Question

A satellite 200 miles above the earth is orbiting the earth once every 6 hours. How far does the satellite travel in 1 hour?

(Assume the radius of the earth is 4,000 miles.) Give your answer as both an exact value and an approximation to three significant digits

Answer 1

The answer is below

Explanation:

Speed is the ratio of total distance travelled to total time taken to cover distance.

The radius of the orbit = radius of earth + height of satellite from earth = 4000 miles + 200 miles = 4200 miles

The total distance around the orbit = perimeter of orbit = 2π(radius of orbit) = 2π(4200) = 8400π miles

`Speed=(distance \ traveled)/(time\ taken) =(8400\pi\ miles)/(6\ hours) =1400\pi\ miles/hour\\\\Distance \ traveled\ in \ 1\ hour=1400\pi\ miles/hour*1\ hour=1400\pi\ miles=4398.23\ miles\\\\Distance=4398\ miles`