Answer
See answers.
Work Step by Step
a. Calculate the rate of mass loss using equation 26–7.
$$\Delta E = (\Delta m)c^2$$
$$\frac{\Delta m}{\Delta t}=\frac{1}{c^2}\frac{\Delta E }{\Delta t}$$
$$=\frac{4\times10^{26}J/s}{(3.00\times10^8 m/s)^2}\approx 4\times10^9 kg/s$$
b. Calculate the time using the mass of the Earth, and the rate we just found.
$$\Delta t = \frac{m_{Earth}}{\Delta m/\Delta t}=\frac{5.98\times10^{24}kg}{4.44\times10^9 kg/s }\approx 1\times10^{15} s $$
c. Calculate the time using the mass of the sun, and the rate we found in part A.
$$\Delta t = \frac{m_{sun}}{\Delta m/\Delta t}=\frac{1.99\times10^{30}kg}{4.44\times10^9 kg/s }\approx 4\times10^{20} s $$
