1) You may assume for this problem that there is no Interstellar Correction Factor (X) to worry about in the inverse square law, that no interstellar material exists along the line of sight to either star. Two stars, A and B, have identical apparent luminosities as seen from the Earth. Parallax measurements show us that star A is about 100 light years from Earth and star B is about 200 light years from the Earth.

a) (3 pts) Aside from using the peak wavelength of the continuous spectrum for each of these stars, describe how we could determine the surface temperature of these stars (i.e. what would we need to observe to figure this out and why?).

b) (5 pts) Suppose star A and B both have the same surface temperature. Which one is likely to have broader spectral lines? Explain fully how you arrived at your answer (referencing any equations or relationship youıve relied upon).

2) Stars are powered by nuclear fusion, a process that requires both high temperature and high density in order to work effectively.

a) (6 pts) Explain why nuclear fusion requires high density and high temperature. Deal with each property separately in 1-2 sentences.

b) (2 pts) The Sunıs corona has temperatures nearing 20 million degrees, similar to temperatures in the core. State briefly why no nuclear fusion occurs there.

3) Throughout this course, we studied the concept of scientific ideas and our confidence in certain theories. Briefly state the most significant difference between scientific and non-scientific ideas, according to the reading "Philosophy and the Scientific Method". Use this difference to help explain why relying on irrefutable beliefs is not an ideal way to set up a system of knowledge and understanding.

4) Although we are very confident that our theory involving nuclear fusion at the Sunıs core is accurate, we have recently come across an interesting issue having to do with neutrinos emitted during nuclear reactions at the Sunıs core. Briefly explain what the "solar neutrino problem" is and explain either one of two possible explanations that resolve this problem.

5) Energy travels outward from the core of the Sun in several different ways, including radiation and convection. Explain why, in the interior of the Sun, energy is transported outward via radiation instead of some other way. As part of your answer, explain what causes the boundary between the radiative and convective zones in the Sunıs interior.

6) Representative samples are an important part of gathering evidence from very large numbers of people, stars or galaxies.

a) (4 pts) State whether a sample of the 1,000 or so stars with the largest measured parallax angles (as seen from Earth) would be representative. Explain your answer.

b) (4 pts) The U. S. Census Bureau has recently decided to *not* use statistical sampling in order to determine the characteristics of the nationıs population. In 2-3 sentences, summarize the argument that statistical sampling *should* be used in the census.

7) While observing an eclipsing binary system, an Astronomer takes a series of spectra, showing the spectral fingerprints of each star as the companion starıs lines shift back and forth around the stationary central starıs lines. The Astronomer measures the amount of this shift and also how long it takes for the shifting pattern to repeat. Explain how this data could be used to determine the mass of the central star in the system.

8) One of the most famous spectral line fingerprints ever observed by Astronomers in interstellar clouds is that of ³Nebulium², an element some scientists thought only existed in interstellar space, since its fingerprint was never observed on Earth. It turns out ³Nebulium² is an example of a forbidden line of ionized Oxygen. Explain what property of an atom, electron and/or energy level causes a line to be considered ³forbidden², and explain why we never see ³forbidden² lines in laboratory spectra on Earth.

9) Suppose an Astronomer compiles a catalog of main sequence stars, observing only stars with an apparent luminosity higher than some given value.

a) (4 pts) This sample will tend to contain very few low mass stars. Explain why.

b) (4 pts) This sample will also tend to contain very few high mass stars. Explain why.

10) Spica is a main sequence star with a very blue color and a mass about ten times the mass of our Sun.

a) (4 pts) Explain why the main-sequence lifetime of Spica will be substantially shorter than our Sun (simply stating the relationship between mass and lifetime is not sufficient ... you must also explain the relationship).

b) (4 pts) How would you expect the metallicity of the star Spica to compare to that of our own Sun? Explain your answer.

11) Explain the observational evidence of the motions in the disk of our galaxy that lead Astronomers to believe that dark matter exists in our galaxy in an abundance about ten times that of visible matter.

12) For the purposes of this problem, assume that the Universe is 10 billion years old. Also assume that the Universe is undergoing no acceleration or deceleration, that it is expanding at a constant velocity and always has been. The graph below shows the Hubble relation between radial velocity and distance for galaxies as it appears today. On the graph, sketch how this relationship will look after the Universe is 20 billion years old. If the graph will remain unchanged, just write ³no change² on the graph. Explain why you changed (or didnıt change) the graph in the way you did.

13) Two possible candidates for the dark matter in our galaxy are MACHOıs (planet-sized and larger objects) distributed throughout our galaxyıs halo and Low Surface Brightness (LSB) galaxies.

a) (4 pts) Explain how we detect MACHOıs and why they are not considered to be the bulk of the dark matter in the Universe.

b) (4 pts) Explain why we think there might be many more LSB galaxies even fainter than the ones we currently can detect (perhaps enough to make up a substantial portion of the dark matter).

14) Suppose we observe a galaxy that we know is very much like our own Milky Way, but it is about 8 billion light years away (we will assume that the age of the Universe is about 10 billion years, for reference). This galaxy would appear to have (more, less, the same amount of) metallicity compared to our own Milky Way. Pick one and justify your answer.