What is the orbital period (in hours) of a satellite in circular orbit 6,000 km above the Earth's surface?

Answer 1

I know three things to use without calculus.
1. near earth orbits(100-200 miles) are about 90 minutes and
2. Geosynchronous(24 hour) orbits are about 27000 miles.
3. a kilometer is about .6 miles
6000 kilometers would be about 3600 miles
3600 is about 13% of 27000
13% of 22.5 is about 3

My approximation of the period of a satellite in a circular orbit of 6000 km would be in the 3 to 5 hour range.