The moons of Mars,Phobos (Fear)and Deimos (Terror),are very close to the planet compared to Earth's Moon.Their orbital radii are 9,378 km and 23,459 km respectively.What is the ratio of the period of revolution of Phobos to that of Deimos?
A) 0.2528
B) 0.3998
C) 1.582
D) 2.858
E) 3.956

Question

Quizplus · Accepted Answer

We can use Kepler's third law, which states that the square of the period of revolution (T) of a satellite is proportional to the cube of its average distance (r) from the planet it orbits. Mathematically, T^2 ∝ r^3. Using this, we can write:

(T_phobos / T_deimos)^2 = (r_phobos / r_deimos)^3

Substituting the values given, we get:

(T_phobos / T_deimos)^2 = (9,378 / 23,459)^3
(T_phobos / T_deimos)^2 = 0.1056
T_phobos / T_deimos = sqrt(0.1056)
T_phobos / T_deimos = 0.325

Therefore, the ratio of the period of revolution of Phobos to that of Deimos is 0.325, which is closest to option A) 0.2528 after rounding to four decimal places.

The Moons of Mars,Phobos (Fear)and Deimos (Terror),are Very Close to the Planet