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

Option B

Explanation:

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

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, : is the average radius of orbit for the satellite Phobos = 9376 km, and : is the average radius of orbit for the satellite Deimos = 23463 km.  

The orbital period of Phobos is:

The orbital period of Deimos is:

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.    

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