You are a space explorer for Nasa investigating an exoplanet which may be habitable orbiting a star exactly like the sun. This exoplanet has a radius of orbit 5 times larger than that of Earth, a radius which is 3 times larger, and a mass twice as large as that of Earth. Two cylindrical space stations are sent to the exoplanet to investigate it, and they spin to simulate the gravitational field on Earth's surface.

(a) If the second space station has a radius 4 times that of the first, what will the period of the second space station be in terms of the period of the first?

(b) What will the period of the exoplanet planet be relative to the period of Earth?

(c) What must the period of the space stations be in terms of their radius and g if they simulate Earth's gravitational field strength?