How Long and Fast Did Apollo 11 Orbit the Moon?

[kashiark]

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.

 

[Kurdt]

111km will be the average altitude above the moon's surface and nothing to do with circumference.

 

[tomcue]

Your calculations and equations are mostly correct, but there are a few minor errors. First, the given average orbit of 111km is not the circumference, but rather the radius of the orbit. So you do not need to multiply by 1000 to convert to meters. Additionally, in the equation for velocity, the mass of the moon should be in kilograms, not in grams. Finally, in the equation for period, the radius should be squared, not cubed.

Corrected solutions:

a. To find the period, we can use the equation T = 2π√(r³/(Gm)). Plugging in the values, we get:

T = 2π√((111000)^3/(6.67*10^-11 * 7.3*10^22)) = 115 minutes

b. To find the velocity, we can use the equation v = √(Gm/r). Plugging in the values, we get:

v = √((6.67*10^-11 * 7.3*10^22)/(111000)) = 1600 m/s

So your answer for the velocity was correct, but the period was incorrect due to the errors mentioned above. Keep in mind that these are average values and the actual period and velocity may vary slightly due to the moon's elliptical orbit.