Answer:
Option B
Explanation:
The orbital periods of Phobos and Deimos can be calculated using the Newton's form of Kepler's third law: Ā
[tex] T^{2} = \frac {4 \pi^{2}}{G*M_{m}} \cdot a^{3} [/tex] Ā
where T: is the period, G: is the gravitational constant = 6.67x10ā»Ā¹Ā¹ mĀ³kgā»Ā¹sā»Ā², Mm: is the mass of Mars = 6.42x10Ā²Ā³ kg, [tex]a_{P}[/tex]: is the average radius of orbit for the satellite Phobos = 9376 km, and [tex]a_{D}[/tex]: is the average radius of orbit for the satellite Deimos = 23463 km. Ā
The orbital period of Phobos is:
[tex] 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 [/tex] Ā Ā Ā Ā
The orbital period of Deimos is:
[tex] 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 [/tex] Ā Ā Ā
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. Ā Ā
I hope it helps you! Ā Ā Ā
