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(D) The intensity of solar radiation at the earth's surface is $I = 1.4 \; kW/m^2 = 1.4 	imes 10^3 \; J/(s \cdot m^2)$.The total power radiated by th

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$3.8 	imes 10^{14} \; kg$

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(D) The intensity of solar radiation at the earth's surface is $I = 1.4 \; kW/m^2 = 1.4 	imes 10^3 \; J/(s \cdot m^2)$.The total power radiated by the sun is $P = I 	imes A$, where $A$ is the surface area of a sphere with radius $r = 1.5 	imes 10^{11} \; m$.$A = 4 \pi r^2 = 4 	imes 3.14 	imes (1.5 	imes 10^{11})^2 \approx 2.827 	imes 10^{23} \; m^2$.Total energy radiated per day $(E)$ is $P 	imes t$, where $t = 86400 \; s$.$E = (1.4 	imes 10^3 \; J/s \cdot m^2) 	imes (2.827 	imes 10^{23} \; m^2) 	imes (86400 \; s) \approx 3.42 	imes 10^{31} \; J$.Using Einstein's mass-energy equivalence, $E = mc^2$, where $c = 3 	imes 10^8 \; m/s$:$m = \frac{E}{c^2} = \frac{3.42 	imes 10^{31}}{(3 	imes 10^8)^2} = \frac{3.42 	imes 10^{31}}{9 	imes 10^{16}} \approx 3.8 	imes 10^{14} \; kg$.

The sun radiates energy in all directions. The average radiation received on the earth's surface from the sun is $1.4 \; kW/m^2$. The average earth-sun distance is $1.5 \times 10^{11} \; m$. Calculate the mass lost by the sun per day $(1 \; \text{day} = 86400 \; s)$.

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