How many degrees does the Moon move per day relative to the fixed stars? About how long does the Moon take to move a distance equal to its own diameter across the sky?

a) in 1 day it covers = 13.19°  b)1 hour

Explanation:

a)

Moon completes one orbit around earth in 27.3 days. This is called siderial period which is measured according to the fixed stars. In other words 360° are covered in 27.3 days.

So, in 1 day it covers = 360/27.3 = 13.19° ~ 13.2°

b)

Velocity of moon = 1.022 km/sec

Diameter of moon = 3474 km

Time taken to cover distance equal to its diameter = 3474/1.022

              = 3399.22 sec = 56.65 minutes ~ 1 hour