# What is the total mass of hydrogen available for fusion, in kg?

1. The mass of the Sun is about 2×1030 kg. The Sun was about 70% hydrogen when it first formed.About 11% of the total amount of the Sun’s hydrogen is available for fusion within the Sun’s core.(a) What is the total mass of hydrogen available for fusion, in kg?(b) The Sun fuses about 600 billion kg of hydrogen each second. Calculate how long the Sun’sinitial supply of hydrogen can last. Give your answer in both seconds and years. Hint: use theresult you calculated in part (a).(c) We know that our Solar System is about 4.5 billion years old. Using your calculation above,how much longer do we have until the Sun runs out of hydrogen?
2. You discover a spectral type G2 star orbiting an unseen companion with a semimajor axis of 10million km, and an orbital period of 2 days.(a) What is the mass of the unseen companion? Give your answer in both kg and Solar masses.You will need to use Newton’s version of Kepler’s 3rd Law, the gravitational constant, G =6.67 x 10-11 m3kg-1 s-2, and the mass of a G2 star (which is the same as the mass of the Sun),2.0 x 1030 kg. Remember to use the TOTAL mass of the stars, not just the mass of one star inyour calculation.(b) Is the unseen companion a white dwarf, a neutron star, or a black hole? What evidence isthere in favour of your choice?
3. Consider these real data for three Cepheid variable stars in a distant galaxy. These luminositieswere calculated using the period-luminosity relationship discovered by Henrietta Swan Leavitt.(a) Calculate the distance to this galaxy using each of the 3 Cepheid variable stars, give thedistance in both m and in parsecs.(b) Do the 3 calculated distances agree? Based on your results, how uncertain is thismeasurement? (Remember that W means Watts, and remember how the brightness of anobject drops off with distance)• Cepheid #1: luminosity = 3.3×1030 W, apparent brightness = 9.3×10-19 W/m2• Cepheid #2: luminosity = 1.1×1030 W, apparent brightness = 3.8×10-19 W/m2• Cepheid #3: luminosity = 2.5×1030 W, apparent brightness = 8.7×10-19 W/m2
4. One of hydrogen’s emission lines has a wavelength of 656.3 nm. You obtain spectra of differentgalaxies and find that the wavelength of this hydrogen emission line shows up at differentwavelengths in 3 different galaxies.• Galaxy #1: 659.8 nm• Galaxy #2: 664.2 nm• Galaxy #3: 679.3 nma) Calculate the redshift, z = (λobserved-λexpected)/λexpected for each of these 3 galaxies.b) From the redshift, calculate the speed that each galaxy is moving away from us. Give youranswers both in km/s and in fraction of the speed of light.c) Use Hubble’s Law to estimate the distance to each galaxy. Use H0 = 22 km/s/Mega-lightyear

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