First slide

Motion of planets and satellites

Question

A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is $R_{0}$ and mass of the earth M, the angular momentum about the centre of the earth is

Easy

A

$m \sqrt{G M R_{0}}$
B

$M \sqrt{G m R_{0}}$
C

$m \sqrt{\frac{G M}{R_{0}}}$
D

$M \sqrt{\frac{G M}{R_{0}}}$

Solution

Angular momentum = Mass ×Orbital velocity ×Radius
$= m \times (\sqrt{\frac{G M}{R_{0}}}) \times R_{0} = m \sqrt{G M R_{0}}$

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