Question

A satellite 200 miles above the earth is orbiting the earth once every 4 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

Answer 1

Exact answer: 2100pi  miles

Approximate answer: 6594 miles

note: I used pi = 3.14 as an approximation. Use more decimal digits for pi if you want a more accurate answer

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Explanation:

Assume for the sake of simplicity that the satellite travels in a circular orbit. The radius of this orbit is 4000+200 = 4200 miles as we account for the earth's radius plus the height of the satellite. Also assume that the satellite's height doesn't change throughout its orbit.

Find the circumference of a circle with radius r = 4200 miles

C = 2*pi*r

C = 2*pi*4200

C = 8400pi

The satellite travels exactly 8400pi miles in one full orbit around the earth. This takes place over 4 hours. So we can write these three ratios

1 orbit : 8400pi miles traveled

1 orbit : 4 hours

4 hours : 8400pi miles traveled

Now divide both sides of the last ratio by 4 to end up with this...

4 hours : 8400pi miles traveled

4/4 hours: 8400pi/4 miles traveled

1 hour: 2100pi mile traveled

The satellite travels exactly 2100pi miles in 1 hour. This is approximately equal to 2100*3.14 = 6594 miles if you use 3.14 for pi

Use more decimal digits for pi if you need better accuracy