First slide

Motion of planets and satellites

Question

Escape velocity on the surface of earth is $11.2 k m / s$ . Escape velocity from a planet whose mass is the same as that of earth and radius 1/4 that of earth is

Moderate

A

2.8 km/s
B

15.6 km/s
C

22.4 km/s
D

44.8 km/s

Solution

$v_{e} = \sqrt{\frac{2 G M}{R}} = 11.2 k m / s v_{p} = \sqrt{\frac{2 G M_{P}}{R_{P}}} = \sqrt{\frac{2 G M}{\frac{R}{4}}} = \sqrt{4 (\frac{2 G M}{R})} = 2 \sqrt{\frac{2 G M}{R}} = 2 \times 11.2 k m / s = 22.4 k m / s$

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