scholarly journals Analytical Theory of A Trapping. In A Two-Body Problem of Variable Mass

1983 ◽  
Vol 74 ◽  
pp. 369-375
Author(s):  
T.B. Omarov ◽  
M.J. Minglibaev
Keyword(s):  
Body Problem ◽  
Model Problem ◽  
Variable Mass ◽  
Analytical Theory ◽  
Two Body Problem ◽  
Nonstationary Model ◽  
Temporal Derivative

SummaryThe new nonstationary model problem is considered. Its solution generalizes by form the known particular Mestschersky-Vinti solution in a two-body problem of variable mass. The equations of the corresponding perturbed motion are deduced. In the case of a two-body problem of variable mass μ. the perturbing force is proportional to second temporal derivative from the value μ-1 . It is possible to describe with a good approximation such qualitative effects in this problem as a trapping and disintegration on a basis of properties of the model problem. Let us consider the example of a trapping.

Two-body problem with variable mass: A new approach

Icarus ◽  
1963 ◽  
Vol 2 ◽  
pp. 440-451 ◽  
Author(s):  
John D. Hadjidemetriou
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
New Approach ◽  
Two Body Problem

scholarly journals On Non-Stationary Problems of Celestial Mechanics

1979 ◽  
Vol 81 ◽  
pp. 49-52
Author(s):  
T. B. Omarov
Keyword(s):  
Celestial Mechanics ◽  
Gravitational Potential ◽  
Arbitrary Function ◽  
Body Problem ◽  
Variable Mass ◽  
Inertial System ◽  
Two Body Problem ◽  
Initial Epoch ◽  
Image Position ◽  
Stationary Problems

Some non-stationary problems of celestial mechanics can be described in an inertial system of right-angled coordinates with gravitational potential of the form: where is a sufficiently arbitrary function of time and is the meaning of in the initial epoch For example, in a two-body problem of variable mass we have:

Regularization of the two body problem with variable mass

1974 ◽  
Vol 10 (2) ◽  
pp. 141-149 ◽  
Author(s):  
Pierre Guillaume
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Two Body Problem

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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