First slide

Gravitaional potential energy

Question

A satellite is moving in a circular orbit at a height R above the surface of earth with kinetic energy K. If the satellite is suddenly stopped, with what kinetic energy will it strike the surface of earth?

Easy

A

2 K
B

4 K
C

3 K
D

K/2

Solution

Initially, $- K = - \frac{G M m}{2 (2 R)} \Rightarrow K = \frac{G M m}{4 R}$
when the satellite is falling on to the surface of earth, conserving energy,
$K^{1} + (- \frac{G M m}{R}) = 0 + (- \frac{G M m}{2 R})$
$\Rightarrow K^{1} = \frac{G M m}{2 R} = 2 K$

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