posted by Anonymous
A satellite orbits the earth at a distance of 10,000 miles from the earth's center. At this distance the force of gravity on the satellite is 90lbs. What would the force on the satellite be if the distance were 5000 miles instead? At what distance from the earth's center would the force on the same satellite be 10 lbs?
Just use the inverse square law.
5000 miles is half the distance compared to 10,000 miles, so the weight (gravity force) is 4 times higher (360 lb).
To reduce the weight to 10 lb, that is a reduction of 9 times. You will have to be sqrt 9 = three times farther away, which is 30,000 miles.