Our moon is 240,000 miles away and takes about 28 days to orbit the earth. how high up (in miles) would a satellite have to be placed if it were to orbit the earth in 24 hours. (this satellite orbits over the same spot on the earth in an equatorial orbit.)

The moon takes 28 days to orbit the earth at a distance of 240,000 miles. The satellite will take 24 hours to orbit the earth at an unknown distance. 

We want to convert hours into days so that we have a constant unit of time for both the moon and satellite.

There are 24 hours in a day. Divide the amount of hours by 24:



The satellite will take 1 day to orbit the Earth.

This question involves Kepler's 3rd law of planetary motion. This law can use a simplified formula:



T is the orbital period, and d is the distance from the earth for the moon and satellite.

We can set k to equal the same formula:



Plug in your values for the moon and satellite:






We can rearrange this proportion so that we can solve for x:









The altitude of this satellite will be 26,027.9 miles. Keeping significant figures in mind, the altitude will be 26,000 miles.