## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) The mass lost by the sun each year is $~~1.33\times 10^{17}~kg$ (b) $(6.65\times 10^{-12})~\%$ (c) $1.5\times 10^{13}~years$
(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: $\frac{2.0\times 10^{30}~kg}{1.33\times 10^{17}~kg/year} = 1.5\times 10^{13}~years$