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 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 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.

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.

scholarly journals J+-Like invariants of periodic orbits of the second kind in the restricted three-body problem

2018 ◽  
Vol 12 (03) ◽  
pp. 675-712 ◽  
Author(s):  
Joontae Kim ◽  
Seongchan Kim
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Three Body

We determine three invariants: Arnold’s [Formula: see text]-invariant as well as [Formula: see text] and [Formula: see text] invariants, which were introduced by Cieliebak–Frauenfelder–van Koert, of periodic orbits of the second kind near the heavier primary in the restricted three-body problem, provided that the mass ratio is sufficiently small.

Numerical exploration of the restricted three-body problem

1966 ◽  
Vol 25 ◽  
pp. 157-169 ◽  
Author(s):  
M. Hénon
Keyword(s):  
Body Problem ◽  
Initial Conditions ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
General Picture ◽  
Numerical Exploration ◽  
The One ◽  
Three Body ◽  
Area Preserving

A number of orbits have been computed in the plane restricted three-body problem; the two main bodies have the same mass and move on a circular orbit. By consideration of the successive intersections of the orbit with thexaxis, the problem can be reduced to the study of a plane area-preserving mapping. A second integral, distinct from Jacobi's integral, seems to exist inside given ranges of initial conditions, but not outside. The general picture is quite similar to the one found in the problem of the third integral of galactic motion. Extension of this work to other values of the mass ratio is under way.

scholarly journals The collinear equilibrium points in the restricted three body problem with triaxial primaries

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 525-538
Author(s):  
Sultan Z. Alamri ◽  
Sobhy E. Abd El-Bar ◽  
Aly R. Seadawy
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Analytical Results ◽  
Three Body

AbstractThe perturbed restricted three body problem has been reviewed. The mass of the primaries are assumed as triaxial. The locations of the collinear points have been computed. Series forms of these locations are obtained as new analytical results. In order to introduce a semi-analytical view, a Mathematica program has been constructed to graph the locations of collinear points versus the whole range of the mass ratio μ taking into account the triaxiality. The resultant figures have been analyzed

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