According to a recent computer model of the Sun's evolution, when the Sun was young its surface temperature was $130 \mathrm{K}$ cooler (than its current value of $5800 \mathrm{K}$ ) and its luminosity was $0.71 L_{\odot}$ When the Sun is approaching the end of its main-sequence lifetime 5.5 billion years from now, its surface temperature will be $650 \mathrm{K}$ cooler than it is currently, and its luminosity will be $2.02 L_{\odot}$. Use the Stefan-Boltzmann law (Unit 57 ) to estimate the Sun's diameter at these past and future times.