How Long and Fast Did Apollo 11 Orbit the Moon?

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SUMMARY

On July 19, 1969, Apollo 11 adjusted its orbit around the Moon to an average altitude of 111 km. The calculations for the orbital period and velocity were derived using the formulas T = 2π√(r³/(Gm)) and v = √(Gm/r). The correct orbital period was determined to be 6892 seconds (or 115 minutes), and the orbital velocity was calculated at 1600 m/s. The initial misunderstanding involved the interpretation of the 111 km as circumference rather than altitude.

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Homework Statement


On July 19, 1969, Apollo 11's orbit around the moon was adjusted to an avearge orbit of 111km. The radius of the moon is 1785km, and the mass of the moon is 7.3 * 10^22kg.
a. How many minutes did Apollo 11 take to orbit the moon?
b. At what velocity did it orbit the moon?


Homework Equations


C=2r*pi
v = √(Gm/r)
T = 2pi √(r³/(Gm))


The Attempt at a Solution


I'm assuming that 111 is the circumference, and I'm finding the radius and adding it to the moon's radius. When I multiply by 1000, it's because the equation calls for it in meters.
111=2r*pi
r=17.7

T = 2pi √((1000(17.7+1785))³/(G*7.3*10^22))
T=6892 seconds or 115 minutes

v = √((G7.3*10^22)/(1000(17.7+1785)))
v=1600 m/s

I'm almost positive that these answers are incorrect, but I'm not sure what I did wrong.
 
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111km will be the average altitude above the moon's surface and nothing to do with circumference.
 

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