In the solar system, the Sun is in the focus of the system for Sun-Earth binding system. Then the binding energy for the system will be [given that radius of the earth's orbit round the Sun is $1.5 \times 10^{11} m$ and mass of the earth $= 6 \times 10^{24} kg$ ]

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$2.7 \times 10^{30} J$

$5.4 \times 10^{30} J$

$2.7 \times 10^{33} J$

$5.4 \times 10^{33} J$

answer is A.

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Detailed Solution

$Binding energy = GMm / R$

$M = mass of the Sun = 10^{30} kg$

$m = mass of the earth = 6 \times 10^{24} kg$

$R = 1 .5 \times 10^{11} m$

Binding energy of the system is

$\frac{6.67 \times 10^{- 11} \times 10^{30} \times 6 \times 10^{24}}{1.5 \times 10^{11}} = 2.7 \times 10^{33} J$

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