[bojan]

Originally Posted by tel.lekatsas

The inverse square law can result in non-Keplerian orbits depending on the form of the gravitational potential and thus ultimately on the mass distribution within the galaxy. An exponential disk potential amongst many others does not give a Keplerian radial profile.
Kepler orbits arise from spherically symmetric static potentials...

Originally Posted by sjastro

As a corollary to this proof one can show that non Keplarian orbits can only arise if the central force is not a "pure" inverse square law.
Keplarian orbits arise under conditions such as spherical symmetry of the field and the absence of external forces.
If these conditions are not met the orbits are non Keplarian and can be derived through perturbation theory. In this case the perturbation results in additional central force terms that are smaller than the unperturbed inverse square term.
The central force is however no longer based on a simple inverse square law.

Regards

Steven

I think you guys are talking about the same issue and have the same arguments, only using slightly different words..