Solve.
-The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth) and inversely as the orbital velocity. If a satellite completes an orbit 890 miles
Above the earth in 17 hours at a velocity of 21,000 mph, how long would it take a satellite to complete an orbit if
It is at 1,700 miles above the earth at a velocity of 25,000 mph? (Use 3960 miles as the radius of the earth.)
A) 166.65 hours
B) 27.28 hours
C) 16.66 hours
D) 5.01 hours

Question

Quizplus · Accepted Answer

The time is calculated using the formula $ T = k \times \frac{R}{V} $, where $ R $ is the total radius (earth's radius plus altitude) and $ V $ is the velocity. First, find $ k $ using the given conditions: $ 17 = k \times \frac{4850}{21000} $. Solve for $ k $, then use it to find the time for the new conditions: $ T = k \times \frac{5660}{25000} $. This results in approximately 16.66 hours.

Solve. -The Time in Hours It Takes a Satellite to Complete