You and your team have the task of designing a space station that will mimic the force due to gravity on the earth, the moon, and Mars. The station’s purpose is to physically prepare astronauts for the transition to the different gravitational forces they will experience on Mars and the moon, but also to acclimate them to Earth’s gravity when they return. The space station should be constructed of concentric cylinders, with a maximum allowed diameter of 300 m.

(a) Draw a sketch of the space station and label the levels (i.e., the cylinders) according to the celestial body whose gravitational force each cylinder simulates.

(b) Determine the required radii of each cylinder. Assume the outermost cylinder has the maximum allowable diameter.

(c) What is the period of rotation of the station? (g_Earth = 9.80 m/s², g_Mars = 3.76 m/s², and g_moon = 1.62 m/s²)