If the ratios of masses and radii of Mars to Earth are 0.11 and 0.53, respectively, calculate the ratio of the escape velocity of Earth divided by that of Mars.
A) 4.8
B) 2.2
C) 0.5
D) 6.6
E) 1.6

Question

Quizplus · Accepted Answer

The escape velocity is proportional to the square root of the mass-to-radius ratio. Thus, the ratio of escape velocities is sqrt((0.11/0.53)/(1/1)) = sqrt(0.11/0.53) ≈ 0.46. Therefore, the ratio of Earth's escape velocity to Mars' is 1/0.46 ≈ 2.2.

If the Ratios of Masses and Radii of Mars to Earth