A satellite of mass $1000$ kg is rotating around the earth in a circular orbit of radius $3$ R. What extra energy should be given to this satellite if it is to be lifted into an orbit of radius $4 R$ ?

2.614 \times 10^{9}

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12.614 \times 10^{8}

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214 \times 10^{9}

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61 \times 10^{9}

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Solution

The correct option is A $2.614 \times 10^{9}$ J
Energy required $= (T E)_{f} - (T E)_{f}$
$= (\frac{- G M m}{2 (4 R)}) - (\frac{- G M m}{2 (3)})$
$= \frac{- G M m}{8 R} + \frac{G M m}{6 R} = \frac{G M m}{24 R} (4 - 3) = \frac{G M m}{24 R}$
$= (\frac{9.8 \times (6400 \times 10^{3})^{2} \times 1000}{24 (6400 \times 10^{3})}) = 2.614 \times 10^{9}$ J

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A satellite of mass 1000kg is rotating around the earth in a circular orbit of radius 3R. What extra energy should be given to this satellite if it is to be lifted into an orbit of radius 4R?

The correct option is A 2.614×109JEnergy required =(TE)f−(TE)f=(−GMm2(4R))−(−GMm2(3))=−GMm8R+GMm6R=GMm24R(4−3)=GMm24R=(9.8×(6400×103)2×100024(6400×103))=2.614×109J

A satellite of mass $1000$ kg is rotating around the earth in a circular orbit of radius $3$ R. What extra energy should be given to this satellite if it is to be lifted into an orbit of radius $4 R$ ?