The integrable cases of the three-body problem at second-order resonance under the high oblateness of the central body

1996 ◽  
Vol 63 (3-4) ◽  
pp. 341-355
Author(s):  
Vladimir N. Shinkin
Keyword(s):  
Body Problem ◽  
Central Body ◽  
Second Order ◽  
Three Body Problem ◽  
Order Resonance ◽  
Three Body

scholarly journals Three Dimensional Stability of A Rectilinear Periodic Solution of the Three-Body Problem, for all Values of the Masses

1977 ◽  
Vol 33 ◽  
pp. 161-161
Author(s):  
M. Hénon
Keyword(s):  
Periodic Solution ◽  
Dimensional Stability ◽  
Body Problem ◽  
Central Body ◽  
Three Dimensional ◽  
Three Body Problem ◽  
Stability And Instability ◽  
The Masses ◽  
Three Body ◽  
Triple Stars

AbstractWe consider a rectilinear periodic solution in which the central body collides alternately with each of the two other bodies. This solution is found to exist for all values of the three masses. Its stability with respect to three-dimensional perturbations is computed. Domains of stability and instability are delimited in a triangular mass diagram. Large domains of stability are found. This reinforces the conclusion that triple stars may have an “interplay” type of motion.

scholarly journals Nonlinear Stability of Oblate Infinitesimal in Elliptic Restricted Three-Body Problem Influenced by the Oblate and Radiating Primaries

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
A. Narayan ◽  
A. Chakraborty ◽  
A. Dewangan
Keyword(s):  
Nonlinear Stability ◽  
Binary Systems ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Order ◽  
Order Resonance ◽  
The Third ◽  
The Stability ◽  
Three Body

This work deals with the nonlinear stability of the elliptical restricted three-body problem with oblate and radiating primaries and the oblate infinitesimal. The stability has been analyzed for the resonance cases around ω1=2ω2 and ω1=3ω2 and also the nonresonance cases. It was observed that the motion of the infinitesimal in this system shows instable behavior when considered in the third order resonance. However, for the fourth order resonance the stability is shown for some mass parameters. The motion in the case of nonresonance was found to be unstable. The problem has been numerically applied to study the movement of the infinitesimal around two binary systems, Luyten-726 and Sirius.

scholarly journals A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
R. C. Domingos ◽  
A. F. Bertachini de Almeida Prado ◽  
R. Vilhena de Moraes
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Second Order ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Elliptic Orbits ◽  
Three Body ◽  
The Impact ◽  
Third Body Perturbation

The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. The disturbing function is expanded in Legendre polynomials up to the second order in both cases. The equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. The results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.

scholarly journals Orientation of a Satellite Located at the Libration Point in the Restricted Three-Body Problem

1983 ◽  
Vol 74 ◽  
pp. 27-35
Author(s):  
Grzegorz Duliński ◽  
Andrej J. Maciejewski
Keyword(s):  
Body Problem ◽  
Central Body ◽  
Libration Point ◽  
Nonlinear Effects ◽  
Hamiltonian Mechanics ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Gravitational Influence ◽  
Three Body ◽  
Initial Results

In this paper the initial results of an investigation of the motion of a rigid body located at the libration point in the planar, restricted three-body problem are given. This problem was analyzed in part by Kane and Marsh (1971), Markeev (1967a,b). However the present investigation is formulated in terms of hamiltonian mechanics. The final results will by used to study nonlinear effects connected with the gravitational influence of the “second” central body.

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