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Satellites

A satellite i...

Question

A satellite is changes it orbit from radius of R to radius of 2R. If its initial kinetic energy is $K_{1}$ then calculate the new kinetic energy.

\frac{K_{1}}{4}

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\frac{K_{1}}{2}

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K_{1}

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2 K_{1}

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4 K_{1}

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Solution

The correct option is B $\frac{K_{1}}{2}$
The expression of kinetic energy of a satellite of circular orbit of radius R is given by , $K_{1} = \frac{1}{2} \frac{G M m}{R}$
When $R = 2 R$ , the new kinetic energy $K_{2} = \frac{1}{2} \frac{G M m}{2 R} = K_{1} / 2$

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