Answer any 8 of the following 10 questions. Each is worth 12 points.
1) The formula relating apparent and absolute luminosity is:
Two stars in the constellation Orion, Alnilam and Bellatrix, have the same apparent luminosity, but we know from parallax measurements that Bellatrix is actually much further away than Alnilam. No explanations are required for this problem. Assume there's no material (e.g. gas and dust) along our line of sight to either star.
2) Below is a visible spectrum of sunlight as seen from Fort Worth at noon on a summer day. On this same graph, sketch the spectrum of the Sun as seen from Fort Worth near sunset. Explain in 1-2 sentences why our atmosphere changes the apparent color of the Sun.
3) Suppose we're observing the absorption line spectrum of another star, X. We notice that the spectral lines of star X have the same strength as those of our Sun, but the spectral lines of star X is much broader than those of our Sun. Assuming that rotation isn't a factor in this problem, answer the following:
4) At a distance of 2000 km above the Sun's photosphere, we detect strong emission lines of Oxygen III (Oxygen that has lost 2 electrons). At a distance of 3000 km above the Sun's photosphere, we detect no Oxygen III, but we do detect a very strong Oxygen VI (Oxygen that has lost 5 electrons) line.
5) Star X is 4 times the size of our Sun, but it is only one-half the temperature of our Sun. We know that the absolute luminosity of a star can be determined as follows:
How does the absolute luminosity of star X compare to the Sun? Show your work and state your answer clearly in a sentence or an equation.
6) Suppose we lived on one of the moons of Neptune. Instead of orbiting the Sun at a distance of 1 AU (93 million miles), we'd be orbiting the Sun at a distance of 30 AU. Using Neptune's orbit as a baseline instead of Earth's orbit, would our ability to measure stellar parallax change for better or worse (or neither)? Explain your answer. You may wish to use a diagram to help answer this question, but a diagram itself is not a sufficient explanation.
7) Suppose we want to determine the orbital velocity of an eclipsing binary star system. It's not a measurement that can be made quickly. It often takes months or even years of observations to determine this information. Explain how we observationally find the orbital velocity of an eclipsing binary system and why it takes so long to do sometimes.
8) For a certain optical telescope with an aperture of 3.5 meters...
9) By observing a few absorption lines caused by an interstellar cloud, we can determine the composition of that cloud without having to travel there and study it in person. Explain we can know the composition just from seeing a few spectral lines.
10) Nuclear fusion occurs only in the core of stars like the Sun. It requires extremely high temperatures to take place.