First slide

Motion of planets and satellites

Question

The work done to increase the radius of orbit of a satellite of mass ’m’ revolving around a planet of mass M from orbit of radius R in to another orbit of radius 3R is

Easy

A

$\frac{2 G M m}{3 R}$
B

$\frac{G M m}{3 R}$
C

$\frac{G M m}{6 R}$
D

$\frac{G M m}{24 R}$

Solution

Work done = change in TE
$W o r k d o n e = \frac{G M m}{2} (\frac{1}{r_{1}} - \frac{1}{r_{2}}) = \frac{G M m}{2} (\frac{1}{R} - \frac{1}{3 R}) (∵ T E = \frac{- G M m}{2 r}) = \frac{G M m}{2} (\frac{3 - 1}{3 R}) = \frac{G m M}{3 R}$

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