Solar energy is incident normally on the eart | vedclass

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(A) The solar energy is radiated from the sun in all directions,effectively forming a sphere of radius $r = 1.5 	imes 10^{11} \, m$.The total power (

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$10^9$

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(A) The solar energy is radiated from the sun in all directions,effectively forming a sphere of radius $r = 1.5 	imes 10^{11} \, m$.The total power (energy radiated per second) emitted by the sun is given by the product of the solar constant and the surface area of this sphere:$P = \Delta E / \Delta t = I 	imes (4 \pi r^2)$$P = 1.4 	imes 10^3 \, W m^{-2} 	imes 4 	imes 3.14 	imes (1.5 	imes 10^{11} \, m)^2$$P \approx 1.4 	imes 10^3 	imes 4 	imes 3.14 	imes 2.25 	imes 10^{22} \approx 3.96 	imes 10^{26} \, J s^{-1}$.Using Einstein's mass-energy equivalence relation $E = mc^2$,the mass equivalent of the energy radiated per second is:$\Delta m / \Delta t = P / c^2$$\Delta m / \Delta t = (3.96 	imes 10^{26}) / (3 	imes 10^8)^2$$\Delta m / \Delta t = (3.96 	imes 10^{26}) / (9 	imes 10^{16})$$\Delta m / \Delta t \approx 0.44 	imes 10^{10} \approx 4.4 	imes 10^9 \, kg s^{-1}$.Rounding to the nearest order of magnitude,the decrease in the mass of the sun is approximately $10^9 \, kg s^{-1}$.

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