Earth's moon is 3.8 X 10 8 m from the planet and is in freefall. Acceleration due to the Earth's gravity acting on the moon is 2.70X 10 -3. What is the moon's speed? How long does it take to make a complete orbit?

Answer 1

I can't believe they did not give you the units (dimensions) of acceleration along the number. In physics, that is a no-no. I will assume the units are m/s^2.

The acceleration of the moon toward the Earth is V^2/R = 2.7*10^-3 m/s^2
Since they told you the value of R, you can solve for V.

For the period P of one revolution can be obtained from for
V P = 2 pi R

P should turn out to be about 27 days. A month is a bit longer because the moon must travel more than one revolution to get back to the same phase, as a result of the Earth-moon system's motion around the sun