First slide

Gravitaional potential energy

Question

The PE of a satellite is –U. Its KE is

Moderate

A

U
B

2U
C

-U
D

U/2

Solution

$P E = - \frac{G M m}{r} ∴ U = \frac{G M m}{r} O r b i t a l s p e e d V = \sqrt{\frac{G M}{r}} K E = \frac{1}{2} m V^{2} = \frac{1}{2} m \frac{G M}{r} = \frac{G M m}{2 r} ∴ K E = \frac{U}{2}$

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