1) Aldebaran and Bellatrix have the same apparent luminosity and the same mass. Neither star is significantly obscured by interstellar material along our line of sight. Bellatrix has the same spectral line widths, but Bellatrix has a shorter peak wavelength in its spectrum.

a) (8 pts) Which of these two stars is larger (or are they the same size)? As part of your answer, briefly explain why spectral line widths are related to the density of a gas.

b) (6 pts) Which of these two stars is closer to the Earth? Explain.

2) Capella and Deneb have the same apparent luminosity and mass. Neither star is significantly obscured by interstellar material along our line of sight. Both stars have the same ionization species in their spectra, but Capella's spectrum shows shows that it has broader spectral lines. Which of these two stars will have a smaller parallax angle as seen from the Earth? Justify your answer.

3) Alkor is about 10 parsecs away and has a surface temperature of 3000 K, and a radius twice that of our Sun.

a) (7 pts) Plot the approximate location of Alkor on the H-R diagram shown below. Show your work done to calculate the position of Alkor off to the side of the diagram.

b) (7 pts) Mizar is a star identical to the Sun, approximately 20 parsecs away. How does the apparent luminosity of Alkor compare to that of Mizar? Show your work and state your answer clearly.

4) Explain why forbidden spectral lines are only seen in very low density gas.

5) Although most stars have a very large abundance of Hydrogen, the strength of Hydrogen absorption lines in stellar spectra varies greatly across the different spectral types.

a) (7 pts) Explain why very hot stars do not show evidence of strong Hydrogen lines.

b) (7 pts) Explain why very cool stars do not show evidence of strong Hydrogen lines.

6) Describe how you would determine the mass of the central star in an edge-on binary system. What would you observe? How do these observations relate to the properties of the orbiting companion? What calculations would you need to make?

7) A recent mission of the European Space Agency sent the satellite "Hipparcos" into orbit around the Earth.

a) (6 pts) What was the purpose of this mission, and what was one useful scientific result that came from this mission?

b) (8 pts) Hipparcos was only able to measure the properties of stars within about 1000 parsecs of the Earth. Stars that were more distant than this were not included in the final data set. If you were to analyze the (approximately) 100,000 stars in the Hipparcos data set, would this constitute a representative sample of stars in the Milky Way? Explain.

8) The scattering effects of gas and dust influence our observations of stars, and these effects must be accounted for in our scientific theories, even for our Sun.

a) (6 pts) Explain why the Sun appears redder and dimmer on the horizon compared to when it is directly overhead.

b) (8 pts) The reddening effect of the interstellar medium (ISM) can affect the apparent properties of a star. Explain briefly how reddening will change our estimate of the temperature, absolute luminosity and distance to a star.