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All Textbook Solutions for Astronomy
How was the rotation rate of Mercury determined?What is the relationship between Mercury’s rotational period and orbital period?The features of Mercury are named in honor of famous people in which fields of endeavor?What do our current ideas about the origins of the Moon and Mercury have in common? How do they differ?One of the primary scientific objectives of the Apollo program was the return of lunar material. Why was this so important? What can be learned from samples? Are they still of value now?Apollo astronaut David Scott dropped a hammer and a feather together on the Moon, and both reached the ground at the same time. What are the two distinct advantages that this experiment on the Moon had over the same kind of experiment as performed by Galileo on Earth?Galileo thought the lunar maria might be seas of water. If you had no better telescope than the one he had, could you demonstrate that they are not composed of water?Why did it take so long for geologists to recognize that the lunar craters had an impact origin rather than a volcanic one?How might a crater made by the impact of a comet with the Moon differ from a crater made by the impact of an asteroid?Why are the lunar mountains smoothly rounded rather than having sharp, pointed peaks (as they were almost always depicted in science-fiction illustrations and films before the first lunar landings)?The lunar highlands have about ten times more craters in a given area than do the maria. Does this mean that the highlands are 10 times older? Explain your reasoning.At the end of the section on the lunar surface, your authors say that lunar night and day each last about two Earth weeks. After looking over the information in Earth, Moon, and Sky and this chapter about the motions of the Moon, can you explain why? (It helps to draw a diagram for yourself.)Give several reasons Mercury would be a particularly unpleasant place to build an astronomical observatory.If, in the remote future, we establish a base on Mercury, keeping track of time will be a challenge. Discuss how to define a year on Mercury, and the two ways to define a day. Can you come up with ways that humans raised on Earth might deal with time cycles on Mercury?The Moon has too little iron, Mercury too much. How can both of these anomalies be the result of giant impacts? Explain how the same process can yield such apparently contradictory results.In the future, astronomers discover a solid moon around a planet orbiting one of the nearest stars. This moon has a diameter of 1948 km and a mass of 1.61022 kg. What is its density?The Moon was once closer to Earth than it is now. When it was at half its present distance, how long was its period of revolution? (See Orbits and Gravity for the formula to use.)Astronomers believe that the deposit of lava in the giant mare basins did not happen in one flow but in many different eruptions spanning some time. Indeed, in any one mare, we find a variety of rock ages, typically spanning about 100 million years. The individual lava flows as seen in Hadley Rille by the Apollo 15 astronauts were about 4mthick. Estimate the average time interval between the beginnings of successive lava flows if the total depth of the lava in the mare is 2 km.The Moon requires about 1 month (0.08 year) to orbit Earth. Its distance from us is about 400,000 km (0.0027 AU). Use Kepler’s third law, as modified by Newton, to calculate the mass of Earth relative to the Sun.List several ways that Venus, Earth, and Mars are similar, and several ways they are different.Compare the current atmospheres of Earth, Venus, and Mars in terms of composition, thickness (and pressure at the surface), and the greenhouse effect.How might Venus’ atmosphere have evolved to its present state through a runaway greenhouse effect?Describe the current atmosphere on Mars. What evidence suggests that it must have been different in the past?Explain the runaway refrigerator effect and the role it may have played in the evolution of Mars.What evidence do we have that there was running (liquid) water on Mars in the past? What evidence is there for water coming out of the ground even today?What evidence is there that Venus was volcanically active about 300600 million years ago?Why is Mars red?What is the composition of clouds on Mars?What is the composition of the polar caps on Mars?Describe two anomalous features of the rotation of Venus and what might account for them.How was the Mars Odyssey spacecraft able to detect water on Mars without landing on it?What are the advantages of using radar imaging rather than ordinary cameras to study the topography of Venus? What are the relative advantages of these two approaches to mapping Earth or Mars?Venus and Earth are nearly the same size and distance from the Sun. What are the main differences in the geology of the two planets? What might be some of the reasons for these differences?Why is there so much more carbon dioxide in the atmosphere of Venus than in that of Earth? Why so much more carbon dioxide than on Mars?If the Viking missions were such a rich source of information about Mars, why have we sent the Pathfinder, Global Surveyor, and other more recent spacecraft to Mars? Make a list of questions about Mars that still puzzle astronomers.Compare Mars with Mercury and the Moon in terms of overall properties. What are the main similarities and differences?Contrast the mountains on Mars and Venus with those on Earth and the Moon.We believe that all of the terrestrial planets had similar histories when it comes to impacts from space. Explain how this idea can be used to date the formation of the martian highlands, the martian basins, and the Tharsis volcanoes. How certain are the ages derived for these features (in other words, how do we check the ages we derive from this method)?Is it likely that life ever existed on either Venus or Mars? Justify your answer in each case.Suppose that, decades from now, NASA is considering sending astronauts to Mars and Venus. In each case, describe what kind of protective gear they would have to carry, and what their chances for survival would be if their spacesuits ruptured.We believe that Venus, Earth, and Mars all started with a significant supply of water. Explain where that water is now for each planet.One source of information about Mars has been the analysis of meteorites from Mars. Since no samples from Mars have ever been returned to Earth from any of the missions we sent there, how do we know these meteorites are from Mars? What information have they revealed about Mars?The runaway greenhouse effect and its inverse, the runaway refrigerator effect, have led to harsh, uninhabitable conditions on Venus and Mars. Does the greenhouse effect always cause climate changes leading to loss of water and life? Give a reason for your answer.In what way is the high surface temperature of Venus relevant to concerns about global warming on Earth today?What is a dust devil? Would you expect to feel more of a breeze from a dust devil on Mars or on Earth? Explain.Near the martian equator, temperatures at the same spot can vary from an average of 135 °C at night to an average of 30 °C during the day. How can you explain such a wide difference in temperature compared to that on Earth?Estimate the amount of water there could be in a global (planet-wide) region of subsurface permafrost on Mars (do the calculations for two permafrost thicknesses, 1 and 10 km, and a concentration of ice in the permafrost of 10% by volume). Compare the two results you get with the amount of water in Earth’s oceans calculated in Example 10.1.At its nearest, Venus comes within about 41 million km of Earth. How distant is it at its farthest?If you weigh 150 lbs. on the surface of Earth, how much would you weigh on Venus? On Mars?Calculate the relative land area-that is, the amount of the surface not covered by liquids-of Earth, the Moon, Venus, and Mars. (Assume that 70% of Earth is covered with water.)The closest approach distance between Mars and Earth is about 56 million km. Assume you can travel in a spaceship at 58,000 km/h, which is the speed achieved by the New Horizons space probe that went to Pluto and is the fastest speed so far of any space vehicle launched from Earth. How long would it take to get to Mars at the time of closest approach?What are the main challenges involved in sending probes to the giant planets?Why is it difficult to drop a probe like Galileo? How did engineers solve this problem?Explain why visual observation of the gas giants is not sufficient to determine their rotation periods, and what evidence was used to deduce the correct periods.What are the seasons like on Jupiter?What is the consequence of Uranus’ spin axis being 98° away from perpendicular to its orbital plane?Describe the seasons on the planet Uranus.At the pressures in Jupiter’s interior, describe the physical state of the hydrogen found there.Which of the gas giants has the largest icy/rocky core compared to its overall size?In the context of the giant planets and the conditions in their interiors, what is meant by “rock” and “ice”?What is the primary source of Jupiter’s internal heat?Describe the interior heat source of Saturn.Which planet has the strongest magnetic field, and hence the largest magnetosphere? What is its source?What are the visible clouds on the four giant planets composed of, and why are they different from each other?Compare the atmospheric circulation (weather) of the four giant planets.What are the main atmospheric heat sources of each of the giant planets?Why do the upper levels of Neptune’s atmosphere appear blue?How do storms on Jupiter differ from storm systems on Earth?Describe the differences in the chemical makeup of the inner and outer parts of the solar system. What is the relationship between what the planets are made of and the temperature where they formed?How did the giant planets grow to be so large?Jupiter is denser than water, yet composed for the most part of two light gases, hydrogen and helium. What makes Jupiter as dense as it is?Would you expect to find free oxygen gas in the atmospheres of the giant planets? Why or why not?Why would a tourist brochure (of the future) describing the most dramatic natural sights of the giant planets have to be revised more often than one for the terrestrial planets?The water clouds believed to be present on Jupiter and Saturn exist at temperatures and pressures similar to those in the clouds of the terrestrial atmosphere. What would it be like to visit such a location on Jupiter or Saturn? In what ways would the environment differ from that in the clouds of Earth?Describe the different processes that lead to substantial internal heat sources for Jupiter and Saturn. Since these two objects generate much of their energy internally, should they be called stars instead of planets? Justify your answer.Research the Galileo mission. What technical problems occurred between the mission launch and the arrival of the craft in Jupiter’s system, and how did the mission engineers deal with them? (Good sources of information include Astronomy and Sky & Telescope articles, plus the mission website.)How many times more pressure exists in the interior of Jupiter compared to that of Earth?Calculate the wind speed at the edge of Neptune’s Great Dark Spot, which was 10,000 km in diameter and rotated in 17 d.Calculate how many Earths would fit into the volumes of Saturn, Uranus, and Neptune.As the Voyager spacecraft penetrated into the outer solar system, the illumination from the Sun declined. Relative to the situation at Earth, how bright is the sunlight at each of the jovian planets?The ions in the inner parts of Jupiter’s magnetosphere rotate with the same period as Jupiter. Calculate how fast they are moving at the orbit of Jupiter’s moon Io (see Appendix G). Will these ions strike Io from behind or in front as it moves about Jupiter?What are the moons of the outer planets made of, and how is their composition different from that of our Moon?Compare the geology of Callisto, Ganymede, and Titan.What is the evidence for a liquid water ocean on Europa, and why is this interesting to scientists searching for extraterrestrial life?Explain the energy source that powers the volcanoes of Io.Compare the properties of Titan’s atmosphere with those of Earth’s atmosphere.How was Pluto discovered? Why did it take so long to find it?How are Triton and Pluto similar?Describe and compare the rings of Saturn and Uranus, including their possible origins.Why were the rings of Uranus not observed directly from telescopes on the ground on Earth? How were they discovered?List at least three major differences between Pluto and the terrestrial planets.The Hubble Space Telescope images of Pluto in 2002 showed a bright spot and some darker areas around it. Now that we have the close-up New Horizons images, what did the large bright region on Pluto turn out to be?Saturn’s E ring is broad and thin, and far from Saturn. It requires fresh particles to sustain itself. What is the source of new E-ring particles?Why do you think the outer planets have such extensive systems of rings and moons, while the inner planets do not?Ganymede and Callisto were the first icy objects to be studied from a geological point of view. Summarize the main differences between their geology and that of the rocky terrestrial planets.Compare the properties of the volcanoes on Io with those of terrestrial volcanoes. Give at least two similarities and two differences.Would you expect to find more impact craters on Io or Callisto? Why?Why is it unlikely that humans will be traveling to Io? (Hint: Review the information about Jupiter’s magnetosphere in The Giant Planets.)Why do you suppose the rings of Saturn are made of bright particles, whereas the particles in the rings of Uranus and Neptune are black?Suppose you miraculously removed all of Saturn’s moons. What would happen to its rings?We have a lot of good images of the large moons of Jupiter and Saturn from the Galileo and Cassini spacecraft missions (check out NASA’s Planetary Photojournal site, at http://photojournal.jpl.nasa.gov, to see the variety). Now that the New Horizons mission has gone to Pluto, why don’t we have as many good images of all sides of Pluto and Charon?In the Star Wars movie Star Wars Episode VI: Return of the Jedi, a key battle takes place on the inhabited “forest moon” Endor, which supposedly orbits around a gas giant planet. From what you have learned about planets and moons of the solar system, why would this be an unusual situation?Which would have the longer orbital period: a moon 1 million km from the center of Jupiter, or a moon 1 million km from the center of Earth? Why?How close to Uranus would a spacecraft have to get to obtain the same resolution as in Example 12.1 with a camera that has an angular resolution of 2 arcsec?Saturn’s A, B, and C Rings extend 75,000 to 137,000 km from the center of the planet. Use Kepler’s third law to calculate the difference between how long a particle at the inner edge and a particle at the outer edge of the three-ring system would take to revolve about the planet.Use the information in Appendix G to calculate what you would weigh on Titan, Io, and Uranus’ moon Miranda.The average distance of Enceladus from Saturn is 238,000 km; the average distance of Titan from Saturn is 1,222,000 km. How much longer does it take Titan to orbit Saturn compared to Enceladus?Why are asteroids and comets important to our understanding of solar system history?Give a brief description of the asteroid belt.Describe the main differences between C-type and S-type asteroids.In addition to the ones mentioned in Exercise 13.3, what is the third, rarer class of asteroids?Vesta is unusual as it contains what mineral on its surface? What does the presence of this material indicate?Compare asteroids of the asteroid belt with Earth-approaching asteroids. What is the main difference between the two groups?Briefly describe NASA’s Spaceguard Survey. How many objects have been found in this survey?Who first calculated the orbits of comets based on historical records dating back to antiquity?Describe the nucleus of a typical comet and compare it with an asteroid of similar size.Describe the two types of comet tails and how each are formed.What classification is given to objects such as Pluto and Eris, which are large enough to be round, and whose orbits lie beyond that of Neptune?Describe the origin and eventual fate of the comets we see from Earth.What evidence do we have for the existence of the Kuiper belt? What kind of objects are found there?Give brief descriptions of both the Kuiper belt and the Oort cloud.Give at least two reasons today’s astronomers are so interested in the discovery of additional Earthapproaching asteroids.Suppose you were designing a spacecraft that would match course with an asteroid and follow along its orbit. What sorts of instruments would you put on board to gather data, and what would you like to learn?Suppose you were designing a spacecraft that would match course with a comet and move with it for a while. What sorts of instruments would you put on board to gather data, and what would you like to learn?Suppose a comet were discovered approaching the Sun, one whose orbit would cause it to collide with Earth 20 months later, after perihelion passage. (This is approximately the situation described in the science-fiction novel Lucifer’s Hammer by Larry Niven and Jerry Pournelle.) What could we do? Would there be any way to protect ourselves from a catastrophe?We believe that chains of comet fragments like Comet Shoemaker-Levy 9’s have collided not only with the jovian planets, but occasionally with their moons. What sort of features would you look for on the outer planet moons to find evidence of such collisions? (As an extra bonus, can you find any images of such features on a moon like Callisto? You can use an online site of planetary images, such as the Planetary Photojournal, at photojournal.jpl.nasa.gov.)Why have we found so many objects in the Kuiper belt in the last two decades and not before then?Why is it hard to give exact diameters for even the larger objects in the Kuiper belt?Refer to Example 13.1. How would the calculation change if a typical comet in the Oort cloud is only 1 km in diameter?Refer to Example 13.1. How would the calculation change if a typical comet in the Oort cloud is larger-say, 50 km in diameter?The calculation in Example 13.1 refers to the known Oort cloud, the source for most of the comets we see. If, as some astronomers suspect, there are 10 times this many cometary objects in the solar system, how does the total mass of cometary matter compare with the mass of Jupiter?If the Oort cloud contains 1012 comets, and ten new comets are discovered coming close to the Sun each year, what percentage of the comets have been “used up” since the beginning of the solar system?The mass of the asteroids is found mostly in the larger asteroids, so to estimate the total mass we need to consider only the larger objects. Suppose the three largest asteroids-Ceres (1000 km in diameter), Pallas (500 km in diameter), and Vesta (500 km in diameter)-account for half the total mass. Assume that each of these three asteroids has a density of 3 g/cm3 and calculate their total mass. Multiply your result by 2 to obtain an estimate for the mass of the total asteroid belt. How does this compare with the mass of the Oort cloud?Make a similar estimate for the mass of the Kuiper belt. The three largest objects are Pluto, Eris, and Makemake (each roughly 2000 km). In addition, assume there are eight objects (including Haumea, Orcus, Quaoar, Ixion, Varuna, and Charon, and objects that have not been named yet) with diameters of about 1000 km. Assume that all objects have Pluto’s density of 2 g/cm3. Calculate twice the mass of the largest 13 objects and compare it to the mass of the main asteroid belt.What is the period of revolution about the Sun for an asteroid with a semi-major axis of 3 AU in the middle of the asteroid belt?What is the period of revolution for a comet with aphelion at 5 AU and perihelion at the orbit of Earth?A friend of yours who has not taken astronomy sees a meteor shower (she calls it a bunch of shooting stars). The next day she confides in you that she was concerned that the stars in the Big Dipper (her favorite star pattern) might be the next ones to go. How would you put her mind at ease?In what ways are meteorites different from meteors? What is the probable origin of each?How are comets related to meteor showers?What do we mean by primitive material? How can we tell if a meteorite is primitive?Describe the solar nebula, and outline the sequence of events within the nebula that gave rise to the planetesimals.Why do the giant planets and their moons have compositions different from those of the terrestrial planets?How do the planets discovered so far around other stars differ from those in our own solar system? List at least two ways.Explain the role of impacts in planetary evolution, including both giant impacts and more modest ones.Why are some planets and moons more geologically active than others?Summarize the origin and evolution of the atmospheres of Venus, Earth, and Mars.Why do meteors in a meteor shower appear to come from just one point in the sky?What methods do scientists use to distinguish a meteorite from terrestrial material?Why do iron meteorites represent a much higher percentage of finds than of falls?Why is it more useful to classify meteorites according to whether they are primitive or differentiated rather than whether they are stones, irons, or stony-irons?Which meteorites are the most useful for defining the age of the solar system? Why?Suppose a new primitive meteorite is discovered (sometime after it falls in a field of soybeans) and analysis reveals that it contains a trace of amino acids, all of which show the same rotational symmetry (unlike the Murchison meteorite). What might you conclude from this finding?How do we know when the solar system formed? Usually we say that the solar system is 4.5 billion years old. To what does this age correspond?We have seen how Mars can support greater elevation differences than Earth or Venus. According to the same arguments, the Moon should have higher mountains than any of the other terrestrial planets, yet we know it does not. What is wrong with applying the same line of reasoning to the mountains on the Moon?Present theory suggests that giant planets cannot form without condensation of water ice, which becomes vapor at the high temperatures close to a star. So how can we explain the presence of jovian-sized exoplanets closer to their star than Mercury is to our Sun?Why are meteorites of primitive material considered more important than other meteorites? Why have most of them been found in Antarctica?How long would material take to go around if the solar nebula in Example 14.1 became the size of Earth’s orbit?Consider the differentiated meteorites. We think the irons are from the cores, the stony-irons are from the interfaces between mantles and cores, and the stones are from the mantles of their differentiated parent bodies. If these parent bodies were like Earth, what fraction of the meteorites would you expect to consist of irons, stony-irons, and stones? Is this consistent with the observed numbers of each? (Hint: You will need to look up what percent of the volume of Earth is taken up by its core, mantle, and crust.)Estimate the maximum height of the mountains on a hypothetical planet similar to Earth but with twice the surface gravity of our planet.Describe the main differences between the composition of Earth and that of the Sun.Describe how energy makes its way from the nuclear core of the Sun to the atmosphere. Include the name of each layer and how energy moves through the layer.Make a sketch of the Sun’s atmosphere showing the locations of the photosphere, chromosphere, and corona. What is the approximate temperature of each of these regions?Why do sunspots look dark?Which aspects of the Sun’s activity cycle have a period of about 11 years? Which vary during intervals of about 22 years?Summarize the evidence indicating that over several hundreds of years or more there have been variations in the level of the solar activity.What it the Zeeman effect and what does it tell us about the Sun?Explain how the theory of the Sun’s dynamo results in an average 22-year solar activity cycle. Include the location and mechanism for the dynamo.Compare and contrast the four different types of solar activity above the photosphere.What are the two sources of particles coming from the Sun that cause space weather? How are they different?How does activity on the Sun affect human technology on Earth and in the rest of the solar system?How does activity on the Sun affect natural phenomena on Earth?Table 15.1 indicates that the density of the Sun is 1.41 g/cm3. Since other materials, such as ice, have similar densities, how do you know that the Sun is not made of ice?Starting from the core of the Sun and going outward, the temperature decreases. Yet, above the photosphere, the temperature increases. How can this be?Since the rotation period of the Sun can be determined by observing the apparent motions of sunspots, a correction must be made for the orbital motion of Earth. Explain what the correction is and how it arises. Making some sketches may help answer this question.Suppose an (extremely hypothetical) elongated sunspot forms that extends from a latitude of 30° to a latitude of 40° along a fixed of longitude on the Sun. How will the appearance of that sunspot change as the Sun rotates? (Figure 15.17 should help you figure this out.) Figure 15.17 Magnetic Field Lines Wind Up. Because the Sun spins faster at the equator than near the poles, the magnetic fields in the Sun tend to wind up as shown, and after a while make loops. This is an idealized diagram; the real situation is much more complex.The text explains that plages are found near sunspots, but Figure 15.18 shows that they appear even in areas without sunspots. What might be the explanation for this? Figure 15.18 Plages on the Sun. This image of the Sun was taken with a filter that transmits only the light of the spectral line produced by singly ionized calcium. The bright cloud-like regions are the plages. (credit: modification of work by NASA)Why would a flare be observed in visible light, when they are so much brighter in X-ray and ultraviolet light?How can the prominences, which are so big and ‘float’ in the corona, stay gravitationally attached to the Sun while flares can escape?If you were concerned about space weather and wanted to avoid it, where would be the safest place on Earth for you to live?Suppose you live in northern Canada and an extremely strong flare is reported on the Sun. What precautions might you take? What might be a positive result?The edge of the Sun doesn’t have to be absolutely sharp in order to look that way to us. It just has to go from being transparent to being completely opaque in a distance that is smaller than your eye can resolve. Remember from Astronomical Instruments that the ability to resolve detail depends on the size of the telescope’s aperture. The pupil of your eye is very small relative to the size of a telescope and therefore is very limited in the amount of detail you can see. In fact, your eye cannot see details that are smaller than 1/30 of the diameter of the Sun (about 1 arcminute). Nearly all the light from the Sun emerges from a layer that is only about 400 km thick. What fraction is this of the diameter of the Sun? How does this compare with the ability of the human eye to resolve detail? Suppose we could see light emerging directly from a layer that was 300,000 km thick. Would the Sun appear to have a sharp edge?Show that the statement that 92% of the Sun’s atoms are hydrogen is consistent with the statement that 73% of the Sun’s mass is made up of hydrogen, as found in Table 15.2. (Hint: Make the simplifying assumption, which is nearly correct, that the Sun is made up entirely of hydrogen and helium.)From Doppler shifts of the spectral lines in the light coming from the east and west edges of the Sun, astronomers find that the radial velocities of the two edges differ by about 4 km/s, meaning that the Sun’s rotation rate is 2 km/s. Find the approximate period of rotation of the Sun in days. The circumference of a sphere is given by 2pR, where R is the radius of the sphere.Assuming an average sunspot cycle of 11 years, how many revolutions does the equator of the Sun make during that one cycle? Do higher latitudes make more or fewer revolutions compared to the equator?This chapter gives the average sunspot cycle as 11 years. Verify this using Figure 15.26. Figure 15.26 Numbers of Sunspots over Time. This diagram shows how the number of sunspots has changed with time since counts of the numbers of spots began to be recorded on a consistent scale. Note the low number of spots during the early years of the nineteenth century, the Little Maunder Minimum. (credit: modification of work by NASA/ARC)The escape velocity from any astronomical object can be calculated as vescape=2GM/R . Using the data in Appendix E, calculate the escape velocity from the photosphere of the Sun. Since coronal mass ejections escape from the corona, would the escape velocity from there be more or less than from the photosphere?Suppose you observe a major solar flare while astronauts are orbiting Earth. Use the data in the text to calculate how long it will before the charged particles ejected from the Sun during the flare reach them.Suppose an eruptive prominence rises at a speed of 150 km/s. If it does not change speed, how far from the photosphere will it extend after 3 hours? How does this distance compare with the diameter of Earth?From the information in Figure 15.21, estimate the speed with which the particles in the CME in parts (c) and (d) are moving away from the Sun. Figure 15.21 Flare and Coronal Mass Ejection. This sequence of four images shows the evolution over time of a giant eruption on the Sun. (a) The event began at the location of a sunspot group, and (b) a flare is seen in far-ultraviolet light. (c) Fourteen hours later, a CME is seen blasting out into space. (d) Three hours later, this CME has expanded to form a giant cloud of particles escaping from the Sun and is beginning the journey out into the solar system. The white circle in (c) and (d) shows the diameter of the solar photosphere. The larger dark area shows where light from the Sun has been blocked out by a specially designed instrument to make it possible to see the faint emission from the corona. (credit a, b, c, d: modification of work by SOHO/EIT, SOHO/LASCO, SOHO/MDI (ESA & NASA))How do we know the age of the Sun?Explain how we know that the Sun’s energy is not supplied either by chemical burning, as in fires here on Earth, or by gravitational contraction (shrinking).What is the ultimate source of energy that makes the Sun shine?What are the formulas for the three steps in the proton-proton chain?How is a neutrino different from a neutron? List all the ways you can think of.Describe in your own words what is meant by the statement that the Sun is in hydrostatic equilibrium.Two astronomy students travel to South Dakota. One stands on Earth’s surface and enjoys some sunshine. At the same time, the other descends into a gold mine where neutrinos are detected, arriving in time to detect the creation of a new radioactive argon nucleus. Although the photon at the surface and the neutrinos in the mine arrive at the same time, they have had very different histories. Describe the differences.What do measurements of the number of neutrinos emitted by the Sun tell us about conditions deep in the solar interior?Do neutrinos have mass? Describe how the answer to this question has changed over time and why.Neutrinos produced in the core of the Sun carry energy to its exterior. Is the mechanism for this energy transport conduction, convection, or radiation?What conditions are required before proton-proton chain fusion can start in the Sun?Describe the two main ways that energy travels through the Sun.Someone suggests that astronomers build a special gamma-ray detector to detect gamma rays produced during the proton-proton chain in the core of the Sun, just like they built a neutrino detector. Explain why this would be a fruitless effort.Earth contains radioactive elements whose decay produces neutrinos. How might we use neutrinos to determine how these elements are distributed in Earth’s interior?The Sun is much larger and more massive than Earth. Do you think the average density of the Sun is larger or smaller than that of Earth? Write down your answer before you look up the densities. Now find the values of the densities elsewhere in this text. Were you right? Explain clearly the meanings of density and mass.A friend who has not had the benefit of an astronomy course suggests that the Sun must be full of burning coal to shine as brightly as it does. List as many arguments as you can against this hypothesis.Which of the following transformations is (are) fusion and which is (are) fission: helium to carbon, carbon to iron, uranium to lead, boron to carbon, oxygen to neon? (See Appendix K for a list of the elements.)Why is a higher temperature required to fuse hydrogen to helium by means of the CNO cycle than is required by the process that occurs in the Sun, which involves only isotopes of hydrogen and helium?Earth’s atmosphere is in hydrostatic equilibrium. What this means is that the pressure at any point in the atmosphere must be high enough to support the weight of air above it. How would you expect the pressure on Mt. Everest to differ from the pressure in your classroom? Explain why.Explain what it means when we say that Earth’s oceans are in hydrostatic equilibrium. Now suppose you are a scuba diver. Would you expect the pressure to increase or decrease as you dive below the surface to a depth of 200 feet? Why?What mechanism transfers heat away from the surface of the Moon? If the Moon is losing energy in this way, why does it not simply become colder and colder?Suppose you are standing a few feet away from a bonfire on a cold fall evening. Your face begins to feel hot. What is the mechanism that transfers heat from the fire to your face? (Hint: Is the air between you and the fire hotter or cooler than your face?)Give some everyday examples of the transport of heat by convection and by radiation.Suppose the proton-proton cycle in the Sun were to slow down suddenly and generate energy at only 95% of its current rate. Would an observer on Earth see an immediate decrease in the Sun’s brightness? Would she immediately see a decrease in the number of neutrinos emitted by the Sun?Do you think that nuclear fusion takes place in the atmospheres of stars? Why or why not?Why is fission not an important energy source in the Sun?Why do you suppose so great a fraction of the Sun’s energy comes from its central regions? Within what fraction of the Sun’s radius does practically all of the Sun’s luminosity originate (see Figure 16.16)? Within what radius of the Sun has its original hydrogen been partially used up? Discuss what relationship the answers to these questions bear to one another. Figure 16.16 shows how the temperature, density, rate of energy generation, and composition vary from the center of the Sun to its surface.Explain how mathematical computer models allow us to understand what is going on inside of the Sun.Estimate the amount of mass that is converted to energy when a proton combines with a deuterium nucleus to form tritium, 3He.How much energy is released when a proton combines with a deuterium nucleus to produce tritium, 3He?The Sun converts 4109 kg of mass to energy every second. How many years would it take the Sun to convert a mass equal to the mass of Earth to energy?Assume that the mass of the Sun is 75% hydrogen and that all of this mass could be converted to energy according to Einstein’s equation E=mc2 . How much total energy could the Sun generate? If m is in kg and c is in m/s, then E will be expressed in J. (The mass of the Sun is given in Appendix E.)In fact, the conversion of mass to energy in the Sun is not 100% efficient. As we have seen in the text, the conversion of four hydrogen atoms to one helium atom results in the conversion of about 0.02862 times the mass of a proton to energy. How much energy in joules does one such reaction produce? (See Appendix E for the mass of the hydrogen atom, which, for all practical purposes, is the mass of a proton.)Now suppose that all of the hydrogen atoms in the Sun were converted into helium. How much total energy would be produced? (To calculate the answer, you will have to estimate how many hydrogen atoms are in the Sun. This will give you good practice with scientific notation, since the numbers involved are very large! See Appendix C for a review of scientific notation.)Models of the Sun indicate that only about 10% of the total hydrogen in the Sun will participate in nuclear reactions, since it is only the hydrogen in the central regions that is at a high enough temperature. Use the total energy radiated per second by the Sun, 3.81026 watts, alongside the exercises and information given here to estimate the lifetime of the Sun. (Hint: Make sure you keep track of the units: if the luminosity is the energy radiated per second, your answer will also be in seconds. You should convert the answer to something more meaningful, such as years.)Show that the statement in the text is correct: namely, that roughly 600 million tons of hydrogen must be converted to helium in the Sun each second to explain its energy output. (Hint: Recall Einstein’s most famous formula, and remember that for each kg of hydrogen, 0.0071 kg of mass is converted into energy.) How long will it be before 10% of the hydrogen is converted into helium? Does this answer agree with the lifetime you calculated in Exercise 16.35?Every second, the Sun converts 4 million tons of matter to energy. How long will it take the Sun to reduce its mass by 1% (the mass of the Sun is 21030 kg)? Compare your answer with the lifetime of the Sun so far.Raymond Davis Jr.’s neutrino detector contained approximately 1030 chlorine atoms. During his experiment, he found that one neutrino reacted with a chlorine atom to produce one argon atom each day. A. How many days would he have to run the experiment for 1% of his tank to be filled with argon atoms? B. Convert your answer from A. into years. C. Compare this answer to the age of the universe, which is approximately 14 billion years (1.41010y) . D. What does this tell you about how frequently neutrinos interact with matter?What two factors determine how bright a star appears to be in the sky?Explain why color is a measure of a star’s temperature.What is the main reason that the spectra of all stars are not identical? Explain.What elements are stars mostly made of? How do we know this?What did Annie Cannon contribute to the understanding of stellar spectra?Name five characteristics of a star that can be determined by measuring its spectrum. Explain how you would use a spectrum to determine these characteristics.How do objects of spectral types L, T, and Y differ from those of the other spectral types?Do stars that look brighter in the sky have larger or smaller magnitudes than fainter stars?The star Antares has an apparent magnitude of 1.0, whereas the star Procyon has an apparent magnitude of 0.4. Which star appears brighter in the sky?Based on their colors, which of the following stars is hottest? Which is coolest? Archenar (blue), Betelgeuse (red), Capella (yellow).Order the seven basic spectral types from hottest to coldest.What is the defining difference between a brown dwarf and a true star?If the star Sirius emits 23 times more energy than the Sun, why does the Sun appear brighter in the sky?How would two stars of equal luminosity-one blue and the other red-appear in an image taken through a filter that passes mainly blue light? How would their appearance change in an image taken through a filter that transmits mainly red light?Table 17.2 lists the temperature ranges that correspond to the different spectral types. What part of the star do these temperatures refer to? Why?Suppose you are given the task of measuring the colors of the brightest stars, listed in Appendix J, through three filters: the first transmits blue light, the second transmits yellow light, and the third transmits red light. If you observe the star Vega, it will appear equally bright through each of the three filters. Which stars will appear brighter through the blue filter than through the red filter? Which stars will appear brighter through the red filter? Which star is likely to have colors most nearly like those of Vega?Star X has lines of ionized helium in its spectrum, and star Y has bands of titanium oxide. Which is hotter? Why? The spectrum of star Z shows lines of ionized helium and also molecular bands of titanium oxide. What is strange about this spectrum? Can you suggest an explanation?The spectrum of the Sun has hundreds of strong lines of nonionized iron but only a few, very weak lines of helium. A star of spectral type B has very strong lines of helium but very weak iron lines. Do these differences mean that the Sun contains more iron and less helium than the B star? Explain.What are the approximate spectral classes of stars with the following characteristics? A. Balmer lines of hydrogen are very strong; some lines of ionized metals are present. B. The strongest lines are those of ionized helium. C. Lines of ionized calcium are the strongest in the spectrum; hydrogen lines show only moderate strength; lines of neutral and metals are present. D. The strongest lines are those of neutral metals and bands of titanium oxide.Look at the chemical elements in Appendix K. Can you identify any relationship between the abundance of an element and its atomic weight? Are there any obvious exceptions to this relationship?Appendix I lists some of the nearest stars. Are most of these stars hotter or cooler than the Sun? Do any of them emit more energy than the Sun? If so, which ones?Appendix J lists the stars that appear brightest in our sky. Are most of these hotter or cooler than the Sun? Can you suggest a reason for the difference between this answer and the answer to the previous question? (Hint: Look at the luminosities.) Is there any tendency for a correlation between temperature and luminosity? Are there exceptions to the correlation?What star appears the brightest in the sky (other than the Sun)? The second brightest? What color is Betelgeuse? Use Appendix J to find the answers.Suppose hominids one million years ago had left behind maps of the night sky. Would these maps represent accurately the sky that we see today? Why or why not?Why can only a lower limit to the rate of stellar rotation be determined from line broadening rather than the actual rotation rate? (Refer to Figure 17.14.) Figure 17.14 Using a Spectrum to Determine Stellar Rotation. A rotating star will show broader spectral lines than a nonrotating star.Why do you think astronomers have suggested three different spectral types (L, T, and Y) for the brown dwarfs instead of M? Why was one not enough?Sam, a college student, just bought a new car. Sam’s friend Adam, a graduate student in astronomy, asks Sam for a ride. In the car, Adam remarks that the colors on the temperature control are wrong. Why did he say that? Figure 17.17 (credit: modification of work by Michael Sheehan)Would a red star have a smaller or larger magnitude in a red filter than in a blue filter?Two stars have proper motions of one arcsecond per year. Star A is 20 light-years from Earth, and Star B is 10 light-years away from Earth. Which one has the faster velocity in space?Suppose there are three stars in space, each moving at 100 km/s. Star A is moving across (i.e., perpendicular to) our line of sight, Star B is moving directly away from Earth, and Star C is moving away from Earth, but at a 30° angle to the line of sight. From which star will you observe the greatest Doppler shift? From which star will you observe the smallest Doppler shift?What would you say to a friend who made this statement, “The visible-light spectrum of the Sun shows weak hydrogen lines and strong calcium lines. The Sun must therefore contain more calcium than hydrogen.”?In Appendix J, how much more luminous is the most luminous of the stars than the least luminous? For Exercise 17.33 through Exercise 17.38, use the equations relating magnitude and apparent brightness given in the section on the magnitude scale in The Brightness of Stars and Example 17.1.Verify that if two stars have a difference of five magnitudes, this corresponds to a factor of 100 in the ratio (b2b1) ; that 2.5 magnitudes corresponds to a factor of 10; and that 0.75 magnitudes corresponds to a factor of 2.As seen from Earth, the Sun has an apparent magnitude of about 26.7 . What is the apparent magnitude of the Sun as seen from Saturn, about 10 AU away? (Remember that one AU is the distance from Earth to the Sun and that the brightness decreases as the inverse square of the distance.) Would the Sun still be the brightest star in the sky?An astronomer is investigating a faint star that has recently been discovered in very sensitive surveys of the sky. The star has a magnitude of 16. How much less bright is it than Antares, a star with magnitude roughly equal to 1?The center of a faint but active galaxy has magnitude 26. How much less bright does it look than the very faintest star that our eyes can see, roughly magnitude 6?You have enough information from this chapter to estimate the distance to Alpha Centauri, the second nearest star, which has an apparent magnitude of 0. Since it is a G2 star, like the Sun, assume it has the same luminosity as the Sun and the difference in magnitudes is a result only of the difference in distance. Estimate how far away Alpha Centauri is. Describe the necessary steps in words and then do the calculation. (As we will learn in the Celestial Distances chapter, this method-namely, assuming that stars with identical spectral types emit the same amount of energy-is actually used to estimate distances to stars.) If you assume the distance to the Sun is in AU, your answer will come out in AU.Do the previous problem again, this time using the information that the Sun is 150,000,000 km away. You will get a very large number of km as your answer. To get a better feeling for how the distances compare, try calculating the time it takes light at a speed of 299,338 km/s to travel from the Sun to Earth and from Alpha Centauri to Earth. For Alpha Centauri, figure out how long the trip will take in years as well as in seconds.Star A and Star B have different apparent brightnesses but identical luminosities. If Star A is 20 light-years away from Earth and Star B is 40 light-years away from Earth, which star appears brighter and by what factor?Star A and Star B have different apparent brightnesses but identical luminosities. Star A is 10 light-years away from Earth and appears 36 times brighter than Star B. How far away is Star B?The star Sirius A has an apparent magnitude of 1.5 . Sirius A has a dim companion, Sirius B, which is 10,000 times less bright than Sirius A. What is the apparent magnitude of Sirius B? Can Sirius B be seen with the naked eye?Our Sun, a type G star, has a surface temperature of 5800 K. We know, therefore, that it is cooler than a type O star and hotter than a type M star. Given what you learned about the temperature ranges of these types of stars, how many times hotter than our Sun is the hottest type O star? How many times cooler than our Sun is the coolest type M star?How does the mass of the Sun compare with that of other stars in our local neighborhood?Name and describe the three types of binary systems.Describe two ways of determining the diameter of a star.What are the largest- and smallest-known values of the mass, luminosity, surface temperature, and diameter of stars (roughly)?You are able to take spectra of both stars in an eclipsing binary system. List all properties of the stars that can be measured from their spectra and light curves.Sketch an HR diagram. Label the axes. Show where cool super-giants, white dwarfs, the Sun, and main-sequence stars are found.Describe what a typical star in the Galaxy would be like compared to the Sun.How do we distinguish stars from brown dwarfs? How do we distinguish brown dwarfs from planets?Describe how the mass, luminosity, surface temperature, and radius of main-sequence stars change in value going from the “bottom” to the “top” of the main sequence.One method to measure the diameter of a star is to use an object like the Moon or a planet to block out its light and to measure the time it takes to cover up the object. Why is this method used more often with the Moon rather than the planets, even though there are more planets?We discussed in the chapter that about half of stars come in pairs, or multiple star systems, yet the first eclipsing binary was not discovered until the eighteenth century. Why?Is the Sun an average star? Why or why not?Suppose you want to determine the average educational level of people throughout the nation. Since it would be a great deal of work to survey every citizen, you decide to make your task easier by asking only the people on your campus. Will you get an accurate answer? Will your survey be distorted by a selection effect? Explain.Why do most known visual binaries have relatively long periods and most spectroscopic binaries have relatively short periods?Figure 18.11 shows the light curve of a hypothetical eclipsing binary star in which the light of one star is completely blocked by another. What would the light curve look like for a system in which the light of the smaller star is only partially blocked by the larger one? Assume the smaller star is the hotter one. Sketch the relative positions of the two stars that correspond to various portions of the light curve. Figure 18.11 Light Curve of an Edge-On Eclipsing Binary. Here we see the light curve of a hypothetical eclipsing binary star whose orbit we view exactly edge-on, in which the two stars fully eclipse each other. From the time intervals between contacts, it is possible to estimate the diameters of the two stars.There are fewer eclipsing binaries than spectroscopic binaries. Explain why. Which is the hottest? Coolest? Most luminous? Least luminous? In each case, give your reasoning.Within 50 light-years of the Sun, visual binaries outnumber eclipsing binaries. Why?Which is easier to observe at large distances-a spectroscopic binary or a visual binary?The eclipsing binary Algol drops from maximum to minimum brightness in about 4 hours, remains at minimum brightness for 20 minutes, and then takes another 4 hours to return to maximum brightness. Assume that we view this system exactly edge-on, so that one star crosses directly in front of the other. Is one star much larger than the other, or are they fairly similar in size? (Hint: Refer to the diagrams of eclipsing binary light curves.)Review this spectral data for five stars. Which is the hottest? Coolest? Most luminous? Least luminous? In each case, give your reasoning.Which changes by the largest factor along the main sequence from spectral types O to M-mass or luminosity?Suppose you want to search for brown dwarfs using a space telescope. Will you design your telescope to detect light in the ultraviolet or the infrared part of the spectrum? Why?An astronomer discovers a type-M star with a large luminosity. How is this possible? What kind of star is it?Approximately 6000 stars are bright enough to be seen without a telescope. Are any of these white dwarfs? Use the information given in this chapter to explain your reasoning.Use the data in Appendix J to plot an HR diagram for the brightest stars. Use the data from Table 18.3 to show where the main sequence lies. Do 90% of the brightest stars lie on or near the main sequence? Explain why or why not.Use the diagram you have drawn for Exercise 18.25 to answer the following questions: Which star is more massive-Sirius or Alpha Centauri? Rigel and Regulus have nearly the same spectral type. Which is larger? Rigel and Betelgeuse have nearly the same luminosity. Which is larger? Which is redder?Use the data in Appendix I to plot an HR diagram for this sample of nearby stars. How does this plot differ from the one for the brightest stars in Exercise 18.25? Why?If a visual binary system were to have two equal-mass stars, how would they be located relative to the center of the mass of the system? What would you observe as you watched these stars as they orbited the center of mass, assuming very circular orbits, and assuming the orbit was face on to your view?Two stars are in a visual binary star system that we see face on. One star is very massive whereas the other is much less massive. Assuming circular orbits, describe their relative orbits in terms of orbit size, period, and orbital velocity.Describe the spectra for a spectroscopic binary for a system comprised of an F-type and L-type star. Assume that the system is too far away to be able to easily observe the L-type star.Figure 18.7 shows the velocity of two stars in a spectroscopic binary system. Which star is the most massive? Explain your reasoning. A plot showing how the velocities of the stars change with time is called a radial velocity curve; the curve for the binary system in Figure 18.6 is shown in Figure 18.7. Figure 18.7 Radial Velocities in a Spectroscopic Binary System. These curves plot the radial velocities of two stars in a spectroscopic binary system, showing how the stars alternately approach and recede from Earth. Note that positive velocity means the star is moving away from us relative to the center of mass of the system, which in this case is 40 kilometers per second. Negative velocity means the star is moving toward us relative to the center of mass. The positions on the curve corresponding to the illustrations in Figure 18.6 are marked with the diagram number (14).