QUESTION
-
The Stefan-Boltzmann Law states that a star’s luminosity, temperature and size are related as:
L = 4πR2σT4
a) If a star has a surface temperature four times higher than that of the Sun and twicethe radius, by what factor is the star more luminous than the Sun? [8]
b) In about 5 billion years, the Sun will become a red giant star with a luminosity that is 7,500 times greater than its current luminosity and a temperature that is half (0.5) its current temperature. How much larger will the Sun get? [8]
c) Which planets would be swallowed up by the Sun when it becomes a red giant? The current radius of the Sun is 695,500 km and the distances to each planet are listed in the Appendix at the end of this problem set. [8]
-
Wien’s Law states that the emission from a Blackbody peaks at a wavelength that be- comes shorter with increasing temperature. The relation between this peak wavelength and temperature is:
λmaxT = 2.9 × 106 nm K
-
a) If the Sun’s surface temperature is 5777 K, at what wavelength does the Sun’s spectrum peak? What color does this wavelength correspond to? [8]
b) Stars less massive that the Sun, such as M-type stars, have lower surface temperatures of T ≈ 4000K. If you were on a planet that orbited an M-type star, what color do you think the sky would be? Explain your reasoning. [8]
Public Answer
