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Satellites

ENERGY OF AN ...

Question

ENERGY OF AN ORBITING SATELLITE
A satellite of mass m is in a circular orbit of radius $2 R_{E}$ about the earth. The energy required to transfer it to a circular orbit of radius $4 R_{E}$ is (where $M_{E}$ and $R_{E}$ is the mass and radius of the earth respectively)

\frac{G M_{E} m}{2 R_{E}}

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\frac{G M_{E} m}{4 R_{E}}

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\frac{G M_{E} m}{8 R_{E}}

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\frac{G M_{E} m}{16 R_{E}}

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Solution

The correct option is C $\frac{G M_{E} m}{8 R_{E}}$
Initial total energy of the satellite is $E_{i} = \frac{G M_{E} m}{4 R_{E}}$

Final total energy of the satellite is $E_{f} = \frac{G M_{E} m}{8 R_{E}}$

The change in the total energy is $Δ E = E_{f} - E i$

$Δ E = - \frac{G M_{E} m}{8 R_{E}} - (- \frac{G M_{E} m}{4 R_{E}}) = - \frac{G M_{E} m}{8 R_{E}} \div \frac{G M_{E} m}{4 R_{E}} = \frac{G M_{E} m}{8 R_{E}}$

Thus, the energy required to transfer the satellite to the desired orbit= $\frac{G M_{E} m}{8 R_{E}}$

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