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 780 km above the surface of the Moon, where the acceleration due to gravity is 0.798 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 used v=sqrt(rgtan(theta)) I got the angle by tan(theta)=1.7*10^6/(1.7*10^6+780000). theta = 34.43. Then i got 964 for the velocity, however it said I was wrong? Can you tell me where I went wrong?

Explanation / Answer

the initial formula used was wrong here v=sqrt(rg') where g' =g*{1.7/(1.7+.78)}^2 and g=0.798m/s2

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