Answer
(a) The mass lost by the sun each year is $~~1.33\times 10^{17}~kg$
(b) $(6.65\times 10^{-12})~\%$
(c) $1.5\times 10^{13}~years$
Work Step by Step
(a) We can find the energy radiated by the sun each year:
$E = (3.8\times 10^{26}~W)(365)(24)(3600~s)$
$E = 1.198368\times 10^{34}~J$
We can find the mass lost by the sun each year:
$E = mc^2$
$m = \frac{E}{c^2}$
$m = \frac{1.198368\times 10^{34}~J}{(3.0\times 10^8~m/s)^2}$
$m = 1.33\times 10^{17}~kg$
The mass lost by the sun each year is $~~1.33\times 10^{17}~kg$
(b) We can express this mass as a percentage of the sun's mass:
$\frac{1.33\times 10^{17}~kg}{2.0\times 10^{30}~kg}\times 100\% = (6.65\times 10^{-12})~\%$
(c) We can estimate the lifetime of the sun:
$\frac{2.0\times 10^{30}~kg}{1.33\times 10^{17}~kg/year} = 1.5\times 10^{13}~years$
