The escape speed from the surface of the Earth is 11.2 km/s.Estimate the escape speed for a spacecraft from the surface of the Moon.The Moon has a mass 1/81 that of Earth and a radius 0.25 that of Earth.
A)2.5 km/s
B)4.0 km/s
C)5.6 km/s
D)8.7 km/s

Question

Quizplus · Accepted Answer

The escape velocity $v$ from a celestial body is given by the formula $v = \sqrt{\frac{2GM}{r}}$, where $G$ is the gravitational constant, $M$ is the mass of the celestial body, and $r$ is its radius. Given that the Moon's mass is $1/81$ that of Earth and its radius is $0.25$ times that of Earth, the escape velocity from the Moon can be calculated relative to Earth's escape velocity ($11.2$ km/s) as follows: $v_{\text{Moon}} = 11.2 \times \sqrt{\frac{1/81}{0.25^2}} = 11.2 \times \sqrt{\frac{1}{81}} \times \sqrt{16} = 11.2 \times \frac{1}{9} \times 4 = 2.5$ km/s.

The Escape Speed from the Surface of the Earth Is