First slide

Motion of planets and satellites

Question

A satellite moves around the earth in a circular orbit with speed v. If m is the mass of the satellite, its total energy is

Moderate

A

$- \frac{1}{2} {mv}^{2}$
B

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

$\frac{3}{2} {mv}^{2}$
D

$\frac{1}{4} {mv}^{2}$

Solution

Total mechanical energy is given by
$\begin{array}{l} E = K + u = - \frac{GMm}{2 a} - \frac{GMm}{a} = \frac{- GMm}{2 a} \\ \frac{GM}{a} = v^{2} \Rightarrow E = - \frac{1}{2} {mv}^{2} \end{array}$

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