Chapter 19: Problem 52
Eventually the Sun's luminosity will increase to the point where the Earth can no longer sustain life. Discuss what measures a future civilization might take to preserve itself from such a calamity.
Chapter 19: Problem 52
Eventually the Sun's luminosity will increase to the point where the Earth can no longer sustain life. Discuss what measures a future civilization might take to preserve itself from such a calamity.
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Get started for freeAs a red giant, the Sun's luminosity will be about 2000 times greater than it is now, so the amount of solar energy falling on the Earth will increase to 2000 times its present-day value. Hence, to maintain thermal equilibrium, each square meter of the Earth's surface will have to radiate 2000 times as much energy into space as it does now. Use the Stefan-Boltzmann law to determine what the Earth's surface temperature will be under these conditions. (Hint: The present-day Earth has an average surface temperature of \(14^{\circ} \mathrm{C}\).)
(a) The main-sequence stars Sirius (spectral type A1), Vega (A0), Spica (B1), Fomalhaut (A3), and Regulus (B7) are among the 20 brightest stars in the sky. Explain how you can tell that all these stars are younger than the Sun. (b) The third-brightest star in the sky, although it can be seen only south of \(29^{\circ}\) north latitude, is \(\alpha\) (alpha) Centauri A. It is a main- sequence star of spectral type G2, the same as the Sun. Can you tell from this whether \(\alpha\) Centauri A is younger than the Sun, the same age, or older? Explain your reasoning.
What is a red dwarf? How are thermonuclear reactions in the core of a red dwarf able to consume hydrogen from the star's outer layers?
Calculate the escape speed from (a) the surface of the presentday Sun and (b) the surface of the Sun when it becomes a red giant, with essentially the same mass as today but with a radius that is 100 times larger. (c) Explain how your results show that a red-giant star can lose mass more easily than a main- sequence star.
Why does a star's luminosity decrease after helium fusion begins in its core?
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