1992
DOI: 10.1103/physrevd.45.1017
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General-relativistic celestial mechanics II. Translational equations of motion

Abstract: The translational laws of motion for gravitationally interacting systems of N arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first postNewtonian approximation of general relativity. The derivation uses our recently introduced multireference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass kame of each body, relativistic inertial effects combine with post-Newtonian self-and externally generated grav… Show more

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Cited by 238 publications
(347 citation statements)
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“…The approach of the BJV and SONYR models consists in integrating the N-body problem (including translational and rotational motions) based on general relativity. The equations have been developed in the DSX formalism presented in a series of papers by (Damour et al 1991(Damour et al , 1992(Damour et al , 1993. For purposes of celestial mechanics, to our knowledge, it is the most suitable formulation of the post-Newtonian (PN) theory of motion for a system of N arbitrarily extended, weakly self-gravitating, rotating and deformable bodies in mutual interactions.…”
Section: The Framework Of the Modelmentioning
confidence: 99%
“…The approach of the BJV and SONYR models consists in integrating the N-body problem (including translational and rotational motions) based on general relativity. The equations have been developed in the DSX formalism presented in a series of papers by (Damour et al 1991(Damour et al , 1992(Damour et al , 1993. For purposes of celestial mechanics, to our knowledge, it is the most suitable formulation of the post-Newtonian (PN) theory of motion for a system of N arbitrarily extended, weakly self-gravitating, rotating and deformable bodies in mutual interactions.…”
Section: The Framework Of the Modelmentioning
confidence: 99%
“…There are some procedures for testing gravity beyond Newtonian gravity, and the most general and cited one is the Parametrised Post Newtonian (PPN) formalism [e.g., [38][39][40][41][42][43][44][45][46][47][48][49]. Here we consider both a version of the PPN formalism and the Laplace-Runge-Lenz (LRL) vector technique [e.g., [50][51][52].…”
Section: Introductionmentioning
confidence: 99%
“…(48) and (49) over the body A, we get the equations for the conservation of the total mass of A, M A = M A , and for the second time derivative of the local dipole moment M i A (Damour et al 1992;Hartmann et al 1994):…”
Section: Determination Of the Tidal Potentialmentioning
confidence: 99%