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Astronomy 120 "Galaxies and the Universe" Fall 2016 Homework Assignment #3 DUE: Wednesday Sept 28, 2016 HOMEWORK PROBLEMS: 1.) (60 points) Calculate the following for a main sequence star with T=10,000K, R=2.00Rsun, M=3.00Msun. Assume that the proton-­‐proton chain is the only nuclear reaction. Assume that 74% of the original mass of the star is in the form of Hydrogen, 25% in the form of Helium, and 1% in heavier elements. Assume that only 30% of the Hydrogen is in the core and can undergo nuclear fusion. a.) What is the total number of Hydrogen nuclei in the core of this star? b.) How much energy is available in each Hydrogen nucleus from nuclear fusion through the proton-­‐proton chain (in Joules)? c.) What is the total amount of energy available for nuclear fusion through the proton-­‐proton chain in the core of this star (in Joules)? d.) What is the luminosity of this star. Give the answer in both solar units and in Joule/sec. e.) Given the luminosity of this star, what is its main sequence lifetime? i.e., how long can the energy supply (Hydrogen nuclei in core) last (in years)? [DO NOT USE THE MASS-­‐LIFETIME RELATION TO SOLVE THIS PART!] f.) How much mass will the star lose over this main sequence lifetime through nuclear fusion (in solar masses)? g.) What will the elemental composition of the star be at the end of its main sequence lifetime? i.e., what fraction of the total mass of the star is in the form of Hydrogen, Helium, and heavier elements? 2.) (20 points) When the Sun becomes a red giant, its luminosity will be about 2000 times greater than it is today. Calculate how long our Sun will be a red giant, assuming: that this luminosity is caused only by the fusing of hydrogen, that only 40% of the Sun's original supply of Hydrogen is fused during the red giant phase, and that 74% of the original mass of the star is in the form of Hydrogen. 3.) (20 points) The temperatures and brightnesses of the stars in three star clusters are measured and plotted in an HR diagram. One of the clusters has a main sequence turnoff at a stellar mass of 0.7 Msun, whereas the others have main sequence turnoff at stellar masses of 1.4 and 2.1 Msun. What are the ages of the 3 star clusters? Use the mass-­‐
lifetime relation for stars, and the lifetime of our Sun as a reference. Give the answers in years. [HINT: Use the ratio method.] 1 solar luminosity = 3.9x1026 joule/sec 1 watt = 1 joule/sec 1 solar mass = 1.989x1030 kg 1 proton mass = 1.673x10-­‐27 kg 1 electron mass = 9.109x10-­‐31 kg 1 yr = 3.1x107 sec 1 eV = 1.602x10-­‐19 joule