Answer
(a) The mass lost by the sun per day is $3.8\times 10^{14}~kg$
(b) The percentage of the sun's mass that is lost per day is $(1.9\times 10^{-14})~\%$
Work Step by Step
(a) We can find the total energy released from the sun every day:
$E = Intensity\times~Area~\times time$
$E = (1400~W/m^2)\times~(4\pi)(1.5\times 10^{11}~m)^2~\times (24)(3600~s)$
$E = 3.42\times 10^{31}~J$
We can find the mass lost by the sun per day:
$E = mc^2$
$m = \frac{E}{c^2}$
$m = \frac{3.42\times 10^{31}~J}{(3.0\times 10^8~m/s)^2}$
$m = 3.8\times 10^{14}~kg$
The mass lost by the sun per day is $3.8\times 10^{14}~kg$
(b) We can find the percentage of the sun's mass that is lost each day:
$\frac{3.8\times 10^{14}~kg}{1.989\times 10^{30}~kg}~\times 100\% = (1.9\times 10^{-14})~\%$
The percentage of the sun's mass that is lost per day is $(1.9\times 10^{-14})~\%$
