ◽  
The Stability ◽  
Three Body ◽  
Ratio Range

This paper investigates the location and linear stability of triangular points under combined effects of perturbations: triaxialty of a massive primary, oblateness of a less massive one, and relativistic corrections. The primaries in this system are assumed to move in elliptical orbits around their common barycenter. It is found that the locations of the triangular points are affected by the involved perturbations. The stability of orbits near these points is also examined. We observed that these points are stable for the mass ratio, ?, range 0 < ? < ?c, where ?c is the critical mass ratio, and unstable for the range ?c ? ? ? 0.5.

scholarly journals Perturbed locations and linear stability of collinear Lagrangian points in the elliptic restricted three body problem with triaxial primaries

2019 ◽  
Vol 28 (1) ◽  
pp. 145-153
Author(s):  
Walid Ali Rahoma ◽  
Akram Masoud ◽  
Fawzy Ahmed Abd El-Salam ◽  
Elamira Hend Khattab
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Equilibrium Points ◽  
Classical Case ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
The Difference ◽  
The Stability ◽  
Three Body

Abstract This paper aims to study the effect of the triaxiality and the oblateness as a special case of primaries on the locations and stability of the collinear equilibrium points of the elliptic restricted three body problem (in brief ERTBP). The locations of the perturbed collinear equilibrium points are first determined in terms of mass ratio of the problem (the smallest mass divided by the total mass of the system) and different concerned perturbing factors. The difference between the locations of collinear points in the classical case of circular restricted three body problem and those in the perturbed case is represented versus mass ratio over its range. The linear stability of the collinear points is discussed. It is observed that the stability regions for our model depend mainly on the eccentricity of the orbits in addition to the considered perturbations.

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