Kepler's laws: 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

According to Kepler's third law, the square of the orbital period is proportional to the cube of the semi-major axis of its orbit. Therefore, the ratio of the periods is the square root of the ratio of the cubes of their orbital radii: (9378/23459)^(3/2) ≈ 0.2528.

Kepler's Laws: the Moons of Mars, Phobos (Fear) and Deimos