Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 160 km above the surface of the Moon, where the acceleration due to gravity is 1.42 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 160 km above the surface of the Moon, where the acceleration due to gravity is 1.42 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.

I know I should use the variation of Newton's second law that says F=ma, or F=m(v^2/r).  I just don't really get how to relate these two problems, since I have a radius of the moon, and a radius of orbit.

Zee Sbt · Answer

a=V^2/r a)find r : 160*10^3 + 1.7*10^6 = ... V=sqrt(ar)= sqrt(1.42r)= ... That's your answer. b) T=(2pir)/V