A planet’s moon revolves around the planet with a period of 37 Earth days in an approximately circular orbit of radius of 4.9×108 m. How fast does the moon move?

Our moon completes one orbit in approximately 28 (Almost a month).

By multiplying 86,400 (the seconds in one Earth day) by 28 you have the time taken to complete the orbit (2,419,200s).  But you still need to know the distance that it travels in that time.

The distance to the moon is approximately 380,000km or 380 million metres (3.8x10^8)m

The circumference of this orbit is therefore 2*pi*3.8x10^8 = 2.4x10^9m  (2.4 billion meters!)

This distance divided by the time taken will give you the speed.

2.4x10^9 m / 2.4x10^6 s = 1000m/s.    This works out to be about 3600km/h

Now, onto your problem.

86400*40 = time in seconds (3.4x10^6s)

2*pi*5.7x10^8 = orbital circumference (3.5x10^9)

Speed = distance / time  =  3.5x10^9 / 3.4 x10^6 = once again 1000m/s or 3,600 km/h  :)

Explanation:

Your welcome.