In the case of a mass object, the center of mass is the only point which can be defined as being at rest. Since the equation describes conditions exterior to the surface of the object, the conclusion is that the space of the object is determined by the object itself. Then if the object has a motion of translation imposed upon it, the space of the object translates with the center of mass. Since the only limit on is that it should be a finite positive integer, it appears that more than one potential may exist. Every potential which exists has a corresponding force form.
Examples are forces of gravity and electrical forces between point charges.
The question of evaluation of coefficients must be considered. This is a potential associated with a rotating mass object. The force form is that of the inverse cube of the radius vector. As applied to earth, the effect is that of the second order in relation to the static gravitational potential. The force corresponding is inverse fourth power of the radius vector.