Superficially, the force between two magnets would seem to be fully analogous to gravity because each is the product of two factors divided by the square of the distance between the objects being attracted.
In other words, if we imagine two celestial bodies with both mass and magnetic poles, it would seem that we could, by adjusting the mass and the magnitude of the magnetic poles, make the forces equal to each other, and as the bodies drew together the two forces would remain equal. In other words, if we were to graph the two forces as a function of distance, the two curves would be identical. Thus, the forces, though they are of a completely different nature, are fully analogous to each other.
Is this correct, or is there some essential difference between the two forces that will always make them behave in a different way?