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Astron. Astrophys. 321, 444-451 (1997)

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An analytical method for inferring the law of gravity from the macroscopic dynamics: Spherical and thin-disk mass distributions with exponential density

C. Rodrigo-Blanco

Laboratorio de Astrofísica Espacial y Física Fundamental (LAEFF), P.O. Box 50727, E-28080 Madrid, Spain (crb@laeff.esa.es)

Received 29 July 1996 / Accepted 17 October 1996

Abstract

We consider the gravitational potential and the gravitational rotation field generated by a mass distribution with exponential density, when the force between any two mass elements is not the usual Newtonian one, but some general central force. The usual integral relations are inverted and the elemental interaction (between two point-like masses) is obtained as a function of the macroscopic gravitational field (the one generated by the distribution). This has been done in two cases of interest: a sphere, where the exact solution has been found, and a thin disk, where the problem has been solved in the Gaussian approximation. This approach gives us a direct way for testing the possibility of finding a correction to the Newtonian law of gravity that can explain the observed dynamics at large scales without the need of dark matter. We also show that the solution for the thin disk, in the Gaussian approximation, can be used in the case of spiral galaxies with a good level of confidence.

Key words: gravitation – galaxies: kinematics and dynamics – methods: analytical – cosmology: dark matter

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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