Question
Name: Page 3/4 3) Lifetime of Proxima Centauri a) Proxima Centauri is a red dwarf star (spectral type M6) and is the closest star to us besides the Sun. It has a mass of 0.12 times the mass of the Sun, a radius about 0.14 times the radius of the Sun, and a surface temperature of 2,800 K. What is the luminosity of Proxima Centauri compared to the Sun? Hint: use a ratio. What color would this star look to your eye? b) Again assume that this star is 70% hydrogen. The interior of this star is convective from core to the surface and so 100% of this hydrogen is available to luse into heluminhe, are over he star's lifetime. What is the total mass of fuel for this star? c) Fusing one kilogram of hydrogen into helium releases 6.3x10" joules of energy. How many joules of energy is generated from fusion of hydrogen over this star's liftetime? d) By conservation of energy, the luminosity of this star (the energy emitted at the surface primarily in infrared and visible light) must be equal to the rate of energy being generated in the core (in gamma rays). Use the luminosity of this star in part (a), the luminosity of the Sun from Question 1, and your answer to part (c) to find how long this star can "burn" hydrogen until it runs out of fuel. Give an answer in years keeping in mind that 1 year is approximately 3.1x10 n that it took about a billion years for life to develop on Earth, which star (Proxima Centauri or Theta1 OriC) is a more likely place to have a planet that eventually develops life? Why?
Explanation / Answer
3.a) L/L0 = (M/M0)3.5 where M is the mass of star and M0 mass of star. L and L0 are the luminoscity of star and sun respectively. = (0.12 M0 / M0 )3.5 L/L0 = 5.98 x 10-4 L0 = 3.828 x 10 26 W Luminosity of star proxima centauri, L = 5.98 x 10-4 x 3.828 x 10 26 =22.89 x 1022 W
