Solve the problem.
-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 630 miles
Above the earth in 14 hours at a velocity of 28,000 mph, how long would it take a satellite to complete an orbit if
It is at 1800 miles above the earth at a velocity of 22,000 mph? Use 3960 miles as the radius of the earth, and
Round your answer to the nearest hundredth of an hour.
A) 22.36 hr
B) 223.6 hr
C) 50.91 hr
D) 6.99 hr

Question

Quizplus · Accepted Answer

The time $T$ it takes for a satellite to complete an orbit varies directly with the radius $r$ of the orbit and inversely with the orbital velocity $v$, which can be represented as $T = k \cdot \frac{r}{v}$, where $k$ is a constant. Given the radius of the Earth as 3960 miles, the orbit radius for the first scenario is $3960 + 630 = 4590$ miles, and for the second scenario, it is $3960 + 1800 = 5760$ miles. Using the given data for the first scenario to find $k$, $14 = k \cdot \frac{4590}{28000}$, solving for $k$ gives $k = 68.8$. Then, for the second scenario, $T = 68.8 \cdot \frac{5760}{22000}$, which calculates to approximately $22.36$ hours.

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