## 2. General definitionsLet us assume that the gravitational potential generated by a point-like mass does not correspond to the usual Newtonian form but can be written in terms of a function that describes the deviation from the Newtonian law, that is, where is the gravitational potential
experienced by two point-like particles of masses
and separated by a
distance This modification could, for example, be due to the many body nature of the mass distribution making up the galaxy, a relativistic theory different from General Relativity... This is irrelevant in what follows. The force per unit mass is, by definition, the gradient of the potential, where we have introduced with as , as required by the Newtonian limit. In this way, to find the total potential or the total force generated by a mass distribution with density , one must integrate over the volume spanned by to get: for the potential experienced by a point mass at a distance
for the force. In the case that the gravitational potential is only a function of the distance to the centre of the distribution, it is convenient to introduce two new functions and such that: and the rotation velocity of a test particle in a circular orbit bound to the distribution will be: where the auxiliary functions and satisfy the following functional relationship: Our goal is to design a procedure where, assuming that
is known (say from observation of the rotation
velocity) for all values of © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |