- #1
June_cosmo
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Missing template due to originally being posted in different forum.
Assuming a neutron star is a uniformly dense sphere of radius 10km and mass =1.4 mass of sun, derive the period of radial oscillations.First use hydrostatic equilibrium to calculate p, then the velocity of sound is $$v= \sqrt{ \gamma p / \rho}$$, so the period of pulsation is time it takes from r=0 to r=R and come back.
I first used hydrostatic equilibrium:$$ \frac{dp}{dr}=- \frac{GM(r)\rho}{r^2}$$
and $$M(r)= \frac{4}{3} \pi r^3 \rho$$ so that $$ p(r)=- \frac {2}{3} \pi \rho^2r^2$$,
so question 1: how does there is a negative value?
question 2:how do I calculate time from r=0 to r=R and back?
I first used hydrostatic equilibrium:$$ \frac{dp}{dr}=- \frac{GM(r)\rho}{r^2}$$
and $$M(r)= \frac{4}{3} \pi r^3 \rho$$ so that $$ p(r)=- \frac {2}{3} \pi \rho^2r^2$$,
so question 1: how does there is a negative value?
question 2:how do I calculate time from r=0 to r=R and back?