First slide

Motion of planets and satellites

Question

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

Easy

A

one
B

two
C

half
D

infinity

Solution

K.E. is required for satellite to escape from earth's gravitational field $\frac{1}{2} m v_{e}^{2} = \frac{1}{2} m {(\sqrt{\frac{2 G M}{R}})}^{2} = \frac{G M m}{R}$ K.E. required for satellite to move in circular orbit
$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m {(\sqrt{\frac{G M}{R}})}^{2} = \frac{G M m}{2 R}$ The ratio between these two energies = 2

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