ERRATUM: “ON THE ORBITAL STABILITY OF TRIANGULAR LAGRANGIAN MOTIONS IN THE THREE-BODY PROBLEM” (2008, AJ, 136, 2533)

2009 ◽  
Vol 137 (3) ◽  
pp. 3730-3730
Author(s):  
Stepan P. Sosnitskii
Keyword(s):  
Body Problem ◽  
Orbital Stability ◽  
Three Body Problem ◽  
Three Body

scholarly journals Orbital stability of high inclination asteroids

1996 ◽  
Vol 172 ◽  
pp. 187-192
Author(s):  
N. A. Solovaya ◽  
E. M. Pittich
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Orbital Stability ◽  
Dynamical Model ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

The orbital evolutions of fictitious asteroids with high inclinations have been investigated. The selected initial orbits represent asteroids with movement, which corresponds to the conditions of the Tisserand invariant for C = C (L1) in the restricted three body problem. Initial eccentricities of the orbits cover the interval 0.0–0.4, inclinations the interval 40–80°, and arguments of perihelion the interval 0–360°. The equations of motion of the asteroids were numerically integrated from the epoch March 25, 1991 forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all planets. The orbits of the model asteroids are stable at least during the investigated period.

scholarly journals The orbital stability of a test body motion in the field of two massive bodies

2018 ◽  
Vol 168 ◽  
pp. 04001
Author(s):  
Medeu Abishev ◽  
Saken Toktarbay ◽  
Aigerim Abylayeva ◽  
Amanhan Talkhat
Keyword(s):  
Body Problem ◽  
Orbital Stability ◽  
Test Body ◽  
Body Motion ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Test Particles ◽  
The Stability ◽  
Three Body ◽  
Insight Into

We investigate the orbital stability of a test particle motion in the restricted three-body problem where all bodies have their own rotation. We have shown that it is possible to get some insight into the stability properties of the motion of test particles in restricted three-body problem, without knowing the exact solutions of the relativistic motion equations.

scholarly journals The orbital stability of relativistic three-body problem in the fremework of general relativity

2019 ◽  
Vol 69 (2) ◽  
pp. 53-60
Author(s):  
A.Z. Talkhat ◽  
◽  
A.Zh. Abylayeva ◽  
A. Muratkhan ◽  
◽  
...  
Keyword(s):  
General Relativity ◽  
Body Problem ◽  
Orbital Stability ◽  
Three Body Problem ◽  
Three Body

scholarly journals Orbital Stability in the Elliptic Restricted Three Body Problem

1978 ◽  
Vol 41 ◽  
pp. 333-337
Author(s):  
C.A. Williams ◽  
J.G. Watts
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Orbital Stability ◽  
Restricted Three Body Problem ◽  
Invariant Relation ◽  
Three Body Problem ◽  
Hill Stability ◽  
Elliptic Restricted Problem ◽  
Three Body

AbstractBased on the concept of orbital stability introduced by G. W. Hill, a method is presented to facilitate the determination of the orbital stability of solutions to the planar elliptic restricted problem of three bodies. The invariant relation introduced by Szebehely and Giacaglia (1964) contains an integral which is expanded here about a Keplerian solution to the problem. If the expansion converges, it can be used to determine the conditions for Hill stability. With it one can also define stability in a periodic sense.

scholarly journals Orbital stability of planets in binary systems: A new look at old results

2007 ◽  
Vol 3 (S249) ◽  
pp. 507-510
Author(s):  
J. Eberle ◽  
M. Cuntz ◽  
Z. E. Musielak
Keyword(s):  
Binary Systems ◽  
Body Problem ◽  
Orbital Stability ◽  
Observational Evidence ◽  
Theoretical Research ◽  
Theoretical Studies ◽  
Large Array ◽  
Three Body Problem ◽  
Validity Of Results ◽  
Three Body

AbstractAbout half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical research, including the derivation of mathematically stringent criteria for the orbital stability of planets in stellar binary systems, valid for the “coplanar circular restricted three-body problem”. In the following, we use these criteria to explore the validity of results from previous theoretical studies.

Rigid-Rotator and Fixed-Shape Solutions to the Coulomb Three-Body Problem

1997 ◽  
Vol 22 (1) ◽  
pp. 37-60 ◽  
Author(s):  
A. Santander ◽  
J. Mahecha ◽  
F. Pérez
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Rigid Rotator ◽  
Three Body
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