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 200 km above the surface of the Moon, where the acceleration due to gravity is 1.36 m/s2. The radius of the Moon is 1.70 106 m. (a) Determine the astronaut's orbital speed. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s (b) Determine the period of the orbit. s

Explanation / Answer

The orbiter was 1.98*10^6 meters above the Moon, (1.70*10^6 meters + 2,8*10^5 meters). The circumference of the orbit was 2pr = 1.24*10^7 meters. g = (G*M)/r^2 where G is universal gravitational constant V orbiter = v((G*M)/r) = v(g*r) = v(1.25* 1.98*10^6) = 1.537 km/s Period = 12,400/1.537 seconds = 2.24 hours

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