An observer in a rocket is in a circular equatorial orbit arounda planet and the period of the orbit is the same as the period of revolution of the planet. The planet has mass M = 1033kg and radius R = 1000km. The observer sends a signal every 20 seconds according to its clock towards an observer on the equator. According to the observer on the planet, each day lasts 10 hours. The Schwarzschild metric is appropriate to describe the geometry outside the planet.
Calculate the radius of the rocket's orbit.
Schwarzschild's metric and the geodesic equations.
The Attempt at a Solution
I tried crying.
I seriously haven't been able to write anything on this. Normally, in a classical Newtonian problem, I would get an expression of the speed "of" circular orbits as a function of the orbit radius knowing the time of 1 revolution is 10 hours and solve for r.
But here there is no gravitational force. I just know that the orbit is a geodesic.