General-relativistic celestial mechanics. II. Translational equations of motion

Journal Article · Sat Feb 15 00:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.45.1017· OSTI ID:7206194

Damour, T ^[1]; Soffel, M; Xu, C ^[2]

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1. Institut des Hautes Etudes Scientifiques, 91440 Bures-sur-Yvette (France) Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Centre National de la Recherche Scientifique, 92195 Meudon CEDEX (France)
2. Theoretische Astrophysik, Universitaet Tuebingen, Auf der Morgenstelle 10, 7400 Tuebingen (Germany)

The translational laws of motion for gravitationally interacting systems of {ital N} arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation (i.e., neglecting terms of order ({ital v}/{ital c}){sup 4} in the equations of motion), our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies.

• OSTI ID: 7206194
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 45:4; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASTROPHYSICS
GRAVITATIONAL INTERACTIONS
GENERAL RELATIVITY THEORY
CLASSICAL MECHANICS
EQUATIONS OF MOTION
MANY-BODY PROBLEM
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
INTERACTIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
661100* - Classical & Quantum Mechanics- (1992-)
661310 - Relativity & Gravitation- (1992-)