(a) A space explorer comes across a spherical planet with a small moon in orbit around it. He observes that the moon completes one full orbit every 33 Earth days and moves at a distance R = 390 million m from the center of the planet. What is the mass of the planet? (One earth day =86400 s)

(b) Upon further exploration he finds another satellite orbiting the planet in one third the time the moon did. What is the orbital radius of the satellite?

(c) Upon further exploration he finds another satellite orbiting the planet in one third the time the moon did. What is the orbital radius of the satellite?

(d) The explorer now lands his spacecraft on the surface of the planet near the North Pole. He weighs himself and finds he weighs only W_planet = 152 lbs while on earth he weighed W_earth = 182 lbs. Assuming the explorer hasn't dieted on his trip, what is the radius of the planet?         

(e) The explorer continues his studies and soon ends up at the equator. There he finds the scale reads 95% of what it did at the North Pole. How long does it take the planet to make one complete rotation?

Solution