# Period of radial oscillations

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1. Oct 4, 2015

### June_cosmo

• 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?

2. Oct 5, 2015

### Staff: Mentor

Don't forget the integration constant. What is the boundary condition for pressure?
That follows from the velocity.

3. Oct 5, 2015

### June_cosmo

Thanks for your answer. No the problem doesn't say the boundary condition. How do I know that?

Last edited: Oct 5, 2015
4. Oct 5, 2015

### Staff: Mentor

What do you expect as pressure at the surface?

5. Oct 5, 2015

### June_cosmo

Because P(r) decrease along r it would be 0? so I can derive the constant?

6. Oct 6, 2015

### Staff: Mentor

It is zero, as particles would move outwards otherwise. Yes, this allows to find the constant.