What is the period (in hours)of a satellite circling Mars 100 km above the planet's surface? The mass of Mars is 6.42 × 10²³ kg,its radius is 3.40 × 10⁶ m,and G = 6.67 × 10^-11 N ∙ m²/kg². A)1.75 h B)1.25 h C)1.15 h D)1.00 h E)1.45 h

Question

Quizplus · Accepted Answer

We can use Kepler's Third Law to calculate the period of the satellite:
$T^2 = \frac{4\pi^2}{GM}r^3$
where T is the period, G is the gravitational constant, M is the mass of Mars, and r is the distance between the satellite and the center of Mars.
Substituting the given values, we get:
$T^2 = \frac{4\pi^2}{(6.67	imes 10^{-11}	ext{ N} \cdot 	ext{m}^2/	ext{kg}^2)(6.42	imes 10^{23}	ext{ kg})}(100000+3.40	imes 10^{6})^3$
Simplifying, we get:
$T^2 \approx 93415$
$T \approx 1.75$ hours (rounded to two decimal places)
Therefore, the best choice is (A).

What Is the Period (In Hours)of a Satellite Circling Mars