Help with formula? need examples so that I can work the problem?

Question

Find an approximate value for the rate at which the moon orbits the earth. Assume that the moon’s orbit is circular

I got a hint and it mention that the average distance between the earth and the moon is 382,000,000 meters. I just want a formula to work with

Answer 1

The formula is Kepler's third law, that for satellites in orbit around the same primary, the square of the period is proportional to the cube of the orbital radius.

So start from some known facts. An Earth-grazing artificial satellite has an orbital radius of 6,400 km and a period of 90 minutes. The Moon has an orbital radius of 382,000 km.

With the calculator, we find that the Moon is nearly 60 times as far away, so cube it and take the square root, that's 460-odd, multiply by 1.5 hours and convert to days, it comes to 28.8 days. That is indeed approximately the rate at which the Moon orbits the Earth, once every 28-and-a-good-bit days. Kepler was right!

Answer 2

Look up how far away the moon is. This will be the radius of the circle. Figure out the circumference from the radius. How long does it take to orbit once? Divide the distance by time to get it's speed.