scholarly journals Primaries Oblateness Effects on the Collinear Libration Points in the Restricted-three Body Problem

2019 ◽  
Author(s):  
M. N. Ismail ◽  
A. H. Ibrahim ◽  
G. H. F. Mohamadin ◽  
W. A. Okasha
Keyword(s):  
Body Problem ◽  
Libration Points ◽  
Restricted Three Body Problem ◽  
Stability Of Motion ◽  
Three Body Problem ◽  
Numerical Application ◽  
Surface Section ◽  
The Stability ◽  
Three Body ◽  
Good Agreement

In this work, the canonical Hamiltonian form of the restricted three- body problem including the effects of primaries oblateness is presented. Moreover, the collinear libration points are obtained. In addition to this, the relation between position of libration points and variation in (mass ration , oblateness coefficients A1 and A2) is studied. The results obtained are a good agreement with Perdios [1] & Singh [2].  The Poincare surface section PSS is used to illustrate the stability of motion around each of the collinear libration points. A numerical application on the real system Earth-Moon is presented.

scholarly journals Non-collinear libration points in CR3BP when less massive primary is an heterogeneous oblate body with N-layers

2016 ◽  
Vol 4 (1) ◽  
pp. 39
Author(s):  
M Javed Idrisi ◽  
Kumari Shalini
Keyword(s):  
Body Problem ◽  
Mass Parameter ◽  
Critical Value ◽  
Libration Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Oblate Body ◽  
The Stability ◽  
Three Body

<p>In the present paper, the existence of non-collinear libration points has been shown in circular restricted three-body problem when less massive primary is a heterogeneous oblate body with N-layers. Further, the stability of non-collinear libration points is investigated in linear sense and found that the non-collinear libration points are stable for the critical value of mass parameter <em>µ</em> ≤ <em>µ<sub>crit</sub></em>= <em>µ</em><sub>o</sub> – 3.32792 <em>k</em><sub>1</sub> – 1.16808 <em>k</em><sub>2</sub>.</p>

scholarly journals POSITIONS AND STABILITY OF LIBRATION POINTS IN THE CIRCULAR RESTRICTED THREE-BODY PROBLEM WHEN THE BIGGER PRIMARY IS RADIATING AND OBLATING

2020 ◽  
Vol 4 (2) ◽  
pp. 523-531
Author(s):  
K. R. Tyokyaa ◽  
Tersoo Atsue
Keyword(s):  
Body Problem ◽  
Positive Real Part ◽  
Libration Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Positive Real ◽  
Stability And Instability ◽  
The Stability ◽  
Three Body ◽  
Lyapunov Sense

This paper investigates the positions and stability of libration points in the framework of the circular restricted three-body problem for the systems: Luyten726-8 and HD98800. The position of the third body lie in the plane almost directly above and below the center of the oblate primary. It is found that radiations and oblateness of the primary have destabilizing effects; the presence of any one or more of the latter makes weak the stabilizing ability of the former, consequently the overall effect is that the range of stability of the libration points decreases. Considering the range of stability and instability, that is  and , the libration points are respectively stable and unstable for HD98800 and Luyten 762-8 systems. Our results show that, all the roots are real, and for each set of values, there exist at least a positive real part and hence in the Lyapunov sense, the stability of the libration points are unstable for the systems HD98800 and Luyten 762-8.

scholarly journals Effect of elliptic angle φ on the existence and stability of libration points in restricted three-body problem in earth-moon system considering earth as an ellipsoid

2015 ◽  
Vol 3 (2) ◽  
pp. 87
Author(s):  
M Javed Idrisi ◽  
Muhammad Amjad
Keyword(s):  
Body Problem ◽  
Libration Points ◽  
Point Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Moon System ◽  
The Earth ◽  
Existence And Stability ◽  
The Stability ◽  
Three Body

<p>This paper deals with the existence and the stability of the earth-moon libration points in the restricted three-body problem. In this paper we have considered the bigger primary as an ellipsoid while the smaller one as a point-mass. This is observed that the collinear and non-collinear libration points exist only in the interval 0˚&lt;<em>φ </em>&lt; 45˚. There exist three collinear libration points and the non-collinear libration points are forming a right triangle with the primaries. Further observed that the libration points either collinear or non-collinear all are unstable in 0˚&lt;<em>φ </em>&lt; 45˚.</p>

scholarly journals LOCATION AND STABILITY OF THE TRIANGULAR POINTS IN THE TRIAXIAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM

2021 ◽  
Vol 57 (2) ◽  
pp. 311-319
Author(s):  
M. Radwan ◽  
Nihad S. Abd El Motelp
Keyword(s):  
Linear Stability ◽  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stability Regions ◽  
Triangular Points ◽  
Problem Frame ◽  
The Stability ◽  
Three Body

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is generalized in the sense that the two primaries are considered as triaxial bodies. It was found that the locations of these points are affected by the triaxiality coefficients of the primaries and the eccentricity of orbits. Also, the stability regions depend on the involved perturbations. We also studied the periodic orbits in the vicinity of the triangular points.

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