Rotation curves for spiral galaxies and non-Newtonian gravity: a phenomenological approach

Rotation curves of spiral galaxies are known with reasonable precision for a large number of galaxies with similar morphologies. The data implies that non-Keplerian fall-off is seen. This implies that (i) large amounts of dark matter must exist at galactic scales or (ii) that Newtonian gravity must somehow be corrected, We present a method for inverting the integral relation between an elemental law of gravity (such as Newton's) and the gravitational field generated by a thin disk distribution with exponential density. This allows us to identify, directly from observations, extensions of Newtonian gravity with the property of fitting a large class of rotation curves. The modification is inferred from the observed rotation curve and is finally written in terms of Newton's constant or the effective potential of a test mass moving. in the field generated by a point-like particle.