RT Book, Section T1 On the orbital motion description with a proper reference frame in a complete schwarzschild field A1 Gambi, J. M. A1 Zamorano, P. A1 Romero Pérez, María Del Pilar A1 García del Pino, M. L. A2 Ferraz-Mello, Sylvio A2 Morando, Bruno A2 Arlot, Jean-Eudes AB The orbital motion of test particles about a central body at rest is described in terms of a coordinate system that, unlike the usual coordinates, can be materialized by a proper (Fermi) reference frame with origin located at the body's centre world line. By means of the world function in the post-Newtonian approximation of the exterior Schwarzchild solution for this system it is demonstrated that the radial coordinate, which initially is shown to be asymptotically equal to the invariant relativistic distance between any test particle's world line and that of the body's centre, when calculated for two particles placed in conjunction with respect to the central body, becomes exactly their euclidean distance. It is also shown that thedifferential equation in the reciprocal of the radial coordinate for any bounded orbit is governed by a function which is asymptotically, but is not, a cubic, and its solution is obtained in terms of elliptic functions. It is finally shown, when the post-Newtonian polar coordinates equations are derived, that a relevant relativistic correction appearing in the usual post-Newtonian approximations of the exterior Schwarzchild solution disappears or, to be more precise, becomes exactly zero. PB Kluwer Academic SN 0-7923-4084-1 YR 1996 FD 1996 LK https://hdl.handle.net/20.500.14352/60598 UL https://hdl.handle.net/20.500.14352/60598 LA eng NO Proceedings of the 172nd Symposium of the International Astronomical Union, held in Paris, France, 38 July, 1995 DS Docta Complutense RD 5 abr 2025