On the orbital motion description with a proper reference frame in a complete schwarzschild field



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Gambi, J.M. and Zamorano, P. and Romero Pérez, Mª Pilar and García del Pino, M.L. (1996) On the orbital motion description with a proper reference frame in a complete schwarzschild field. In Dynamics, ephemerides, and astrometry of the solar system. Kluwer Academic, Dordrecht, pp. 325-326. ISBN 0-7923-4084-1

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Official URL: http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1996IAUS..172..325G&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf


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 the
differential 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.

Item Type:Book Section
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Proceedings of the 172nd Symposium of the International Astronomical Union, held in Paris, France, 38 July, 1995

Subjects:Sciences > Physics > Astronomy
ID Code:18076
Deposited On:31 Jan 2013 09:39
Last Modified:09 Sep 2020 08:16

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