Chongming Xu

Relativistic Celestial Mechanics and Reference Frames

A new formalism for treating the relativistic celestial mechanics of systems of N , arbitrarily composed and shaped, weakly self-gravitating, rotating, deformabile bodies is presented. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such N -body systems (“external problem”), (ii) the local gravitational structure of each body (“internal problem”), and, (iii) the way the external and the internal problems fit together (“theory of reference systems”).

General-relativistic Linear Perturbation Theory on Elastical Astronomical Bodies

The general relativistic perturbations of a uniformly rotating and axisymmetric elastic deformable astronomical body in the first post-Newtonian approximation of Einsteins general relativity is discussed in a co-rotating coordinates. The main new results presented here are the post-Newtonian variations of the energy and Euler equation, which at the Newtonian level of accuracy is so called Jeffreys-Vicente equation and it play a fundamental role for the description of global geodynamics in the classical geophysics. Our results will be useful to treat the relativistic nutation and precession of the Earth and other planets.