General-relativistic celestial mechanics. I. Method and definition of reference systems
Abstract
The translation 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 felt by the body.
- Publication:
-
Physical Review D
- Pub Date:
- May 1991
- DOI:
- 10.1103/PhysRevD.43.3273
- Bibcode:
- 1991PhRvD..43.3273D
- Keywords:
-
- Celestial Mechanics;
- Equations Of Motion;
- Gravitational Fields;
- Relativity;
- Tides;
- Translational Motion;
- Center Of Mass;
- Deformation;
- Multipoles;
- Relativistic Effects;
- Rotating Bodies;
- Astrophysics