Consider a star of Radius R and mass M, with a pressure gradient given by(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{dP}{dr}[/itex] = [itex]\frac{4\pi}{3}[/itex]G[itex]\rho[/itex]^{2}r 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 = M^{2}

rr = r2

[itex]\lambda\lambda[/itex] = [itex]\lambda[/itex]^{2}

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# Homework Help: Puzzling problem (using virial theorem)

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