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Equations of motion for isolated bodies with relativistic corrections including the radiation reaction force

Published online by Cambridge University Press:  04 August 2017

L. P. Grishchuk  and
S. M. Kopejkin
L. P. Grishchuk
Affiliation:
Sternberg State Astronomical Institute, University Prospect, 13, 119899 Moscow, USSR
S. M. Kopejkin
Affiliation:
Sternberg State Astronomical Institute, University Prospect, 13, 119899 Moscow, USSR

Abstract

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We have derived in an explicit form the equations of motion for two spherically-symmetric non rotating bodies in the slow motion approximation. The equations include relativistic corrections of order (v/c)2, (v/c)4 and (v/c)5 to the newtonian equations of motion. It is shown that the equations depend on the only parameter characterizing each body, namely on its relativistic mass, regardless of its internal structure and degree of compactness. This means that the equations can also be applied to bodies with a strong internal gravity, such as neutron stars and black holes. It is shown that in the (v/c)2 and (v/c)4 approximations the equations can be derived from a Lagrangian. The Lagrangian is given in an exact form. The integration of the equations of motion is performed by the method of osculating elements. The formulae for secular change of the semi-major axis and eccentricity coincide precisely with the standard ones whose derivation is based on a calculation of the energy flux in the outgoing gravitational waves.

Type
Dynamical Effects in General Relativity
Information
Symposium - International Astronomical Union , Volume 114: Relativity in Celestial Mechanics and Astrometry , 1986 , pp. 19 - 34
Copyright
Copyright © Reidel 1986 

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