# Puzzling problem (using virial theorem)

1. Jun 19, 2011

### Findg

Consider a star of Radius R and mass M, with a pressure gradient given by

$\frac{dP}{dr}$ = $\frac{4\pi}{3}$G$\rho$2r exp(-$\frac{rr}{\lambda\lambda}$)

where $\rho$ is the central density. calculate the gravitational energy, using the Virial theorem. Show that in the limit $\lambda$ « R this energy is given by

E = $\frac{RGMM}{3R\lambda}$

for tecnical reasons:
MM = M2
rr = r2
$\lambda\lambda$ = $\lambda$2

Last edited: Jun 19, 2011