Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 400 km above the surface of the Moon. At this altitude, the free-fall acceleration is 1.11 m/s2. The radius of the Moon is 1.70 106 m.

Question

Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 400 km above the surface of the Moon. At this altitude, the free-fall acceleration is 1.11 m/s2. The radius of the Moon is 1.70  106 m.
(a) Determine the astronaut's orbital speed. (b) Determine the period of the orbit.

drwls · Answer

V^2/R = a = 1.11 m/s^2 For R, use the distance from the center of the Moon, 1.70*10^6 m + 4*10^5 m. Solve for V For the period P, solve V*P = 2 pi R, the orbit circumference