First slide

Motion of planets and satellites

Question

For the moon to cease to remain the earth's satellite, its orbital velocity has to increase by a factor of

Easy

A

$2$
B

$\sqrt{2}$
C

$1 / \sqrt{2}$
D

$\sqrt{3}$

Solution

$v_{e} = \sqrt{2} v_{0},$ i.e. if the orbital velocity of moon is increased by factor of $\sqrt{2}$ then it will escape out from the gravitational field of earth.

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