7. What is chromatic aberration in a telescope? (b) The light of different colors comes to a focus at different points inside the telescope.

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1 ASTR 1020 Stellar and Galactic Astronomy Professor Caillault Fall 2009 Semester Exam 2 Multiple Choice Answers (Each multiple choice question is worth 1.5 points) 1. Light enters the smooth, flat surface of a glass from the vacuum of space (e.g., a spacecraft window). What is the speed of light inside the glass compared to that in a vacuum? (b) Since the glass is denser than the vacuum, it is slower. 2. What is the refraction of light? (d) The change in direction of a light ray as it crosses from a less dense, transparent material to a more dense one 3. A typical refracting telescope is made up of (a) a long-focal-length lens at the front and a short-focal-length lens at the rear (next to your eye as you look through the telescope). 4. When light from the concave primary mirror of a telescope is reflected by a small secondary mirror through a hole in the primary, it is called a (c) Cassegrain focus telescope. 5. A refracting telescope has an objective lens of focal length 80 cm, a diameter of 10 cm, and an eyepiece of focal length 5 cm and diameter 1 cm. What is the magnifying power of this telescope? (c) For many years, the Palomar telescope (5 m diameter) in California was the largest fully steerable telescope in the world; in the 1990 s that honor fell to the first of the two Keck telescopes (each of diameter 10 m) in Hawaii. How many times larger is the lightgathering power of a Keck telescope than the Palomar telescope? (c) 4 times larger 7. What is chromatic aberration in a telescope? (b) The light of different colors comes to a focus at different points inside the telescope. 8. The largest refracting telescope in the world is the 102-cm (40 in.) diameter telescope at Yerkes Observatory, built in Refracting telescopes with larger diameter have never been built because they would (a) sag too much under their own weight. 9. A reflecting telescope in which light is reflected by one curved mirror and a second plane mirror at 45 to the original beam, to reach a focus at the side of the telescope, is being used at its (a) Newtonian focus.

2 10. A spherical mirror suffers from spherical aberration because (c) different parts of the mirror focus the light at different distances from the mirror. 11. In telescopes, the angular resolution is worse for (d) smaller diameter lenses or mirrors and longer wavelength electromagnetic radiation. 12. What does the word seeing mean to an astronomer using a telescope? (a) The twinkling and blurring of the image due to air currents in Earth's atmosphere. 13. During the past few decades a number of techniques have been developed to enhance the performance of optical and radio telescopes. These include all of the following except one. Which one is the exception? (b) building refracting telescopes comparable in size to the largest reflecting telescopes 14. What is the main reason for combining many radio telescopes together into an interferometer with large distances between telescopes? (a) to obtain much sharper images of sources 15. When four protons collide to form helium, what fraction of the original mass of the protons is converted to energy? (b) 0.7% 16. How much longer can the Sun continue to generate energy by nuclear reactions in its core? (c) about 5 billion years 17. What happens to the positrons produced by the nuclear reactions in the core of the Sun? (a) They are annihilated upon interacting with electrons, producing energy. 18. What happens to the neutrinos produced by the nuclear reactions in the core of the Sun? (d) They escape from the Sun into space. 19. Hydrogen burning by fusion reactions occurs only in the deep interior of the Sun (and other stars), because this is the only place in the Sun where (d) the requisite conditions of high temperature and high density occur. 20. The phrase hydrostatic equilibrium in the Sun refers to (d) the balance of gravity inward and gas pressure outward. 21. The solution to the solar neutrino problem is thought to be that (b) neutrinos oscillate and change their nature en route from the Sun to the Earth. 22. When we look at the Sun, what do we see? (c) Its photosphere.

3 23. The granulation pattern seen on the surface of the Sun results from (d) convection of gas in the region under the photosphere. 24. The center of the disk of the visible Sun appears brighter than its edges because (b) we see into deeper and hotter layers at the center of the solar disk. 25. The extremely high gas temperatures in the solar corona mean that this region is best observed at wavelengths of (d) X-rays. 26. What causes sunspots? (d) Magnetic fields inhibit gas motion in regions of the convective zone where the field is strong, lowering the amount of heat transferred to the surface. 27. What is the average length of time from one maximum in the number of sunspots on the Sun to the next maximum? (d) 11 years 28. The Zeeman effect refers to (d) the splitting of spectral lines when magnetic fields are applied to atoms. 29. The Babcock magnetic-dynamo model, which explains many of the features of the solar cycle, makes use of which two basic properties of the Sun s photosphere? (d) convection and differential rotation 30. The spectrum of an ordinary main sequence star is a (a) continuum of colors crossed by dark absorption lines, caused by absorption of cooler atoms and molecules at the surface. 31. Stellar parallax is the (d) apparent shift in the position of a nearby star because of Earth's motion. 32. The spectral class of the Sun is G2 and the star Enif is K2. From this information, we know that Enif is (c) cooler than the Sun. 33. What does apparent magnitude tell us about a star? (c) the brightness of a star as it appears in our sky 34. Star A has a luminosity L A = 100 L o and it is 1000 pc away. Star B has the same luminosity as the Sun, L A = 1 L o, and it is 100 pc away. What can you say about the brightnesses of these two stars? (d) Star A and Star B have the same brightness.

4 35. The Hertzsprung-Russell diagram is a plot of (d) luminosity vs. temperature. 36. What is the physical reason that astronomers can find the luminosity class (I, II, III, IV, or V) of a star using the star's spectrum? (b) The absorption lines in the spectrum are affected by the density and pressure of the star's atmosphere. 37. Spectroscopic parallax is the (d) distance to a star measured using the spectral-luminosity class of the star and the inverse square law. 38. The star Elnath is classified as B7 III, and the star Al Na'ir is classified as B7 IV. This tells us that compared to Al Na'ir, Elnath is (d) about the same temperature, but intrinsically much brighter. 39. Which important stellar parameter can be determined only by the study of binary stars? (b) mass 40. Which of the following pairs of stars is an example of stars for which the massluminosity relation applies? (a) G2 V and M1 V. 41. A radial-velocity curve is a plot of (a) radial-velocity vs. time for a spectroscopic binary. 42. What physical parameter of a star is usually determined indirectly, but with an eclipsing binary can be measured directly? (b) radius 43. What is the predominant atomic or molecular mechanism that produces the light we see from emission nebulae? (d) UV light from hot stars ionizes atoms, and the subsequent recombination of electrons with these ions produces spectral lines. 44. The distinct blue color of the nebulosity around stars in young clusters, such as the Pleiades, is caused by (b) preferential scattering of blue starlight by small dust grains in the interstellar material. 45. Suppose the light leaving a star has equal intensities in the blue and the red. The starlight passes through a dust cloud on its journey to Earth. When you observe the light reaching Earth you will find (b) the red part of the spectrum will be more intense than the blue.

5 46. The source of a protostar's heat is (a) gravitational energy, released as the protostar contracts. 47. At what point in its evolution will a protostar stop shrinking and stabilize into a star? (a) when nuclear processes generate enough energy and internal pressure to resist gravitational contraction. 48. A star's evolutionary track is (a) its movement when plotted on a HR diagram, as it evolves in luminosity and temperature. 49. What is the relationship between the mass of a protostar and the time needed for it to reach the main sequence, after it forms inside an interstellar cloud? (a) More massive protostars reach the main sequence in a shorter time than less massive protostars. 50. If we plot the stars in a 10 million year old star cluster on a Hertzsprung-Russell diagram, we would expect to see (d) the more massive stars on the main sequence and the less massive stars above the main sequence.

6 ASTR 1020 Stellar and Galactic Astronomy Professor Caillault Fall 2009 Semester Exam 2 Problems Solutions (Each problem is worth 5 points; show all of your work!) 1. If all effects caused by Earth's atmospheric variations (i.e., seeing) could be removed from the visible image of a star obtained with one of the 10-m diameter Keck telescopes on Hawaii, what would be the angular resolution achievable by this telescope for light of wavelength 500 nm? (Give your answer in arcseconds.) θ = ( )λ/d = ( )( m)/(10 m) = arcseconds = The mass of a hydrogen nucleus = kg. The mass of a helium nucleus = kg. How much energy is released by the formation of a single helium nucleus in the proton-proton chain? The proton-proton chain results in 4 H He + E, so E = (m 4H m He )c 2 = (( kg) kg)( m/s) 2 = J Consider a star with an apparent magnitude of and a parallax angle of arcseconds. 3. What is the distance to this star? d = 1/p = 1/ (0.010) = 100 pc 4. What is the absolute magnitude of this star? Is this star intrinsically brighter or fainter than the Sun (the Sun s absolute magnitude = +4.8)? m M = 5 log d 5, so rewrite to solve for absolute magnitude M: M = m 5 log d + 5 = log (100) + 5 = 12.1 (5 2) + 5 = 7.1 The star is intrinsically fainter than the Sun since its absolute magnitude is larger.

7 5. At one stage during its pre-main sequence phase, the protosun had a luminosity equal to 100 L o and a surface temperature of about 2900 K (= ½ T o ). At that time what was the protosun s radius (in terms of the Sun s present-day radius, R o )? Since L = 4πR 2 σ T 4, we know that L protosun = 4π(R protosun ) 2 σ(t protosun ) 4 and L o = 4πR o2 σt o4. Take the ratio: L protosun /L o = [4π(R protosun ) 2 σ(t protosun ) 4 ]/[4πR o 2 σt o 4 ] = [(R protosun ) 2 /R o2 ] [(T protosun ) 4 /T o4 ] Solve for R protosun /R o : R protosun /R o = [T o2 / (T protosun ) 2 ] (L protosun /L o ) = [T o2 /(½ T o ) 2 ] (100 L o /L o ) = 4 10 = 40

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