Imagine that you are kidnapped by some aliens and they drop you on an arbitrary planet in an arbitrary arm of the Milky Way, which does not even have a star to support it. Before leaving you there, the aliens tell you: “Far away from here, in the direction of the star you call Spica, there is a portal which will take you back to the Earth.” You see that the stars appear to go around you once in 25.1 earth hours, around a welldefined axis, which is exactly horizonal at your location. The planet has a tiny moon, which orbits in the planet’s equatorial plane with roughly the same angular size at all times. The direction of the moon’s revolution is the same as the rotation of the planet. You measure the angular speed of the moon with respect to the distant stars when it is rising and find it to be 2.13 × 10−6 rad s−1 . You do the same when the moon is directly overhead and find it to be 1.06 × 10−6 rad s−1 .
Use this information to find the revolution period (Trev) of the moon with respect to the distant stars. Assume dm ≥ Rp (dm is the distance to the moon from the centre of the planet and Rp is the radius of the planet).
