Whenever two Apollo astronauts were on the surface of the Moon, a third astronau

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

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 Times 106 m. Determine the astronaut's orbital speed. Determine the period of the orbit.

Explanation / Answer

The orbiter was 1.98*10^6 meters above the Moon, (1.70*10^6 meters + 1.6*10^5 meters). The circumference of the orbit was 2?r = 1.24*10^7 meters.
g = (G*M)/r^2 where G is universal gravitational constant
V orbiter = ?((G*M)/r) = ?(g*r) = ?(1.25* 1.98*10^6) = 1.537 km/s
Period = 12,400/1.537 seconds = 2.24 hours

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