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Physics 55 Final Exam 5/3/11 General Instructions In answering word problems, try to make your answers concise, but complete. This is best achieved by figuring out what is the main point you want to convey and concentrating on that point. This works a lot better than writing scattershot about everything that could conceivably be remotely connected to the issue at hand, in the hope of scoring some hits. Some of the problems ask more than one specific question about a subject. Check that your answer addresses all of the questions. In solving problems, it would help if you explain (minimally) what the logic is that you are following, and make your calculations and intermediate results clearly visible. Pay attention to the units in which various quantities are expressed, including your answers! If you make a calculation error, I am usually generous with partial credit, but if all I have is the incorrect answer this is hard to do. Also, incorrect answers that are completely unreasonable (e.g. the distance to a galaxy computed to be 1.27 × 1011 m – can this be right?) will cost you credit. If you can’t find the error, at least explain if the answer is unreasonable and why. Make sure you answer all parts of a problem! I hope you enjoyed PHY55 and learned something. I surely did both. You are invited to keep in touch in the future, to ask science questions or to tell me where you’ve gone on from here. You know where to find me. Keep looking up! Solve 4 of the following problems (15 pts each) 1. The star Menkent in the constellation Centaurus is located at RA 14h 7m Decl. −36◦ 220 1300 . (a) At what time of year would we be most likely to see Menkent from Durham at the time of day we like to observe – around 10 pm? (b) What would be its maximal altitude above the horizon? (c) When Menkent is at its maximal altitude, where would you look for Spica, in Virgo, located at RA 13h 25m Decl. −11◦ 90 4000 ? 2. The two stars that make up the overcontact binary W Ursae Majoris have estimated masses of 0.99 M and 0.62 M . The light curve of the binary system shows an orbital period of 8.0 hours. (a) Find the average separation of the two stars. (b) The radii of the two stars are estimated to be 1.14 R and 0.83 R respectively. Draw a picture, roughly to scale, of the system. (c) If, in the future, W Ursae Majoris produces a nova, which of the two members of the pair would most likely be the source of this. Why? 3. The bright star Spica in Virgo has a parallax angle of 0.02300 . (a) What is the distance to Spica? (b) Spica appears to be 8.4 × 10−12 as bright as the Sun. Find the luminosity of Spica in terms of L . (c) Spica is classified as spectral type B1 V. How will it end it stellar life? 4. A planet orbiting the star HD209458 has been discovered by finding a variability in the star’s apparent brightness when the planet eclipses it. The star has a surface temperature of 6065 K. (a) Find the wavelength of maximum emission for this star. What type of light is this? (b) The light curve yields a period for the planet’s orbit of 3.52 days and astrometric measurements lead to an estimated orbital radius of 0.047 AU. Use this data to estimate the mass of HD209458 in terms of the Solar mass. Does this fit with the surface temperature given above? (c) HD209458 has a luminosity of approximately 1.47 L . Find the surface temperature of its planet, assuming an albedo of 0.2 and neglecting possible greenhouse effects. (d) Explain how your calculation above explains the discovery of a periodic dip in the star’s apparent luminosity when observed in the infrared. How long after the dip in visual brightness would this occur? 5. Consider a type-Ia supernova at a redshift of z = 2.2. (a) One identifying characteristic of type-Ia supernovae is the presence of a strong absorption line of ionized Silicon. In the lab, this line is observed at a wavelength of 35 micrometers. At what wavelength would we find this line in the spectrum of this high-z supernova? (b) Estimate the distance to this supernova and the lookback time (how long ago we are observing it). (c) Type-Ia supernovae reach peak luminosities of 109 L . Estimate the peak apparent brightness of this supernova. Would it have been visible to the naked eye on a clear night? Briefly answer 4 of the following questions (10 pts each) 6. The galaxy NGC1275 is observed to contain bright blue globular clusters. Explain why these are assumed recent and why this is evidence of a possible recent galactic collision or other drastic event that triggered their formation. 7. I have often, in class, described close binary systems as stars with “built-in probes.” Give two examples in which the existence of a binary partner has allowed us to learn something about a star that would otherwise have been difficult to find. Give one example of a phenomenon that occurs in close binary systems that would not have existed without them, and describe something we have learned from this. 8. An important thread in our discussions has been the construction of the three-dimensional universe from the two-dimensional picture we see in the sky. This construction relies on the cosmic distance ladder. Describe conceptually what the distance ladder is and how it is constructed; for two stages of the ladder describe how they are calibrated and how they are used, as well as the distance range over which they are effective and the limitations that prevent their use beyond that range. 9. Astronomers tell us most of the matter in the universe is not visible. Give two examples of ways in which we can observe the presence of “dark matter” and explain what they tell us about its nature. 10. Many scientists consider Pluto to be not really a planet, but a Kuiper belt object. What is the Kuiper belt? What evidence do we have that it is out there, and what do we know of its properties? 11. I have tried to emphasize this term how discoveries in astronomy and our understanding of fundamental physics reinforce each other. Give two examples in which astronomical observations have led to insights into the fundamental laws of physics and explain briefly how these insights follow from the observations.