Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 720 km above the surface of the Moon, where the acceleration due to gravity is 0.839 m/s2. The radius of the Moon is 1.70 106 m.

Question

(a) Determine the astronaut's orbital speed.
m/s

(b) Determine the period of the orbit.
s

Answer 1

(a) First you need the value of the acceleration of gravity at the orbit location. Call it g. Here are the steps.

Moon radius = Rm = 1.7*10^6 m
Orbit height = H = 7.2*10^5 m
Orbit radius = R = Rm + H
= 2.42*10^6 m
R/Rm = 1.424
gm (at moon's surface) = 0.839 m/s^2
g(at orbit radius location) =
gm/(1.424)^2 = 0.414 m/s^2

Now set M g = M V^2/R

Satellite mass M cancels out.
V^2 = (R*g)
V = 1000 m/s

(b) orbit period = 2*pi*R/V
= 15,210 s
= 4.2 hours

Answer 2

The acceleartion due to Gravity is already given at the orbital height. Proceed to use to value of gravitational acceleration given of 0.839m/2^2. The rest of the strategy is all good.
-m

Answer 3

Why does this look like this in 2018, fire your programmer please thanks <3