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By what percent the energy of satallite has to be increased to shift it from an orbit of radius r to $\large\frac{3}{2}$$r$

\[(a)\;66.7 \% \quad (b)\; 33.3\%\quad (c)\;15 \% \quad (d)\;20.3 \%\]

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1 Answer

energy of satellite in the first case
energy in the second case is
$E_2=\large\frac{GMm}{2\bigg(\Large\frac{3}{2}r \bigg)}$
$\Delta E =\large\frac{GMm}{r} \bigg(\frac{1}{2}-\frac{1}{3}\bigg)=\frac{GMm}{6}$
$\%$ increase $=\large\frac{\Large \frac{GMm}{6r}}{\Large \frac{GMm}{2r}}$$ \times 100$
$\qquad= 33.3 \%$
Hence b is the correct answer


answered Aug 20, 2013 by meena.p
edited Feb 17, 2014 by meena.p

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