Computing the mass of a neutron star from a planet's orbit

A small planet orbits a static neutron star in a circular orbit whose proper circumference is $\displaystyle 6 \times 10^{11} \ \mbox{m} $. The orbital period takes 200 days of the planet's proper time. Estimate the mass M of the star.

I'm assuming I should use the far field metric

$\displaystyle ds^{2} = -(1 - \frac{2M}{r})dt^2 + (1 - \frac{2M}{r})(dx^2 + dy^2 + dz^2) $

but I'm not sure were to go from there.

Re: Computing the mass of a neutron star from a planet's orbit

The orbit of the planet will be a geodesic with respect to this metric. My guess is that calculating the geodesics and substituting in the given condtions should yield $\displaystyle M$. Also, the calculation should be easier in spherical coordinates.