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Question

# ENERGY OF AN ORBITING SATELLITEA satellite of mass m is in a circular orbit of radius 2RE about the earth. The energy required to transfer it to a circular orbit of radius 4RE is (where ME and RE is the mass and radius of the earth respectively)

A
GMEm2RE
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B
GMEm4RE
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C
GMEm8RE
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D
GMEm16RE
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Solution

## The correct option is C GMEm8REInitial total energy of the satellite is Ei=GMEm4REFinal total energy of the satellite is Ef=GMEm8REThe change in the total energy is ΔE=Ef−EiΔE=−GMEm8RE−(−GMEm4RE)=−GMEm8RE÷GMEm4RE=GMEm8REThus, the energy required to transfer the satellite to the desired orbit=GMEm8RE

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