First slide

Gravitaional potential energy

Question

A planet is moving in a circular orbit around earth. Then the minimum increase of its orbital speed for which the planet will escape to infinity is _____

Moderate

A

26.3 %
B

41.4 %
C

50 %
D

73.2 %

Solution

New orbital speed must be equal to the magnitude of escape velocity at any position of the orbit.
$\begin{array}{l} V = \sqrt{\frac{G M}{r}}, V^{'} = \sqrt{\frac{2 G M}{r}} = \sqrt{2} V \\ ∴ % i n c r e a s e = \frac{V^{'} - V}{V} = (\sqrt{2} - 1) \times 100 % = 41.4 % \end{array}$

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