What Happens if Masses are Negative in Newtonian Potential?

[jack7992]

Homework Statement

Imagine that you have two particles with masses m and M, interacting with the standard Newtonian potential V=-G*m*M/r . When both masses are positive, you have a textbook example of central force motion. What happens if masses are negative? Discuss the cases 1) m<0, M<0; 2) m>0, M<0, m>|M|; 3) m>0, M<0, m<|M|; and 4) m>0, M=-m respectively.

Homework Equations

The Attempt at a Solution

I was planning on just doing more of a analytic approach versus a computational, but my professor want's me to solve it explicitly, and I'm not to sure how to do that. Any hints for just one of the cases would be great!

 

[Matterwave]

So, note that the Electro-static potential is V=-kqq'/r

Here q and q' can be either positive or negative. So...try to see some analogy with that maybe? k->G, q->M, q'->m.