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 . 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

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 . Also, the calculation should be easier in spherical coordinates.