  We consider the gravitational potential and the gravitational rotation field
generated by an spherical mass distribution with exponential density, when the
force between any two mass elements is not the usual Newtonian one, but some
general central force. We invert the usual integral relations and obtain the
elemental interaction (between two point-like masses) as a function of the
macroscopic gravitational field (the one generated by the distribution). Thus,
we have 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 show that this method can be used even in
the case of spiral galaxies with a good level of confidence.
