First slide

Gravitaional potential energy

Question

The escape velocity from a spherical planet is v_o. What is the escape velocity corresponding to another planet of twice the radius and half the mean density?

Moderate

A

$(\sqrt{2}) v_{0}$
B

$\frac{v_{0}}{\sqrt{2}}$
C

2v₀
D

4v₀

Solution

$v_{o} = \sqrt{\frac{2 G M}{R}} = \sqrt{\frac{2 G (\frac{4}{3} {πR}^{3} ρ)}{R}} = 2 R \sqrt{\frac{2}{3} πGρ}$
$v_{0}' = 2 (2 R) \sqrt{\frac{2}{3} πG (\frac{ρ}{2})} = \sqrt{2} v_{0}$

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