First slide

Motion of planets and satellites

Question

In a satellite if the time of revolution is T, then K.E. is proportional to

Moderate

A

$\frac{1}{T}$
B

$\frac{1}{T^{2}}$
C

$\frac{1}{T^{3}}$
D

$T^{- 2 / 3}$

Solution

$v = \sqrt{\frac{G M}{r}} ∴ K . E . \propto v^{2} \propto \frac{1}{r} - - - (1) a n d T^{2} \propto r^{3} \Rightarrow T^{\frac{2}{3}} \propto r \Rightarrow \frac{1}{r} \propto T^{- \frac{2}{3}} - - - (2) F r o m (1) a n d (2) w e g e t ∴ K . E . \propto T^{- 2 / 3}$

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