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

**JohnDMalcolm** · August 7th 2012, 03:37 AM

A small planet orbits a static neutron star in a circular orbit whose proper circumference is $6 \times 10^{11} \ \mbox{m}$ . 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

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

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

**ojones** · August 13th 2012, 02:57 PM

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

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