How long does this trip around the Moon take?

Question

An astronaut on the surface of the Moon fires a cannon to launch an experimental package, which leaves the barrel moving horizontally. Assume that the free-fall acceleration on the Moon is one sixth that on the Earth.
(a) What must be the muzzle speed of the probe so that it travels completely around the Moon and returns to its original location?
km/s
(b) How long does this trip around the Moon take?
h

Answer 1

In a surface-level orbit
centripetal acceleration Ac = g
Ac = v^2/r(moon), so v = sqrt(g(moon)*r(moon)) (ans. a)
t = 2pi*r(moon)/v (ans. b)
You can solve these given r(moon) = 1737400 m