## 7. Summary and conclusionsWe have found the solution to the problem of inverting the integral
relation between the elemental law of gravity and the overall
gravitational field generated by two interesting mass distributions:
(i) a sphere with exponential density (where the solution is exact),
and (ii) a thin-disk with exponential density. The problem in the case
of the thin disk has been solved in an approximation that has been
called In summary, we now have a method for inferring
given the observed rotation velocity. It can be
said, in some sense, that we have a We are now ready for applying the differential expression that we have found to the observed rotation curves of spiral galaxies, and find the required for explaining those rotation curves. We have given an example of how it can be done for a particular galaxy. By repeating the exercise for a sample of several galaxies, we will see whether it is possible or not to find a universal law of gravity that can explain all the rotation curves requiring only the observed luminous matter. This will be done in a separate publication (Rodrigo-Blanco & Pérez-Mercader 1997). © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |