Solution To Elementary Astrophysics Problem

 Problem: For a uniform sphere with a polytropic index n = 0 with uniform density, show that:

 V = -6/5 (GM²/R). 

Take the potential energy to be:

W=  3/ (n – 5) (GM²/ R )

Solution:

We may simplify using n = 0 to get:

W=  3/ (0 – 5) (GM²/ R ) = -3/5 (GM²/ R ),

And we have already shown that: V = 2W,  i.e. from  July 6 post,

Therefore: V = 2W  = 2 [-3/5 (GM²/ R )] = -6/5 (GM²/ R)