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 Qualitative Dynamics of the Sun-Jupiter-Saturn System

1978 ◽  
Vol 41 ◽  
pp. 53-55
Author(s):  
V. Szebehely
Keyword(s):  
Body Problem ◽  
Stellar Systems ◽  
The Sun ◽  
Three Body Problem ◽  
Moon System ◽  
The Earth ◽  
Qualitative Dynamics ◽  
Binary Orbit ◽  
The Stability ◽  
Three Body

AbstractThe stability of the three-body problem formed by the Sun, Jupiter and Saturn is investigated using surfaces of zero velocity. The results obtained with the models of the restricted and general problems of three bodies are compared with numerical integration. The system is found to be stable in the sense that Saturn will neither interrupt the (perturbed) binary orbit of Jupiter around the Sun, nor will it escape from the system. It is shown that the known classical triple stellar systems are “more stable” than the solar system, which in turn is “more stable” than the Earth-Moon system.

scholarly journals Restricted three-body problem with stokes drag effect when less massive primary is an ellipsoid

2016 ◽  
Vol 4 (1) ◽  
pp. 61 ◽  
Author(s):  
M Javed Idrisi ◽  
Mamta Jain
Keyword(s):  
Drag Force ◽  
Body Problem ◽  
Mass Parameter ◽  
Libration Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stokes Drag ◽  
Existence And Stability ◽  
Three Body ◽  
The Given

The present paper deals with the effect of Stokes drag force on the existence and stability of collinear and non-collinear libration points in circular restricted three-body problem when less massive primary is an ellipsoid. During the investigation, it is found that there exist five libration points Li (i = 1, 2… 5) out of which three are collinear and two are non-collinear. We observed that the Stokes drag force does not affect the collinear libration points while non-collinear libration points are affected by it and all the libration points either collinear or non-collinear are unstable in Lyapunov sense for the given range of dissipative constant k and mass parameter µ.

scholarly journals Libration points in the restricted three-body problem: Euler angles, existence and stability

2019 ◽  
Vol 12 (4-5) ◽  
pp. 703-710 ◽  
Author(s):  
Hadia H. Selim ◽  
◽  
Juan L. G. Guirao ◽  
Elbaz I. Abouelmagd ◽  
◽  
...  
Keyword(s):  
Body Problem ◽  
Libration Points ◽  
Euler Angles ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Existence And Stability ◽  
Three Body

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 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.

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