Now calculate the total potential energy of the Plummer mass distribution. Hint:
The answer should depend only on G, M, and a
The Attempt at a Solution
looking at my notes i find a formula to find total potential energy
U=-4pieG integral from 0 to R M(r)P(r)r dr
What i am confused about is that it says hint answer only depends on G M a, but what about the R from the integral? it also said in the problem that hint integral from o to infinity x4dx/(x2+1)4 = pie/32
so looking at the hint integral, instead of doing integral from 0 to R would I just do it from 0 to infinity? That than would get rid of the R and just have answer of just G M a.
Is this right?