General relativistic celestial mechanics. 2. Translational equations of motion

Technical Report · Tue Oct 01 00:00:00 EDT 1991

OSTI ID:5803397

Damour, T; Soffel, M; Xu, C

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 post-Newtonian approximation of general relativity. The derivation uses the authors' 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 global equilibrium (relativistic generalization of d'Alembert's principle). Within the post-Newtonian approximation i.e. neglecting terms of order v/c to the 4th power in the equations of motion, the authors' 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. The authors 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 the body to the post-Newtonian tidal moments (recently defined by them) felt by the body. They then give the explicit expression of these tidal moments in terms of the post-Newtonian multiple moments of the other bodies.

• Research Organization: Institut des Hautes Etudes Scientifiques, 91 - Bures-sur-Yvette (France)
• OSTI ID: 5803397
• Report Number(s): PB-92-125020/XAB
• Country of Publication: United States
• Language: English

Related Subjects

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