Pulsar Radius from its rotational period

[TFM]

1. The problem statement, all variables and given/known data

A pulsar emits bursts of radio waves with a period of 10 ms. Find an upper limit to the radius of the pulsar.

2. Relevant equations

Not Sure

3. The attempt at a solution

Can anyone help with this, I cannot see how the period will help tell you the upper limit to the radius. I know that pulsars are basically neutron stars, and they have high densities (10^15 kg/m^3), but I ams lightly unsure how to get the radius of the pulsar from its period.

Any helpful suggestions would be most helpful,

Thanks in advanced,

TFM

[mgb_phys]

What happens when the rotation rate is fast enough that centrifugal force on a point on the surface as is stronger than gravity?

[TFM]

Well, Gravity is pulling down, the centrifugal force is pushing outwards, so items on the surface would be "pushed" off of the surface.

[mgb_phys]

Correct - so at a certain speed the surface would break off, doesn't this set a maximum radius for a given rotation rate?

[TFM]

Indeed it would,

So:

mg = m\omega^2r

g = \omega^2r


And since:

Omega = \frac{2\pi}{Period}

Thus:

g = \frac{4\pi^2}{Period^2}r

Does this look okay?

[mgb_phys]

You will need to write 'g' for the star in terms of it's mass (or density) and radius.

[TFM]

True, but we aren't given a mass for the star? Would we use the density as being 10^15?

[TFM]

Okay, so if we use:

g = -\frac{MG}{r^2}

and

M = density*volume

M = density*(\frac{4}{3}\pi r^3)

g = -\frac{(density*(\frac{4}{3}\pi r^3))G}{r^2}


Thus:

-\frac{(density*(\frac{4}{3}\pi r^3))G}{r^2} = \frac{4\pi^2}{Period^2}r

Since we need the magnitude only for g:

\frac{(density*(\frac{4}{3}\pi r^3))G}{r^2} = \frac{4\pi^2}{Period^2}r

(density*(\frac{4}{3}\pi ))G = \frac{4\pi^2}{Period^2}

Does this look better?

TFM