Calculate the energy required to move a body of mass m from an or… - Vidyadip

Question

Calculate the energy required to move a body of mass $m$ from an orbit of radius $2 R$ to $3 R$.

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Answer

Gravitational PE of mass m in orbit of radius $R=U=-\frac{G M m}{R}$
$
\begin{aligned}
& \therefore U_i=\frac{G M m}{2 R} \\
& U_f=-\frac{G M m}{3 R}
\end{aligned}
$
Energy required = Potential energy of the Earth(mass system when mass is at distance 3R) - Potential energy of the Earth (mass system when mass is at distance 2R)
$
\begin{aligned}
& \Delta U=U_f-U_i=G M m\left[\frac{1}{3}-\frac{1}{2}\right] \\
& =\frac{G M m}{6 R}
\end{aligned}
$

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