## An analytical method for inferring the law of gravity from the macroscopic dynamics: Spherical and thin-disk mass distributions with exponential density
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
## Contents- 1. Introduction
- 2. General definitions
- 3. Spherical mass distribution with exponential density
- 4. Thin-disk mass distribution with exponential density
- 5. Real thin disks: comparison between the spherical and the Gaussian approximations
- 6. An example of how to work with real data
- 7. Summary and conclusions
- Acknowledgements
- Appendix A
- References
© European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |