Question

Two small, irregularly-shaped moons, Phobos and Deimos, orbit Mars. They are believed to be captured asteroids. What are the approximate orbital periods of Phobos and Deimos respectivelyA. 7 days, 12 hours; 1 day, 2 hours
B. 7 hours 35 minutes; 1 day, 6 hours

C. 14 days, 10 minutes; 2 days, 12 hours

D. 15 hours; 2 days, 12 hours

Answer 1

Answer:

Option B

Explanation:

The orbital periods of Phobos and Deimos can be calculated using the Newton's form of Kepler's third law:  

$T^{2} = \frac {4 \pi^{2}}{G*M_{m}} \cdot a^{3}$  

where T: is the period, G: is the gravitational constant = 6.67x10⁻¹¹ m³kg⁻¹s⁻², Mm: is the mass of Mars = 6.42x10²³ kg, $a_{P}$: is the average radius of orbit for the satellite Phobos = 9376 km, and $a_{D}$: is the average radius of orbit for the satellite Deimos = 23463 km.  

The orbital period of Phobos is:

$T = \sqrt {\frac {4 \pi^{2}}{6.67 \cdot 10^{-11} m^{3} kg^{-1} s^{-2}*6.42 \cdot 10^{23} kg} \cdot (9.376 \cdot 10^{6} m)^{3}} = 2.75 \cdot 10^{4} s = 7 hours 36 min$        

The orbital period of Deimos is:

$T = \sqrt {\frac {4 \pi^{2}}{6.67 \cdot 10^{-11} m^{3} kg^{-1} s^{-2}*6.42 \cdot 10^{23} kg} \cdot (2.35 \cdot 10^{7} m)^{3}} = 1.09 \cdot 10^{5} s = 1 day 6 hours$      

Therefore, the approximate orbital periods of Phobos and Deimos are 7 hours 35 minutes and 1 day 6 hours, respectively, so the correct answer is option B.    

I hope it helps you!