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 orbital speed 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

The orbital speed $v$ of a moon is given by $v = \sqrt{\frac{GM}{r}}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, and $r$ is the orbital radius. The ratio of the orbital speeds of Phobos to Deimos is thus $\sqrt{\frac{r_{Deimos}}{r_{Phobos}}}$ = $\sqrt{\frac{23459}{9378}}$ ≈ 1.582, because the mass of Mars $M$ and the gravitational constant $G$ cancel out.

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