ASTRONOMY - Summer 1999
Dr. Robert Gardner
Chapters 14-22 Homework Solutions

Chapter 14 - The Sun: A Garden-Variety Star.
2. Make a sketch of the Sun's atmosphere showing the location of the photosphere, chromosphere, and corona. What is the approximate temperature of each of these regions? Answer: Consider

Layer Temperature
Photosphere 4,500 - 6,000 K
Chromosphere 4,500 - 10,000 K
Corona 1,000,000 K
3. Why do sunspots look dark? Answer: They are much cooler than the surrounding photosphere and therefore emit less energetic radiation. This makes them dimmer than the surroundings and so they appear dark.
5. Describe the three different types of solar activity. Answer: (1) Granulation: grainy appearance on the photosphere. This is actually the tops of the cells of convection. (2) Sunspots: Dark regions on the photosphere where distortions in the magnetic field block heat from escaping and causing them to appear dark.
13. Suppose an (extremely hypothetical) elongated sunspot forms that extends from a latitude of 30o to a latitude of 40o along a fixed line of longitude. How will the appearance of that sunspot change as the Sun rotates? Answer: Since the Sun rotates faster at the equator than at the poles, that part of the sunspot closer to the solar equator will move ahead of its other end and get stretched out across the surface of the Sun.

Chapter 15 - The Sun: A Nuclear Powerhouse.
3. What is the ultimate source of energy that makes the Sun shine? Answer: The conversion of hydrogen into helium in the proton-proton chain. During this process, some of the mass of the original hydrogen (0.7 percent) dissappears and is converted into energy. It is this energy that eventually leaves the surface of the Sun as sunshine.

Chapter 16 - Analyzing Starlight.
1. What two factors determine how bright a star appears to be in the sky? Answer: Its intrinsic brightness (or luminosity) and its distance.
5. What two women astronomers made significant contributions to the understanding of stellar spectra? Discuss what each of them did. Answer: Annie Cannon assigned spectral classifications to stars and ordered the classification system into the system we use today. Cecelia Payne proved that all stars are mostly composed of hydrogen and that the differences in their spectra are due to different temperatures.

Chapter 17 - The Stars: A Celestial Census.
6. Sketch an H-R diagram. Label the axes. Show where cool supergiants, white dwarfs, the Sun, and main-sequence stars are found.

13. Consider the following data on five stars:
Star Apparent Magnitude Spectrum
1 12 G, main sequence
2 8 K, giant
3 12 K, main sequence
4 15 O, main sequence
5 5 M, main sequence
a. Which is the hottest? Answer: Star 4 is the hottest, since O stars are the hottest.
b. Coolest? Answer: Star 5 is the coolest, since M stars are the coolest.
c. Most luminous? Answer: Star 4 is the most luminous, since main sequence O stars are the most luminous.
d. Least luminous? Answer: Star 5 is the least luminous, since main sequence M stars are the least luminous. e. Nearest? Answer: Star 5 is the nearest, since it is the least luminous, yet has the brightest apparent magnitude.
f. Most distant? Answer: Star 4 is the most distant, since it is the most luminous, yet has the faintest apparent magnitude.

Chapter 18 - Celestial Distances.
17. Give the distances to stars having the following parallaxes: a. 0.1 arcsec. Answer: The relationship between distance d (in parsecs) and parallax p (in arcseconds) is d=1/p. Therefore d = 1/0.1 = 10 parsecs.
b. 0.5 arcsec Answer: Well, d = 1/0.5 = 2 parsecs.
c. 0.005 arcsec Answer: Well, d = 1/0.005 = 200 parsecs.
d. 0.001 arcsec Answer: Well, d = 1/0.001 = 1000 parsecs.

Chapter 20 - The Birth of Stars and the Search for Planets.
5. Why is it so hard to see planets around other stars, and so easy to see them around your own? Answer: Looking at other stars to see planets, the star is so much brighter than the planets that they get lost in the glare. Seeing planets around our Sun is easy because we don't have to look towards the Sun to see them (and they are often not in the Sun's glare), and most of them appear bright in the sky.
6. What techniques have been used to search for planets around other stars? Answer: The motion of the stars as the planet moves around it has been measured in two different ways. The motion may produce movements of the star in the plane of the sky (movement detected by the wooble of the star's proper motion). It may also produce a radial motion which can be detected by the Doppler shifts in spectroscopic lines.

Chapter 21 - Stars: From Adolescence to Old Age.
2. What is the main factor that determines where a star falls along the main sequence? Answer: Its mass.
4. Describe the evolution of a star with a mass similar to that of the Sun, from the protostar stage to the time it becomes a red giant. First give the description in words and then sketch the evolution on an H-R diagram. Answer: In the protostar stage, it is a dense cloud of gas that is contracting due to its own gravity. As it contracts, it heats up. What light it gives off is from this heat. Once the center of the protostar besomes hot enough, hydrogen fusion begins. This marks the start of being a main sequence star. It also stops collapsing at this point, reaching a balance between gravity pulling in and energy pushing out (hydrostatic equilibrium). When the core of the star has completely used up all of the hydrogen, fusion stops and the star begins collapsing again, causing the center to get hotter. A region around the core becomes hot enough for hydrogen fusion (in a shell of hydrogen around the core). The energy from these reactions produces an outward force and the star gets very large. This is an orange giant. The core continues to collapse and get hotter, until it is hot enough for helium to be fused into carbon. Once helium fusion begins, it is a red giant. The energy from the helium fusion stops the contraction and produces more outward pressure, making the star much larger.

5. Describe the evolution of a star with a mass similar to that of the Sun, from just after it first becomes a red giant to the time it exhausts the last type of fuel its core is capable of fusing. After the stages in words, sketch them on an H-R diagram. Answer: Once the red giant has used all the helium in the core, fusion stops and the core begins to contract again. The shells around the core get hotter. The hydrogen shell continues to produce more helium, creating a helium shell around the core. When this shell gets hot enough, there is a helium flash that blows off the outer atmosphere of the star, revealing the hot, carbon core. The small, hot core (which is dim because of its size) becomes a white dwarf.
8. Where did the carbon atoms in the trunk of a tree on your college campus come from originally? Where did the neon in the fabled "neon lights of Broadway'' come from originally? Answer: Carbon atoms are created inside of red giants from the fusion of helium. Neon is formed inside more massive red giants.

Chapter 22 - The Death of Stars.
1. How does a white dwarf differ from a neutron star? Answer: A white dwarf differs from a neutron star in composition and in size. White dwarfs are composed mostly of carbon, while neutron stars are simply a giant ball of neutrons. White dwarfs are about the size of Earth, while neutron stars are about the size of a city. How does each one form? Answer: White dwarfs form after a low mass red giant (under 1.4 solar masses at the end of its main-sequence life) has used all its helium in the core. The core collapses under its own weight, but never gets hot enough for further fusion (since it is small). A neutron star forms when a star of mass greater than 1.4 solar masses (and less than 3 solar masses) exhausts its nuclear fuel and the core collapses. The collapse is hautled when a core of neutrons is produced. The abrupt end of the contraction produces shock waves outside the core which blow the outer layers off of the star in a supernova. What keeps each from collapsing under its own weight? Answer: White dwarfs don't collapse due to "electron degeneracy pressure," which means that the electrons in the atoms push against each other. The electrons can only be so close together. Neutron stars don't collapse due to the "Pauli Exclusion Principle" which prevents two particles from being in the same place and having the same energy at the same time. This means that the neutrons can only get so close together.
10. Arrange the following stars in order of age: a. A star with no nuclear reactions going on in the core, which is made primarily of carbon and oxygen.
b. A star of uniform composition from center to surface; it contains hydrogen but has no nuclear reactions going on in the core.
c. A star that is fusing helium to carbon in its core.
d. A star that is fusing helium to carbon in the core, and hydrogen to helium in a shell around the core.
e. A star that has no nuclear reactions going on in the core, but is fusing hydrogen to form helium in a shell around the core.

Answer: Youngest to oldest: Star b (uniform composition and no nuclear reactions means that it is a protostar), Star c (hydrogen fused into helium in the core means it is a main sequence star), Star e (hydrogen fusion in a shell around a dormant core means it is an orange giant), Star d (helium fusion in the core and hydrogen fusion in the shell means it is a red giant), Star a (a core entirely of carbon and oxygen means that it is at then end of the red giant stage).


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