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Consider a star of Radius R and mass M, with a pressure gradient given by
[itex]\frac{dP}{dr}[/itex] = [itex]\frac{4\pi}{3}[/itex]G[itex]\rho[/itex]2r exp(-[itex]\frac{rr}{\lambda\lambda}[/itex])
where [itex]\rho[/itex] is the central density. calculate the gravitational energy, using the Virial theorem. Show that in the limit [itex]\lambda[/itex] « R this energy is given by
E = [itex]\frac{RGMM}{3R\lambda}[/itex]for tecnical reasons:
MM = M2
rr = r2
[itex]\lambda\lambda[/itex] = [itex]\lambda[/itex]2
[itex]\frac{dP}{dr}[/itex] = [itex]\frac{4\pi}{3}[/itex]G[itex]\rho[/itex]2r exp(-[itex]\frac{rr}{\lambda\lambda}[/itex])
where [itex]\rho[/itex] is the central density. calculate the gravitational energy, using the Virial theorem. Show that in the limit [itex]\lambda[/itex] « R this energy is given by
E = [itex]\frac{RGMM}{3R\lambda}[/itex]for tecnical reasons:
MM = M2
rr = r2
[itex]\lambda\lambda[/itex] = [itex]\lambda[/itex]2
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