# Universal Gravitation and neutron stars

1. Dec 1, 2009

### 1st2fall

1. The problem statement, all variables and given/known data
Certain neutron stars (extremely dense stars) are believed to be rotating at about 6 rev/s. If such a star has a radius of 15 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

G=6.67*10-11m3 kg-1 s-2
2. Relevant equations
$$F_c{}=\frac{mv^{2}}{r}$$
$$F_g{}=\frac{GM_1{M_2{}}}{r^{2}}$$

3. The attempt at a solution
30$$\pi$$km*6rev/s=180$$\pi$$km/s
which gives the linear velocity of something on the surface of the neutron star.... but I'm clueless as to how to arrive at a mass of the star from it. I could the Centripetal acceleration but I'm not sure how that's related here. the only thing I can think of there is setting the centripetal acceleration equal to the gravitation acceleration which gives

Gm/r2=v2/r
m=v2r/G
which yields something like 7.28635682 × 10^24(kg?)

I'm just looking for advice on what I'm actually looking to do. I don't know what I should be looking for....

2. Dec 2, 2009

### ehild

Your formula is correct, but check the calculation.

ehild

3. Dec 2, 2009

### 1st2fall

Thank you very much! I realized a dropped a "pi" at some point when I went back over it.