Question

The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

(1) \(\frac {v}{3}\)

(2) \(\frac {v}{4}\)

(3) \(\frac {v}{12}\)

(4) \(\frac {v}{6}\)

Answer 1

(1) \(\frac {v}{3}\)

\(V_{escape}=\sqrt {\frac {2GM}{R}}\)

\(V_{planet}=\sqrt {\frac {2GM}{R}}=V\)

\(V_{Moon}=\sqrt {\frac {2GM \times 16}{144\,R}}=\frac {1}{3}\sqrt {\frac {2GM}{R}}\)

\(V_{moon} = \frac {V_{Planet}}{3} =\frac {V}{3}\)