Solution Manual for Astronomy Today, 9th Edition

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy1Chapter 1: Charting the HeavensThe Foundations of AstronomyOutline1.1 Our Place in Space1.2 Scientific Theory and the Scientific Method1.3 The “Obvious” View1.4 Earth’s Orbital Motion1.5 The Motion of the Moon1.6 The Measurement of DistanceSummaryChapter 1 begins with a “Big Picture” overview of our place in the Universe. This is followed by a briefintroduction to the science of Astronomy and the definition of “Universe.” Common units of measurement thatare important to astronomers are introduced, along with the convention of scientific notation. Section 1.2discusses the scientific method, giving the students an understanding of some of the differences between scienceand pseudoscience or non-science ways of knowing such as religion. Section 1.3 introduces constellations and thecelestial sphere, which serve as a springboard to descriptions in Section 1.4 of the apparent daily and annualmotions of celestial bodies such as the Sun, Moon, and stars. Most of these motions are actually illusory, causedby various motions of the Earth. Section 1.4 also explains the nature and cause of the Earth’s seasons. Section1.5deals with the relationship between the Earth and the Moon that causes the phases of the Moon as well as solarand lunar eclipses. Chapter 1 concludes with the concept of parallax and its use in performing measurements ofdistance and size.Major ConceptsThe Big Picture—Our Place in the UniverseScientific TheoriesTestableSimpleElegantAstronomy and the Scientific MethodObservationHypotheses/ExplanationObservation/ExperimentationConstellationsThe Celestial SphereEarth’s MotionRotation on its Axis (Daily Motion)The Tilt of the Axis and the SeasonsRevolution Around the Sun (Yearly Motion) and the ZodiacPrecessionThe Moon’s OrbitLunar PhasesLunar Eclipses

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy2Solar EclipsesDistanceTriangulation and ParallaxSizing Up the EarthTeaching Suggestions and DemonstrationsOne of the challenges of studying astronomy is developing the ability to view the universe from differentperspectives. The biggest challenge is in shifting from the perspective we have from Earth, where we see the Sunand stars rise in the east and set in the west, to the perspective from “outside,” where we “see” Earth spinningonits axis and orbiting the Sun. Models and diagrams are essential to teaching this introductory material, to helpyour students practice shifting viewpoints. Many students have poorly developed visualization skills, so the morevisual aids the better. This chapter contains lots of new vocabulary, so take time to define the new terms.This will likely be students’ first exposure to a formal class in astronomy. They will come to the class with someconcrete knowledge, but also with a great deal of misinformation and misconceptions derived from years ofexposure to multimedia sources. It is not unusual for people to believe some aspects of what they know as sciencefiction. Most students are still comfortable with Aristotelian thinking. This chapter provides your first opportunityto slowly move your students toward a new way of thinking—a new perspective. There are many problem areasand misconceptions for students, especially in the early chapters of this text. This is to be expected. Students havefew misconceptions about active galaxies because most have never heard of them.Section 1.1Students almost universally think of the light-year as a unit of time rather than distance. This confusion comesabout simply because of the word “year.” Spend some time discussing a light-year by first introducing the speedof light. Tell them that light travels at a finite speed and therefore takes time to get to where it’s going. Studentsmay be familiar with “lag time” in a long-distance cell-phone callor in a “live via satellite” interview on thetelevision news; part of this is because the radio signals take time to travelup to the satellites and “bouncearound” to their destination.Emphasize “distance” here. Since the speed of light is about 3105km/s, one light-second is adistanceof 3105km. Next, describe a few examples, such as the fact that light travels fast enough to go around the Earth more thanseven times in one second; therefore, one light-second is equivalent to a bit more than seven times thecircumference of the Earth. Another example is that the Sun is about 8 light-minutes away. Students are usuallyintrigued by the idea that if the Sun were to burnout or explode right now, then we would have no way of learningthat fact for another 8 minutes. Finally, use the distance to far away galaxies as another example. The galaxies areso distant that it takes millions of years for their light to reach us. Therefore, they are millions of light-years away.This is good conceptual foreshadowing for things to come later in the semester. When we look at distant objects,we see them as they were when their light left them. We see things not as they are “right now,” but as they werewhen the information—light—left them. The Sun appears to us as it was 8 minutes ago. Distant galaxies appear tous as they were millions of years ago. When we look at distant objects, we are effectively looking back in time.Section 1.2Since many of your students are likely to have had minimal exposure to science, this section is worth focusing onfor class discussions. In introducing the scientific method, refer to Figure 1.6 now as well as throughout thesemester. Remind the students that science is a process rather than some fixed set of ideas or laws. Furthermore, itis an iterative process that really has no end, as theories are constantly being re-tested and improved. Therefore,scientific theories are always subject to challenge and change. In fact, it is a good thing when a theory is

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy3challenged, because it may be an opportunity to enhance our understanding. This is astrength, not a weakness, ofscience. Ask the students to provide examples of ideas in their own minds that had changed once additional piecesof data or knowledge were made available to them. The foundation of science rests on the fact that it does not relyon the authority of political or religious systems or on the interpretation of text, ancient or otherwise. It relies on aconstant process of improvement.When talking about the process of science, it is important to distinguish between facts, the things we observe andmeasure, and theory, our explanations for those observations. Emphasize that no matter how good, useful, orthorough a theory is, it canneverbe a fact. The fact is that apples fall from trees; the theory that explains how andwhy they fall is the theory of gravity. Theories should never be given too much credit, and they should not be soldshort. Theories are not just guesses or statements of belief. Theories are our best possible explanations for thethings we see happening around us, backed up by data and the hard work of men and women who are striving tounderstand the universe more completely.To use the phrase “just a theory” is to demean that hard work. Theoriesare powerful things, even if they are not facts. Students appreciate it when instructors are candid about thestrengths—andlimitations—of scientific theories, so don’t be afraid tobe honest about the nature of science.Section 1.3Your students will all have heard of constellations and will probably be able to name at least a few, usually signsof the Zodiac or “big names” like Orion. Emphasize that the stars in a given constellation are probably notphysically close to each other in space; they just appear close to each other as seen from Earth. Compare Figures1.8 and 1.9. Use an analogy with how close buildings may appear to each other when observing a large city froma distance.The stars in the northern part of the sky were grouped together by observers in ancient times, and we continue touse nearly the same groupings (mostly from Eastern Mediterranean cultures) today. You can pass out or project asky chart without constellations drawn in and challenge students to make up their own. You could even create awriting project in which students research an ancient culture—I usually disallow the Greeks and the Romans tomake it challenging—and come up with constellations for that culture.Students may be surprised to find that there are 88 constellations, and that constellations are used to divide the skyinto sections, the way that county, state, and national boundaries are used on Earth. It is also interesting tocompare names of northern and southern constellations. The northern constellations are mostly traditional,typically named after animals and mythological characters, such as Cygnus (the Swan), Cassiopeia (the Queen),and Orion (the Hunter). The Southern Hemisphere sky includes more modern constellation names such asTelescopium (the Telescope), Microscopium (the Microscope), and Antlia (the Air Pump). Ask your students ifthey can explain why there is a difference. The constellation names we have inherited today derive from northern-sky observers, mostly in ancient Greece. The northern constellation names, therefore, date from ancient times, butthe names from the southern sky date from the travels made by northern explorers to the Southern Hemisphere inmore recent times.I find that mythological stories not only give students time to “rest their hands,” but can also help refocus theirattention and see the connections to the past. The story of Cassiopeia, Cepheus, Andromeda, Cetus, and Perseus isa nice way to show the connections among a “family” of constellations. I also use the myth of Orion and Scorpiusto explain the different appearances of the summer and winter skies, as shown in Figure 1.14. The two mortalenemies, placed on opposite ends of the sky, continuously chase each other around. Their “guardians”—Taurusfor Orion and Sagittarius for Scorpius—insure that they don’t “cheat” and take a shortcut over the Earth. Theseare all constellations your students can find in the night sky, depending on the time of year you are teaching thecourse. Provide star charts and encourage your students to find major constellations in the night sky throughoutthe course.

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy4The concept of the celestial sphere is an important one. We are missing depth perception when we look out at thenight sky, and so we perceive the three-dimensional Universe as a two-dimensional sphere.DEMO—If available, bring in a transparent model of the celestial sphere with Earth inside and point out thenorth and south celestial poles and the celestial equator. Emphasize that this is not an accurate model of theuniverse, but a good illustration of the geocentric model. This is a good time to discuss Polaris and clear up anymisconceptions; often, introductory astronomy students believe the North Star must be the brightest star in thesky. The ancient Chinese saw Polaris as the Celestial Emperor, and while the Emperor may not be the brightestperson in the kingdom, everyone still has to do what he says! Introduce students to right ascension and declinationby comparing these to latitude and longitude. Compare the grid lines on the transparent sphere to the grid on thecentral Earth. Emphasize that the celestial coordinates are attached to the sky. Over the course of a night, starsmove from east to west and the coordinate system moves with them. Look up the coordinates of a few well-known stars (including Polaris) and help students determine their positions on the transparent sphere. Askstudents to compare the two different methods of describing star locations, by coordinates and by constellation,and discuss the advantages of each.Section 1.4Students usually know the terms “rotation” and “revolution” but often confuse them. For this reason, I try to avoidtheir use in class, and encourage students to do the same. It is much simpler and clearer to use “spin” and “orbit,”so try to get yourself in the habit of using these terms. Remember: students will be more impressed by someonewho is clear than by someone who “sounds scientific!” Likewise, they will probably know that Earth takes a dayto turn on its axis and a year to orbit the Sun, but will not know the difference between a solar day and a siderealday, or a tropical year and a sidereal year. Use diagrams such as Figure 1.13, to help explain. Models also help.DEMO—Demonstrate rotation and revolution with globes, or bring students to the front of the class to modelEarth’s motions. For instance, one student can spin around (slowly) while orbiting another. Ask the class toconcentrate on one point on the Earth, say, the spinning student’s nose, and imagine when it is lit and when it isdark. Use this model to explain day and night, sidereal vs. solar days, and why different constellations are visiblein the night sky during different months.Figures 1.15 and 1.16 are very important and particularly insightful when used in conjunction with one another.Make sure students understand that Figure 1.16 shows the apparent path of the sun on the celestial sphere, andthat this path passes through the constellations of the zodiac, as can be seen by taking the “Earth perspective” inFigure 1.15. Ifyou ask students how many constellations are along the Sun’s path in the zodiac, the commonanswer will be 12. Although this is true of the “astrological zodiac,” students are usually surprised to learn thatthere are actually 13 zodiacal constellations, including Ophiuchus. Ask students to use Figure 1.15 to determinewhat constellation the Sun appears to be in at a certain time of year. Then ask students if they notice any “errors”in those dates. There may be several students who mention that their birthdays are not within the dates shown fortheir astrological “sign.” This usually serves as a perfect lead-in to the history of the modern calendar, includingthe concept of precession.DEMO—A gyroscope or top in motion on a table or desk makes a good demonstration of precession. Bychanging the direction that Earth’s axis is pointing, precession is responsible for the fact that the zodiacconstellations no longer correspond to their astrological dates. Another example, the heliacal rising of Sirius—Sirius rising right next to the Sun—was an important date in the ancient Egyptian agricultural calendar, since itsignaled the flooding of the Nile. Thanks to precession, this no longer occurs on the same date today.My experience has shown that few students have a good understanding of the cause of the seasons. Afterpresenting a mythological explanation for the seasons—the Greek myth of Pluto and Persephone—I ask students

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy5to write a brief paragraph explaining why it is cold in winter and hot in summer. This would also make a good“clicker” question.Many students, especially those who have not yet read the text, will say the cause is thevarying distance between the Earth and the Sun. I then present four pieces of information demonstrating why thiscan’t be so.1.The Earth is closest to the Sun in January.2.The Earth’s orbit is only a few degrees off from a perfect circle.3.The tropics are warm all year round.4.The seasons “flip” when you cross the equator.It is important to attack this misconception with evidence, rather than simply present the correct alternative. Thesefour pieces of evidence may induce some “cognitive dissonance” and help studentslet go of their deeply rootedmisconception and be more open to a better explanation. After all, in science, explanations are refuted with facts,not with alternative explanations.DEMO—Using an overhead projector or flashlight and a tilted globe, show how the angle of sunlight changes asthe Earth goes around the Sun. Remember always to have the axis pointing the same direction! Note that not a lotchanges in the tropical zone, while the polar regions have the light blocked by the curve of the Earth for half ayear. Shine a flashlight directly down on a tabletop or on the floor, and then shine it at an angle to show how theangle of the Sun’s rays affects the distribution of solar heating.Section 1.5DEMO—When explaining the motions of the Earth, Moon, and Sun, you can bring a common Earth globe toclass. An overhead projector or a flashlight will do for the Sun. For the Moon, any sphere that is a quarterdiameter of the Earth globe—softballs or baseballs—will work well. The students can be the “fixed” stars.Onedemonstration can attack the common misconception that the Moon always shows the same face to Earth becausethe Moon does not spin. Ask a student to sit in a chair and hold a globe of the Earth. Have yourself or anotherstudent “orbit” the chair without spinning—say, by always keeping his or her nose pointing at the studentsplaying the stars. Have the student representing the Earth describe what he or she sees. Then have the studentrepresenting the Moon orbit again, this time always facing the Earth. Ask the “stars” what they see the Moondoing.Don’t assume your students actually understand the phasesof the Moon. Using a whiteboard, chalkboard, ortransparency on an overhead projector, draw the orbit of the Moon around the Earth, as in Figure 1.20. Place theMoon at key points in the orbit, represented as a circle. Using one color, shade in the half of the Moon that alwaysfaces the Earth. In another color, shade in the half of the Moon that is lit up by the Sun. You may even want topass out worksheets and have the students do this themselves. Stress to the students that the phase of the Moondepends on how much those two regions coincide. The lecture-tutorial “The Cause of Moon Phases” is also verygood for reinforcing these ideas. After defining the basic phases of the Moon, ask questions such as “When doesthe full moon rise?” or “At what time of dayor night is the first quarter moon highest in the sky?” The answer toboth questions is sunset. Demonstrate this with your model. Since it is not practical to have each student sit in the“Earth chair,” you may want to take a short movie from that perspective, with just one light source illuminatingthe Moon proxy. As the person holding the Moon model spins in the chair, it will appear to go through phases.DEMO—You can create a simple model to illustrate Moon phases by getting a bunch of small Styrofoam balls afew inches in diameter and some pencils. Stick each sphere onto a pencil and give one to each student or group ofstudents. Darken the room except for a single light source representing the Sun. Have the students spin around sothat the Styrofoam balls “orbit” their heads. Each sphere will appear to go through phases as it orbits a student’s

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy6head. Have the students pause frequently and note the configurations of the faux celestial bodies. Be sure to havethe students hold the balls over their heads so that they do not inadvertently demonstrate eclipses!DEMO—To demonstrate eclipses, use the same Earth globe and sphere for the Moon as at the start of thissection. Now set up a true-scale model of this system by placing the Moon at 30 Earth diameters from the Earth.Establish the plane of the ecliptic and raise and lower the Moon by ±10 of its diameters to demonstrate the rangeof its inclination to the ecliptic (which is ±5° and the Moon is about 0.5° in apparent angular diameter). It is notpossible for any textbook picture or diagram to represent realistically the Earth–Moon system to scale.With this model, students will see how easy it is for the lunar shadow to miss Earth during the new Moon phase orhow the Moon misses the Earth’s shadow during full Moon phase (the Earth’s shadow being about 2.5 lunardiameters). When describing eclipses, ask students what they would see if they stood on the Moon’s surface whilelooking in the direction of the Earth or the Sun. Would the lunar surface be in darkness or light? What about theEarth or Sun? Remember that the Sun will appear to be the same size in the sky but Earth will appear four timeslarger in diameter than the Moon does from Earth. Let the shadow of the Earth globe fall on the Moon model, andnote, as Aristotle did, that the curve of the shadow means the Earth is spherical.Section 1.6Make sure that students understand that the techniques of parallax and triangulation are not just for astronomers.Ask if students have seen surveyors sighting through small telescopes. Relate what surveyors do to whatastronomers do to find distance.DEMO—The traditional way of demonstrating parallax is to instruct the students to hold up a finger (or pencil),close one eye, and line their finger up with some object on the far wall of the classroom. When they do the samewith the other eye open instead, it lines up at a different position. Ask students to try the exercise several timeswith their finger at different distances from their eyes to determine the relationship between the distance and theamount of shift.DEMO—A second method of demonstrating parallax is to make marks on the board that represent the fixedstars. Distinguish these stars by color or number. Hold a small ball about 1 m or so in front of the board. Withyour other hand, prepare to make a mark on the board at the location given to you by two students at the oppositesides of the back of the room. Select a student in the back left part of the room and have them tell you where theysee the ball relative to the background stars. Make a mark on the board corresponding to that location. Repeat theprocedure by selecting a student at the back of the room on the right side. The two apparent locations will bedistinctively different, allowing for a clear demonstration of the concepts related to the geometrical foundations ofparallax, namely baseline and parallax angle. Figure 1.30shows this method applied to astronomy using Earth’sdiameter as a baseline. Challenge students to come up with a method in which observers restricted to the surfaceof the Earth can create an even longer baseline to measure parallaxes of more distant stars. (Observations can bemade at different points in Earth’s orbit around the Sun; see Figure 17.1.) Even with the diameter of Earth’s orbitas a baseline, the parallax method only works for the stars in the solar neighborhood.Angular measure is very important in astronomy. Discuss More Precisely 1-1 carefully. Emphasize theastronomical connection by discussing why there are 360º in a circle. One reason is that the ancient Babyloniansfound the number 360 very easy to work with, since it is divisible by so many things. Remind students that theancients did not have calculators, the decimal point, or even the idea of zero! Also, the Sun takes about 360 daysto complete a “circle” in the skyover the course of a year. Thus, the Sun moves about 1º per day.DEMO—Demonstrate angular measure by holding up a penny. At a distance of about 1 m, a penny subtends anangle of about 1º. Students can hold up a penny and see what objects at different distances in the classroom have

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy7an angular size of about 1º. Have students try this at night and estimate the angular size of the Moon, which, tomany students’ surprise, is onlyhalf a degree.More Precisely 1-2 discusses finding the distances to (and diameters of) astronomical objects. Go over angularmeasurements and then try several examples. Many problems throughout the text use the equations in this section,so it is worth spending some time to ensure that students understand. Use the fact that the Sun and Moon have thesame angular size to emphasize the dependence of angular size on actual size and distance. The text gives aformula that is useful for angular sizes expressed in degrees:actual diameterangular diameter57.3distanceSince angular sizes of celestial objects are usually measured in seconds of arc (when they are measurable at all),you may wish to give students an alternate equation. One radian contains 206,265 arc seconds, so the equationbecomes:actual diameterangular diameter206265distanceA fist held out at arm’s length is about 10across, but that is highly variable. To give students some practicemeasuring and calculating angular sizes, you can actually have them test out this notion. Have students measurethe distance across their fists, and the distance from their eye to their fists. The first piece of data is the actualdiameter, and the second is the distance. Students can then calculate the actual angular diameters of their fists.Compile andaverage the results to see if a fist at arm’s length really is 10º across.You may wish to have the students construct an instrument that can measure angles in the sky more accurately. Asimple version of such an instrument, called a “cross staff”, can be made from just a meter stick (serving as thestaff) and a shorter slender object, such as a ruler or length of pipe (the cross). The idea is to place the cross on thestaff and perpendicular to it so that it subtends an angle of 20º when viewed from the end of the meter stick. If thecross has an actual size of 20 cm, then a simple calculation reveals that it should be attached to the 57.3-cm pointon the meter stick. Have the students come to this conclusion working in small groups rather than just tellingthem. Once the cross staff is built, it can be used for a variety of purposes:Measuring the angle between the Sun and the Moon, to see how that angle changes with Moonphase. Students could even use those angles to reconstruct the Moon’s orbit.Measuring the height of stars above the horizon. Students are often amazed at how much thataltitude can change in just an ortwo. They can also note the “fixed” altitude of Polaris.Measuring the angular distances between the stars in a constellation, such as Ursa Major orCassiopeia. Students can note how constant those distances remain, and could even use thedistances to construct a star chart.Measure the distance between a planet and some bright stars, to see how the planet moves.I have students buy their own meter sticks, and use whatever they have available for the cross. I feel this givesthem more ownership of the device, and they are much more careful and creative with it.The text describes how Eratosthenes was able to calculate the circumference of the Earth using geometry. Youmay also want to describe how Eratosthenes’ contemporary Aristarchus of Samos was able to find out the relativesizes of the Sun and Moon. As with any three points, at any time the Sun, Moon, and Earth form a triangle.

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy8During the phases of first and third quarter, one of the angles of that triangle—the one at the Moon—isapproximately 90º.This is, of course, a right triangle. The distance from the Earth to the Sun is the hypotenuse of that triangle, andthe distance from the Earth to the Moon is one of the sides. Therefore, if we can figure out the value of the angleat the Sun, we can use the trigonometric sine function to find the ration between those two sides of the triangle.Aristarchus did not have the modern sine function, but understood the ratios.Aristarchus measured the angle at the Earth and found it to be about 87º—it is actually much smaller, butAristarchus’ instruments for measuring angles did not have modern levels of accuracy.This leaves only about 3ºfor the angle at the Sun, and the sine of 3º is approximately 1/19. This means that the Sun is 19 times farther awayfrom the Earth than the Moon is. This is, of course, off by many orders of magnitude, but the exact numbers areunimportant in this case.However, this also allows us to make a conclusion about the relative sizes of the Sun and Moon. Because the Sunand Moon are roughly the same apparent size, the ratio of their distances from the Earth is the same as the ratio oftheir actual sizes. So Aristarchus also discovered that the Sun is larger than the Moon, something we take forgranted today but was far from obvious to the ancients. Furthermore, since the Earth is only about 3 times the sizeof the Moon, which can be judged from the Earth’s shadow during a lunar eclipse, Aristarchus concludedthat theSun is much larger than the Earth. This was completely unsuspected, and led Aristarchus to ultimately assert thatthe huge Sun had to be orbited by the smaller Earth. This story takes a long time to unfold in class, but it alsopoints out that not everyone in ancient Greece bought into the Heliocentric Model.SunMoonEarth

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy9Relevant Lecture-TutorialsPosition, p. 1Motion, p. 3Seasonal Stars, p. 7Solar vs. Sidereal Day, p. 11Ecliptic, p. 13Star Charts, p. 19The Cause of Moon Phases, p. 81Predicting Moon Phases, p. 85Path of the Sun, p. 89Seasons, p. 93Sun Size, p. 113Student Writing Questions1.What is the smallest object you have ever seen? The largest? The longest distance you have ever traveled?What is the largest number of objects you have ever knowingly encountered? (You may encounter manybacteria, but not knowingly.) What was the longest you ever spent doing one activity? How do the largestand the smallest of these compare? How do the distances compare to the size of the Earth? To thedistance to the Moon? How does your time spent on your longest activity compare to your lifetime?2.Test your horoscope. Each day, write two or three sentences of the most significant events that occurredto you that day. Cut out or copy your horoscope for that day and save it. Continue this every day for about3 weeks and make sure you write down your daily events before you read the horoscope. After 3 weeks,check what you wrote against your horoscope for each day and see if there is a match. Count the numberof “hits” and “misses.” Discuss the results and whether there is any significance to the number of hits. Ifyou know someone born close to the same day as you, compare your experiences to his or hers. Arehoroscopes truly predictive?3.Describe an ordinary situation in which people regularly apply the scientific method, even though they arenot aware they are doing so. Relate the situation to the three basic steps in the scientific method: gatherdata, form theory, and test theory.4.If you can, find a location to view the night sky with little interference from city lights. Do this on as cleara night as possible. What do you see? Look all over and make note of the brightest stars. Are there anyplanets? How can you tell? Is the Moon out? What does it look like? What sort of details can you see onits surface?Chapter Review AnswersREVIEW AND DISCUSSION1.The universe is defined as the sum total of all space, time, energy, and matter.2.Looking at the data in the text, we can see that the diameter of the Sun is about 100 times that of Earth,about 1,500,000 km for the Sun compared to about 12,000 km for Earth. A galaxy such as the Milky Way isabout 100,000 light-years in diameter. Since a light-year is about 1013km, this means the Galaxy has adiameter of approximately 1018km, or about 1014times (100 million million times) the radius of Earth. The

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy10most distant objects visible define the limits of thevisibleuniverse (which is likely only a small part of theentire universe). These objects are about 10 billion light-years away, or 1023km. This is 1019times (10billion billion times) the radius of Earth.3.The scientific method is a process for discovering the best possible explanation as to why something occurs.The process begins when observations lead to the formulation of a hypothesis, a preliminary explanationthat makes testable predictions. Investigators gather information—called data—to test the predictionsthrough observation and experimentation. The information is analyzed to find patterns in the data. If thepatterns agree with the predictions, the hypothesis is considered a viable theory. If they do not agree, thehypothesis must be discarded or modified. Science therefore relies on measurable quantities and testablepredictions to search for answers. By contrast, pseudosciences such as astrology typically make predictionsthat cannot be tested, and offer explanations that do not fit within a coherent framework of ideas. If a claimis not testable, it cannot be considered scientific.4.In the common usage of the term, a constellation is a pattern of stars in the sky. Officially, however, aconstellation is a section of sky that contains stars, galaxies, nebulae, and many more celestial objects. Justas every section of Earth’s land surface is considered part of a country, every part of the sky is within theborders of a constellation. Constellations are thus useful in naming and locating celestial objects.5.The motion of the Sun in the sky is an illusion caused by the Earth’s spin. The Sun appears to rise in theeast and move westward throughout the day because the Earth beneath us is spinning eastward, orcounterclockwise, as viewed from the north. Therefore, all non-artificial celestial objects have this apparentmotion, including the Moon and stars. The motion of the Earth in its orbit around the Sun produces anotherset of illusions that unfold over the course of the year. The Sun appears to move among the signs of theZodiac over the course of a year, as the Moon does over the course of a month. The appearance of the nightsky gradually changes over the year, as the night side of the Earth points toward different parts of theGalaxy.6.The Sun is a special object because Earth is in orbit around it. By comparison, the stars are “fixed,” and wemeasure Earth’s “true” rotation—the sidereal day—compared to the stars. Over the course of the siderealday, Earth has moved along a small portion of its orbit. This causes the Sun to appear to move slightlyamong the stars from our perspective, and so Earth must spin a few minutes more to “catch up” and bringthe Sun back to its position from the previous day. Therefore, the solar day is slightly longer than thesidereal day.7.At any given time during the year, we can only see the part of the Galaxy that the “night side” of Earth isfacing as it orbits the Sun. In July, this part of the Galaxy includes, for example, the stars of Scorpio. Sixmonths later, Earth has moved over to the other side of the Sun, and the night side of Earth is facing anentirely different section of the Galaxy, with the stars of Orion. We cannot see the stars of Scorpio inJanuary because the Sun is between them and us.8.Discovered by the Greek astronomer Hipparchus, precession is a slow shift in the orientation of the Earth’saxis of spin. Although Earth’s axis maintains an axis tilt of 23.5º compared to the axis of the Sun, the axismoves in a circle over the course of 26,000 years. This causes the location of the celestial poles to shift,along with the entire sky. For individual stars, this means that their celestial coordinates change slowly overtime. It is caused by the gravitational influence of the Moon and Sun on the spinning Earth.9.There are seasons on Earth because the rotation axis of Earth is tilted with respect to the axis of the Sun.This tilt means that a given location on Earth receives different angles and intensities of sunlight over thecourse of Earth’s orbit. When it is summer at your location, the Sunis almost directly overhead at noon.Therefore, the sunlight strikes the ground at almost a 90º angle and is very concentrated. In winter,

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy11however, the Sun never gets very high, even at noon, and the sunlight comes in at an extreme angle. Thisindirect sunlight is very diffuse and not efficient at heating.10.Half of the Moon is lit by the Sun at all times. However, due to the Moon’s motion around Earth, it is notalways the same half. The phase of the Moon depends on which portion of the“near”side of the Moon (theside that faces Earth) is lit by the Sun, which in turn is influenced by where the Moon is in its orbit aroundEarth. If 100% of that side is illuminated, we see a full Moon. If none of the side facing Earth isilluminated, we have a new Moon.11.A lunar eclipse occurs when the Sun, Earth, and Moon align so that the Moon enters the shadow of theEarth. A solar eclipse occurs when the three objects align so that the shadow of the Moon falls on Earth’ssurface. From the perspective of someone in the shadow, the Moon passes in front of the Sun. Eclipses canonly occur when the Sun, Moon, and Earth line up in all three dimensions. This occurs rarely because theorbit of the Moon around Earth is not aligned with the orbit of Earth around the Sun. The two orbits form anangle of 5.2º, so most of the time the shadow of the Moon misses the surface of Earth, and the Moon doesnot fully enter Earth’s shadow. Only on those rare occasions when the three bodies come into alignment andthe Moon crosses the plane ofEarth’s orbit (the ecliptic) can we have an eclipse.12.So long as the planet’s moon (or moons) can enter the shadow of the planet, observers on other planets cansee their versions of lunar eclipses. Solar eclipses are a different matter: the moon must be close enough orbig enough (or both) to have the same apparent size as the Sun or greater. Only then can it completely coverthe Sun from the observer’s perspective.This is very possible; for example, we have seen the shadows ofthe Galilean moons passing over the clouds of Jupiter.13.Parallax is the apparent shift in a foreground object’s position compared to the background. It is an illusioncaused by a change in the observer’s point of view. For example, when we look at our finger with one eyeopen and then switch eyes, the finger will appear to move against the background. Surveyors use parallax tofind the distances to objects.14.Since parallax is an illusion caused by a change in perspective, a very large change in perspective (calledthe baseline) is required to see a parallax shift in a distant object. If the baseline is too small compared tothe object’s distance, the difference in perspective will not be enough to cause a visible shift.15.To determine the true diameter of an object from a distance, we need to know how large the object appearsto be (the angular diameter) and how far away the object is (distance).CONCEPTUAL SELF-TEST1.B2.B3.D4.A5.C6.A7.C8.C9.A10.D

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy12PROBLEMS1.In 1 second, light travels about 300,000 km. This is almost 80% of the distance to the Moon.2.(a) 1000 = 1 × 103; 0.000001 = 1 × 10–6; 1001 = 1.001 × 103; 1,000,000,000,000,000 = 1 × 1015;123,000 = 1.23 × 105; 0.000456 = 4.56 × 10–4(b) 3.16 × 107= 31,600,000; 2.998 × 105= 299,800; 6.67 × 10–11= 0.0000000000667; 2 × 100= 2(c) 2 × 103+ 10–2= 2000 + 0.01 = 2000.01; (1.99 × 1030)/(5.98 × 1024) = 333,000;(3.16 × 107) × (2.998 × 105) = 9.47 × 10123.There are 12 constellations in the Zodiac. Since there are 360º in a circle, each constellation in the Zodiacoccupies about 30º. The year 10,000 AD is roughly 8000 years from now. Since 8000/26,000 = 0.31, this8000-year span represents 31% of the total 26,000-year precession cycle. Therefore, the Sun will move 31%of the way around the circle, or 111º. This is a little less than four constellations worth of motion, so the Sunwill be well into Scorpio by 10,000 AD.4.The Moon appears to orbit Earth in 29.5 days (the synodic month). Thus, every day it appears to move360º/29.5= 12.2º among the stars. Therefore:(a) One hour is 1/24 = 0.042 day, and in that time the Moon will move 12.2º × 0.042 = 0.51º, or about 31minutes of arc.(b) One minute is 1/60 of an hour, so the motion will be 1/60 of the motion above, or about 31 seconds ofarc.(c) Once second is 1/3600 of an hour, so the motion will be 1/3600 of the motion in part a, or about 0.52seconds of arc.The angular diameter of the Moon is about half a degree, or about 30 minutes of arc. By our calculationsabove, this means the Moon moves its own diameter in one hour compared to the stars.5.In this case, we can find the distance using the formula:parallax1000 km3602D(a)P= 1º, soD= 57,300 km.(b)P= 1/60º, soD= 3,440,000 km.(c)P= 1/3600º, soD= 206,000,000 km.6.First, we must change the angular size of Venus into degrees.55 seconds ×13600 seconds= 0.0153ºInserting this into the formula for angular size givesactual sizeactual sizeangular size57.30.0015357.3distance45,000,000 km 

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy13This gives an actual size of 12,000 km.7.Since their angular sizes are the same, the Moon’s advantage in distancemust be offset by a disadvantage inactual size. The Sun is 391-times farther away (150,000,000/384,000) than the Moon, so the Sun must be391-times larger than the Moon to compensate.8.Assuming a thumb diameter of 2 cm and an arm length of 75 cm, we can use the angular size formula.actual size2 cmangular size57.357.31.5distance75 cm9.There are a number of answers to this question, and a number of ways to get an answer. One way isexplained here:http://www.npr.org/sections/krulwich/2012/09/17/161096233/which-is-greater-the-number-of-sand-grains-on-earth-or-stars-in-the-skySuggested ReadingsWebsitesThere are a huge number of astronomy-based sites on the World Wide Web. Here are a couple devoted to theconstellations and their mythology:The Constellations and their Stars—http://www.astro.wisc.edu/~dolan/constellations/. The “references” section ofthe site has an extensive list of star myths from many cultures.The Constellations Web Page—http://www.dibonsmith.com/.http://amazingspace.org/tonights_sky/is a NASA video about the night sky. This URL always lands on thecurrent month, but you can browse the archive for other constellations during other months. Planet positions andmoon phases are also shown.The famous 1977 film “Powers of Ten” can be found on YouTube:https://www.youtube.com/watch?v=0fKBhvDjuy0Cary and Michael Huang have created the excellent Web app “The Scale of the Universe.” Users can zoom in andout from the smallest to the largest scales, and get information about the objects to be found at those scales. Theapp can be found athttp://htwins.net/scale2/. Well worth a look.One of many videos comparing the sizes of celestial objectsis titled “Star Size Comparison 2”:https://www.youtube.com/watch?v=GoW8Tf7hTGA’An activity to help students better understand the seasons can be found athttp://nationalgeographic.org/activity/the-reason-for-the-seasons/http://www.mreclipse.comandhttp://aa.usno.navy.mil/data/docs/LunarEclipse.htmlgive information abouteclipses of the moon and sun.The “Crash Course” channel on YouTube has a series about astronomy:https://www.youtube.com/playlist?list=PL8dPuuaLjXtPAJr1ysd5yGIyiSFuh0mIL

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy14The first five videos are especially relevant to this chapter.The phenomenon of precession can be difficult for students to visualize. A short video demonstrating theprecession of the Earth’s axis and its effect on the locations of the Vernal Equinox and the NorthCelestial Pole istitled “Precession of the earth”:https://www.youtube.com/watch?v=qlVgEoZDjok.BooksA number of books are available about the constellations and their mythology. Here is a sampling:Allen, R. H.Star Names: Their Lore and Meaning. New York: Dover Publications, 1990. A reprinting (withcorrections) of a work first published in 1899. It has fascinating information and more detail than you will everneed to know.Rey, H. A.The Stars: A New Way to See Them.New York: Houghton Mifflin, 1976. Our modern view of theconstellation patterns is due in large part to Rey, the creator of theCurious Georgeseries of children’s books.Ridpath, I.Star Tales. Cambridge: Lutterworth Press, 1989. Includes a story for every constellation, althoughsome are quite brief.Stott, C.Celestial Charts, Antique Maps of the Heavens.New York: Crescent Books, 1991. Traces thedevelopment of the constellations through beautiful photos of ancient star maps. A striking “coffee table” book.Magazine ArticlesBeldea, Cătălinand Joe Cali. “Chasing totality from the stratosphere.”Sky & Telescope(October 2013). p. 66. Astory about observing an eclipse from above ground level.Berman, B. “Theoutsider.”Astronomy(October 2003). p. 48. Illuminating article about a modern astronomer.Helpful when discussing the scientific method with students and a good reminder that science is a humanendeavor/activity. Relevant to Chapters 1 and 2.Berman, Bob. “Five-five-uh-oh.”Astronomy(May 2000). p. 93. Discusses the effects of the “planetaryalignment” of May 2000, and provides arguments against astrology.Bordeleau, A. “Polestars of the future.”Sky & Telescope(March 2008). p. 66. Overview of how precessionaffects the position of the celestial poles.Brown, Jeanette.“It’sjust a phase.”Astronomy(April 1999). p. 76. Describes an activity designed to demonstratethe phases of the moon.Camino, N. and A. Gangui.“Diurnalastronomy: using sticks and threads to find our latitude on Earth.”PhysicsTeacher50:1 (2012), p. 40. A unique way of determining latitude in the daytime.Crossen, Craig. “The very ancient origins of the water constellations.”Sky & Telescope(March 2015). p. 36.Describes how a section of the sky filled with faint stars acquired a number of water-themed constellations.Cunningham, C. J. “Updating Eratosthenes.”Mercury.(March/April 2003). p. 10. Discusses a method by whichstudents can measure the size of the Earth using the Internet.

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy15Gurshtein, Alexander A. “Insearch of the first constellations.”Sky & Telescope(June 1997). p. 46. A detaileddiscussion of the origin and history of constellations.Hirshfeld, A. “The Universe of Archimedes.”Sky & Telescope(November 2010). p. 32. A discussion of howArchimedes conceptualized astronomical quantities.Krupp, E. C. “Slitheringtoward solstice.”Sky & Telescope(June 2000). p. 86. Discusses the symbolism ofsnakes, serpents, and solstices.Leschak, Peter. “Thesky’sancient light.”Night Sky(January/February 2006). p. 52. Article with a variety ofexamples of how we look back in time as we look out into space.Livio, M. “Is God amathematician?”Mercury(January/February 2003). p. 26. Brief discussion of the role playedby mathematics in scientific theories.Mallmann, J. A. “Treeleaf shadows to the Sun’sdensity: A surprising route.”Physics Teacher51:1 (2013). p. 10.Using the images of the Sun created by leaves to calculate some of the Sun’s properties.Paczynski, B. “Astronomy: Aproblem of distance.”Nature(January 2004). p. 299. An example of determiningdistances to astronomical objects (along with associated practical considerations).Panek, Richard. “Theastrology connection.”Natural History(April 2000). p. 20. Discusses conjunctions and thehistorical connection between astrology and astronomy.Panek, Richard. “Thatsneaky solstice.”Natural History(June 2000). p. 20. Describes the meaning of the solstice,and discusses why the earliest sunrise does not happen on the solstice.Plait, Phil. “Thereason for the seasons.”Astronomy(July 1999). p. 75. Brief and accurate description of the causeof the seasons, with good diagrams.Ryan, Jay. “SkyWise: Equinox.”Sky & Telescope(March 2000). p. 114. Comic strip drawing illustrating theequinoxes.Ryan, Jay. “SkyWise: Gregorian calendar.”Sky & Telescope(February 2000). p. 109. A cartoon strip showingsystems of calendars.Ryan, Jay. “SkyWise: Lunarskies.”Sky & Telescope(April 2000). p. 114. A cartoon strip illustrating the view ofthe Earth as seen from the Moon.Sadler, P. M. and C. Night “Daytime celestial navigation for the novice.”Physics Teacher48:3 (2010). p. 197.Tracing the analemma with simple tools.Sweitzer, J. “Doyou believe in the Big Bang?”Astronomy(December 2002). p. 34. Discusses “theory” andevidence in general and as applied to the Big Bang Model.Takemae, S., P. Kirwin, and G. McIntosh “Reproducing Eratosthenes’ determination of Earth’s circumference ona smaller scale.”Physics Teacher51:4 (2013). p. 222. Illustrating Eratosthenes’ technique on a balloon.Talcott, R. and R. Kelly. “Illustrated:How we see the sky.”Astronomy(June 2009). A description of the usefulconstruct of the Celestial Sphere.

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Astronomy Today, 9th Edition Instructor GuideChapter 1: Charting the HeavensThe Foundations of Astronomy16Trefil, James. “Architects oftime.”Astronomy(September 1999). p. 48. Discusses history of astronomical timekeeping, from Stonehenge to pulsars.Vanderbei, Robert and Ruslan Belikov. “Measuring theastronomical unit from your backyard.”Sky & Telescope(January 2007). p. 91. Technique for using the parallax of asteroids and planets to determine the value of theastronomical unit.Zeiler, Michael. “Theevolving eclipse map.”Sky & Telescope(November 2012), p. 34. Describes how we canpredict the time and place of eclipses.

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science1Chapter 2: The Copernican RevolutionThe Birth of Modern ScienceOutline2.1 Ancient Astronomy2.2 The Geocentric Universe2.3 The Heliocentric Model of the Solar System2.4 The Birth of Modern Astronomy2.5 The Laws of Planetary Motion2.6 The Dimensions of the Solar System2.7 Newton’s Laws2.8 Newtonian MechanicsSummaryChapter 2 continues the view from Earth started in the previous chapter by discussing the apparent motions of theplanets, which leads to two very important concepts that are introduced in this chapter: the historical developmentof astronomy and the laws of planetary motion and gravity. The historical context in which these concepts arecouched provides a framework for demonstrating the scientific process and for portraying that process as a humanendeavor. Although the chapter takes a mostly European view, as is traditional, it does speak to the larger issue ofcontributions from cultures all over the world and throughout history. Modern astronomy is anything but limitedto western contributions; it is a truly international science, as will be seen in later chapters.Chapter 2 is very important, not just for its historical context, but because it describes the ideas of gravity andorbital motion that pervade the rest of the text. There is hardly a chapter that follows that does not make referenceto this material and build on it. It is therefore imperative that students understand this material; without thisunderstanding, very little of the following 26 chapters will make sense. The material is also highly relevant toissues of technology and modern life. For example, students often take the many satellites that serve us in orbit forgranted, and may have a poor understanding (and some misconceptions) about what it takes to get them in orbitand keep them there. Cartoons as well as some science fiction movies and television programs can promote thesemisconceptions that havebecome the “lived reality” of our students.Major ConceptsAncient AstronomyEarly Uses of the SkyAstronomy During the “Dark Ages”Motions of the PlanetsWanderers Among the StarsRetrograde MotionGeocentric Models of the UniverseAristotlePtolemyHeliocentric Models and the Birth of Modern AstronomyCopernicusBrahe

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science2GalileoKepler’s Lawsof Planetary MotionIsaac NewtonLaws of MotionGravityExplaining Orbits and Kepler’s LawsTeaching Suggestions and DemonstrationsSection 2.1Point out to the students that in ancient times, astronomical observations were tightly intertwined with themythological/spiritual aspects of human life as well as agricultural practices that were important to the well-beingof ancient cultures. Food sources, whether animal or vegetable, were found to be dependent on the annualseasonal cycles. Ask the students if they can come up with examples of things in their own lives that aredependent on celestial phenomena, including the Earth’s rotation and the cyclical revolution period as we movearound the Sun. When modern farmers plan, they simply look at the modern calendar and consult withtechnologically advanced meteorological tools such as“Dopplerradar”and weather satellites. Ancient cultureslacked these tools and instead relied on other instruments such as Stonehenge or the Caracol Temple as describedin the text. It is worth noting that we have only deduced after the fact that these ancient monuments hadastronomical applications; it’s not as if they came with instruction manuals! There are also instances where anancient site was thought to have astronomical significance that later proved to be spurious, such as the NazcaLines in South America.Students may be surprised that even today the spiritual components of society can still be intermingled withastronomical phenomena. For example, the Christian holiday of Easter falls on the first Sunday following the firstfull Moon after the Vernal Equinox.Section 2.2While a few students might be eager to move on to the black holes and string theory, my experience is that moststudents enjoy hearing about the history of astronomy. Hearing the stories of some of the “big names” inastronomy, the things they got right, and even the things they got wrong, goes a long way toward “humanizing”science for the students. Talking about wrong turns is especially important, because it demonstrates the power ofthe scientific process. Be sure to emphasize that “bad” theories are brought down byevidence, not just by “better”theories. People such as Aristotle and Ptolemy were not wrong because they lacked intelligence, they were wrongbecause they lackedinformation.A disturbing number of authors depict ancient astronomers in a patronizing manner; for example, some have saidthat the ancients clung to an idea of an Earth-centered solar system because they wanted a“special place in theuniverse.” This is not only an arrogant 21st century perspective, it is utterly wrong. Ancient astronomers wererational, mature people who relied on their experiences and information to shape their ideas, just as we do. Theycould not “feel” the Earth spinning or orbiting, for example, and so believed that it was stationary beneath arotating sky. Aristotle himself said that if the Earth were moving, then we should feel the wind from its motion. Inaddition, they could not see the phenomenon of stellar parallax, and thus concluded that our perspective on thestars did not change because we were not moving. Be sure to give credit to ancient astronomers for being rationalpeople. When talking about the ancient practice of using models to describe the universe, discuss the idea of“Saving the Appearance.” Early astronomers were concerned with creating models of theuniverse that werecapable of providing accurate reproductions of what they were seeing in the sky without a deep regard for

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science3physical explanation or justification. The need for such justification was simply not part of their tradition, as it ispart of ours.One of the ways that Aristotle tried to justify the geocentric view of the universe was with the five classicalelements. Four of these elements were found only in our world: earth, water, air, and fire. The fifth element(sometimes called the Aether) was found only outside Earth. It was a perfect, glowing, and unchanging material,unlike the chaotic elements of Earth. An object’s natural motion (what it did when nothing was exerting a forceon it) depended on its composition. An object made mostly of earth or water fell downward, and an object madeof air or fire rose upward. The celestial objects did neither, but moved in perfect circles around Earth. These ideasseemed reasonable for describing motions in the sky for centuries, until the work of Copernicus, Galileo, andKepler brought them down.The text notes that not all Greeks subscribed to the geocentric model, and mentions Aristarchus of Samos as anexample. Students may be interested to know just how Aristarchus came to the conclusion that the Sun is at thecenter. It began when Aristarchus undertook a project to measure the relative sizes of the Sun and Moon, and thusadd to the earlier work of measuring the size of the Earth done by Eratosthenes (see Chapter 1). He reasoned thatat certain times, the Sun, Moon, and Earth would form a right triangle with the right angle at the Moon, like so:To determine exactly when the angle at the Moon was 90º, he built a model of the Earth–Moon–Sun system. Hefound that when the Moon was half-lit as seen from Earth (first and third quarter) the angle was 90º. He thenknew when to go out and measure the angle at the Earth—the angle between the Sun and Moon as seen fromEarth. He measured that angle to be about 87º; it is measured with modern instruments to be over 89º. With solittle left over for the angle at the Sun, it became clear that the triangle was of the “long and skinny” variety. TheSun had to be much further away than previously thought. Aristarchus calculated that the Sun was about 19 timesfarther from Earth than was the Moon. In modern terms we would use the sine function, and say thatsince sin 3º ≈1/19, the hypotenuse (Earth–Sun distance) is about 19 times the side opposite the 3º angle (Earth–Moon distance).This number is actually too small, due to the error in measuring the angle at the Earth, but the implications arewhat matters here. Since the Sun is much farther than the Moon, it must be proportionately larger, since the twoobjects have roughly the same angular size (see Section 1.5). The size of Earth’s shadow during a lunar eclipseindicates that Earth is about 3 times larger than the Moon. If the Sun is then 19 times larger (or more!) than theSunMoonEarth

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science4Moon, then the Sun has to be larger than Earth. An elementary school student knows this today, but 2000 yearsago, it was by no means obvious. Aristarchus reasoned that it was ludicrous to expect the Earth to command anobject so much larger than itself, and so he placed the Sun at the center of motion. The lack of evidence for theEarth’s motion, however, proved to be more convincing for many people, including Ptolemy.The evolution of our understanding of the structure of the Universe is a remarkable story of the scientific process,in which each successive model took care of some problem of the previous model. In many ways, the history ofastronomy is the history of the scientific process itself. One common example of the scientific process at work isPtolemy’s geocentric model of the Universe; its epicycles and deferents were ultimately overthrown by theconceptually simpler Copernican heliocentric model. Students are often surprised to learn that aesthetics(simplicity, elegance, etc.) are one metric by which a scientific theory is measured. Although the early Copernicanheliocentric model made no significant improvements with regard to predictive power, the scientific communityat that time eventually accepted it—albeit after some resistance and skepticism. However, since accuracy ofpredictions is indeed a feature of scientific theories, even the Copernican model had to be modified, asobservations revealed more subtle details including the shapes of planetary orbits, which were discovered byKepler to be ellipses rather than perfect circles. The process of refinement continued when Isaac Newton revealedthat the Earth does not technically orbit the Sun, but the Sun and Earth both orbit around a common focus.Section 2.3Retrograde motion is never obvious to students, and can be hard for them to visualize. Go over Figure 2.9carefully with students. Emphasize that the foreground of the figure is what’s really happening, and thebackground is what we see from Earth. Ask the students what the faster-moving Earth is doing to Mars at points5, 6, and 7. Hopefully they will respond that Earth is “lapping” Mars, just as the faster driver in an automobilerace does. Then ask the students what a slower car appears to be doing as they are passing it on the highway.Hopefully they will see how the “backward” motion of Mars is explained by Copernicus’s model.DEMO—First, explain to students that the larger the orbit, the slower the planet moves. Draw some stars acrossthe entire board. Ask a student volunteer to play the role of an outer planet. Have the student walk slowly fromright to left (from the perspective of the class). You play the role of the observer on Earth. Without moving, notethat the outer planet appears to move from west (right) to east (left). However, if you now walk parallel to thestudent (letting the student start first) and you move at a faster pace, you will appear to overtake and pass thestudent. This will be obvious. Now, try it again, but stop both your motions before you pass the student and notethe position of the student relative to the background stars on the board several times while passing. If the studentwalks slowly enough and you walk fast enough, you should get a good retrograde effect. (Try this out first beforegoing into the classroom to find an effective pace to use.)Expand on this idea by showing the roughly circular orbits of the planets and explain how retrograde motion onlyoccurs while Earth is“passing” the outer planet. This will always occur when the outer planet is near opposition.Ask students which planets would have retrograde motion if they were standing on Mercury or Venus. Wouldother objects appear in retrograde motion or only outer planets? Emphasize that the effect is not unique to viewingfrom Earth, nor does it only occur in planets.Section 2.4Before discussing Galileo’s observations with the telescope,give a little background on the prevailing worldviewof the time, to helpstudents understand just how dramatic Galileo’s discoveries were. The Aristotelian viewmaintained that all astronomical objects were made of a perfect and unchanging substance unknown to Earth, andthat these celestial bodies orbited Earth in perfect circles. Earth was flawed and chaotic, but heavenly objects wereperfect, unblemished, and unchanging. Furthermore, Aristotle’s view had been inextricably linked with

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science5Christianity through “medieval scholasticism,” so contradicting Aristotle was extremely serious since it wasequivalent to contradicting the Roman Catholic Church. Galileo’s discoveries gave evidence that objects not onlyorbited something other than Earth (e.g., Jupiter’s moons, phases of Venus) but also that heavenly bodies wereblemished (e.g., sunspots, mountains on the Moon). Galileo’s experiments with falling bodies also directlycontradicted the Aristotelian view that heavier objects fall faster than do lighter ones.You may want to mention that Galileo did not actually invent the telescope, nor was he actually the first to use itto observe the heavens. A Dutch optician named Hans Lippershy first got the idea to look through two lenses atonce, allegedly from his children. An Englishman named Thomas Harriot mapped out the surface of the Moonwith a telescope a few months before Galileo built one in 1609. It is still amazing that Galileo was able to buildhis own telescope purely from a physical description, and that he made such meticulous observations that literallyrevolutionized the discipline of astronomy and helped make it a science.If Jupiter is visible at night when you are teaching the course, encourage your students to view Jupiter throughbinoculars from a reasonably dark site. The four Galilean moons are visible through binoculars, and students canfollow their motions over a week or so to recreate Galileo’s observations.Anyone wishing to experience the sky as Galileo did may wish to purchase a “Galileoscope” (atwww.galileoscope.org) or similar small telescope kit. Even a moderately priced pair of binoculars have optics asgood as, or superior to, Galileo’s.However, the man himself had one huge advantage that we cannot match, sadly:four centuries ago the world had incredibly dark skies, even in urban areas!Section 2.5It will probably surprise students that Galileo and Kepler were contemporaries. In terms of conceptualdevelopment, it seems that Galileo built on and provided evidence for Copernicus’s heliocentric model, and thenKepler refined the heliocentric theory with details about the orbits of the planets. In fact, Galileo and Kepler wereworking at the same time, and exchanged some correspondence. Galileo was placed under house arrest forpromoting the heliocentric model and was forced to declare that it was useful as a mathematical tool only, not as adescription of reality. Meanwhile, Kepler was not only assuming that the planets orbit the Sun, but he wasdescribing their actual paths and speeds in those orbits. Why were the results of these two men so differentlyreceived? Point out to students the differences in their societies and situations that resulted in these very differentclimates for scientific research and discussion. Kepler was essentially an agent of the Holy Roman Empire at thetime he published his work, while Galileo was mostly supported by private patrons like the Medici family. Inaddition, note that there was a radical difference in personalities: Galileo was an opinionated and evenantagonistic person who frequently alienated the people he was trying to educate; Kepler had humility thatbordered on low self-esteem. This difference in personality ultimately brought a lot of grief to Galileo, whileKepler’s more deferential, “here-are-the-facts” approachmay have led to quicker acceptance of his conclusions.Throughout your discussion of the historical development and final acceptance of the Copernican system, sprinklein interesting details of the lives of the people involved.Copernicus’s theory wasnot even published until he lay on his deathbed because he fearedridicule. It might never have been published without the efforts of his friend, Georg Rheticus.Brahe wore prosthetic metal noses after he had his nose cut off in a duel, and represented himselfas an astrologer to get funding for his research.Galileo was a flamboyant character who loved to engage in debate, sometimes too much.Galileo published in Italian, as opposed to Latin, and often expressed his ideas in dialogue formto make them accessible to both the scholar and the“common man.”

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science6Galileo was friends with Pope Urban VIII and the Pope offered to fund the publication of one ofGalileo’s books. But when Galileo wrote the book, he put some of the Pope’s words in the mouthof a buffoonish character, and made his friend look very bad.Kepler rose up from a life of abject poverty to become an accomplished musician andmathematician.Kepler tried for almost a decade to make the data that he inherited from Brahe fit traditionalideas; it was when he decided to listen only to the data that he made progress. In some ways,Kepler can be seen as the first person to fully employ the “Scientific Method.”Begin your discussion of Kepler’s laws of planetary motion by drawing an ellipse on the board or overhead, usingthe method shown in Figure 2.15 if possible. Define the various parameters of an ellipse: perihelion, aphelion,semi-major axis, and eccentricity. Show how a circle is the special case of an ellipse with an eccentricity of 0.Have students draw ellipses with the same eccentricities as the planets and point out that most of the planetaryorbits are nearly circular (see Table 2.1 for data). Extend Kepler’s second law to comets, and ask students todescribe the relative speeds of a comet with a very elliptical orbit when it is close to the Sun and when it is faraway. Finally, for Kepler’s third law, pick one or two planets and use the semi-major axes given in Table 2.1 tocalculate the periods. Compare to the periods given in the table.Review the mathematical meaning of “squaring”and “cubing.” Many students will confuse a3with 3a. The students who are more mathematically aware are oftenconcerned that the units of the third law do not work out correctly. Reassure them that the equation is tailor-madefor specific units, and that there are constant terms with a value of 1 that can cancel the units.Finally, point out that one of the weaknesses of Kepler’s laws is that they are empirical; that is, they have plentyof “proof” or evidence,but no physical explanation. The nature of the motion was clear to Kepler, but the causewas mysterious. The explanations would have to wait for Isaac Newton.Section 2.6Students will find it helpful if you review something as basic as similar triangles here. Draw two triangles withone perhaps two times larger than the other but with the same angles. Show that if you know the angles and thelength of one of the sides, then you can easily calculate the lengths of the remaining sides. The ratio of lengths forthe known side of the similar triangles will be the same as the ratios of the sides where the length is to bedetermined.Section 2.7Newton’s laws of motion are extremely important and not necessarily intuitive. Give plenty of examples of each.For instance, ask students to imagine an airplane trip on a beautiful day with no turbulence. If you throw a peanutup in the air, does it hit the person behind you or fall back in your lap? In addition, consider the motion of Earth.If you jump up in the air, does the wall of the classroom slam into you? (Galileo already had a pretty good idea ofthe notion of inertia when he argued against the geocentric view and used ships at sea as an example.) Emphasizeto students that as far asNewton’s lawsare concerned, an object moving at a constant velocity (i.e., in a straightline and at a constant speed) is pretty much the same as an object at rest: both have no net force acting on them,and thus neither is accelerating, or changing velocity.Define acceleration carefully and calculate an acceleration that students can relate to, such as the acceleration of acar merging on the highway. You can use more familiar units at first, such as miles per hour per second, and thenconvert to the more standard meters per second squared to help students gain a feel for the acceleration due toEarth’s gravity. Students often confuse acceleration and velocity, so be sure to distinguish carefully between thetwo.

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science7DEMO—You can demonstrate Newton’s second law and the role ofmass by attaching a rope to a rolling chairand asking a student to pull it across the floor. Then sit in the chair and repeat. Ask the student to compare(qualitatively) the force used to accelerate the empty chair with the force applied to the chair with an occupant.DEMO—Use an air track with carts or an air hockey table with pucks to demonstrate Newton’s laws, if possible.Seeing the behavior of objects in a nearly frictionless environment can help students overcome Aristotelianmisconceptions about motion.Newton’s law of gravitation is explained at theend of this section. Emphasize that gravity is always attractive and(unlike forces such as the electromagnetic force) is felt by every object in the Universe. Also, note that it is properto speak of the gravitational forcebetween twoobjects, not the gravitational forceofan object. To examine thesignificance of the various terms, ask students what would happen to the force of gravity between Earth and theSun if the mass of Earth doubled or if the distance between them doubled. Note that while we may understand thedependence of gravity on mass—more “pullers” means more pull—the dependence on the square of the distanceremains mysterious.To help drive home the factors that influence the gravitational force, I present the students with the followingfanciful thought experiment. Imagine that malevolent aliens come to Earth and demand that we capitulate, or elsethey will turn their “shrink ray” on the Sun and reduce its radius to 1 kilometer. Thatis enough to turn the Suninto a black hole! Three things could then happen: the Earth could get sucked into the black hole Sun, Earth couldgo flying off into the void of space, or the Earth could stay in its orbit. Have students briefly weigh the optionswith a neighbor, then take a poll to see which outcome is most likely, according to the class. Students willprobably be surprised that the gravitational force will not change, since none of the important factors—the massesof the Sun and Earth and the distance between their centers—have changed. Black holes are not “cosmic vacuumcleaners” as popular fiction depicts them.You can recall this example later in the semester during your discussionon black holes.Section 2.8This section serves a summative purpose by using Newton’s laws to provide a theoretical foundation forunderstanding the discoveries of Galileo and Kepler. For example, students often confuse the force of gravity withacceleration due to gravity. Derive the expression for acceleration due to gravity and show that it is consistentwith Galileo’s experiments regarding the motion of falling bodies. In addition, emphasize that Earth alone doesnot “have” gravity—gravity is a force between two objects. For instance, the weight of an object is the forcebetween it and Earth. Use the gravitational formula to compare the weight of a 70-kg person on Earth and theweight of that same person on the Moon.Use Figure 2.23 to help explain to students how gravity is responsible for objects falling and orbiting. Ask yourstudents to picture the Moon as constantly falling towards the Earth, but missing because it has velocity!Alternatively, students could picture the situation as the Moon wanting to head off into space in a straight line, butbeing prevented from doing so by the “leash” of gravity.DEMO—To demonstrate orbital motion, whirl a ball around on a string in a horizontal circle. In thedemonstration, the tension in the string provides the centripetal force. In the case of a planet, gravity is thecentripetal force. Ask students to predict what would happen if the force suddenly “turned off,” and thendemonstrate by letting go of the string. This is also a good time to discuss the fact that an object in a circular orbitis constantly accelerating. Although moving at a constant speed, the object is always changing its direction.Reiterate that the speed may remain constant, but the direction change means a change in velocity nonetheless.Any change in velocity means that the acceleration is not zero.

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science8DEMO—Point out to the students that Newton’s third law states that you are pulling on the Earth just asstrongly as it is pulling on you. Then, tell students to brace themselves as you jump in the air, perhaps off a step orlow platform. Ask the students why they did not jerk upwards to meet you, while you certainly fell down to meetthe Earth. This can lead to deeper understanding of Newton’s second law, and the distinction between cause(force) and effect (acceleration). Follow this up with a discussion of the orbits in Figure 2.25. To betterunderstand the orbits of objects with different masses, ask the students to imagine a parent whirling a childaround. The child makes a big circle, while the parent moves in a much smaller circle. This will be importantwhen discussing the discovery of new “exoplanets” later on.DEMO—Ask your students whether it is possible to throw an object into orbit around the Earth. If they haveread the text before coming to lecture they will probably answer “no.” (Orbital velocity is about 18,000 mpharound the Earth.) Next, bet them that you can actually throw an object into orbit and will even demonstrate it inclass (brag a little about your fast pitch!). After they express their doubts, throw an object up and across the roomso they can easily see the curve of the projectile path. Tell them that the object was in orbit but ran into the Earth!Objects orbit around the center of mass; for all practical purposes, this is the center of the Earth in this case. Drawon the chalkboard what the orbit would have been if the object had not run into the Earth, or use Figure 2.26. Bythrowing the object harder, it goes further. If thrown fast enough (orbital velocity) it will curve (fall) around theEarth at the same rate the Earth’s surface curves.Relevant Lecture-TutorialsKepler’s Second Law, p. 21Kepler’s Third Law, p. 25Newton’s Laws and Gravity, p.29Observing Retrograde Motion, p. 99Student Writing Questions1.Look up one of the historical figures mentioned in this chapter. Find out as much as you can about his orher life and the period of time in which he or she lived. Describe whatthe scientist’sdaily life must havebeen like. In what ways was astronomy a part ofthe person’slife?2.Describe what it would be like to live without any gravity. What would be easier? Harder? Impossible?Fun? Annoying? Do you think you would like to live like this for an extended period?3.Kepler had to fight a legal battle to get access to Tycho Brahe’s observations. What if Kepler hadbeenprevented from gaining that access? Speculate how this might have affected Newton’s work on gravity.Would he still have been successful in formulating his law of gravity? Would he even have worked onthis problem? Do you think someone else would have worked on it if Newton had not? Would such asmall change in historical events that occurred 400 years ago affect science today?Chapter Review AnswersREVIEW AND DISCUSSION1.Astronomers in the Islamic world preserved the writings and discoveries of the ancient Greeks through theDark Ages in Europe. They translated the works of ancient astronomers such as Ptolemy and expanded onthem; many of the proper names of bright stars are Arabic or Persian in origin. They developed manymethods in mathematics, including algebra and trigonometry. Chinese astronomers kept careful records of

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science9eclipses, comets, and “new” stars, extending back many centuries. They also were likely the first to seesunspots, many years before Galileo.2.The geocentric model of Aristotle had the Sun, Moon, planets, and stars orbiting a stationary Earth. Amodification by Ptolemy had most of the planets moving in small circles called epicycles. The center ofthese epicycles moved around the Earth in larger circles called deferents. Over the centuries, however, otherastronomers further altered the model, and dozens of circles were needed to fully describe the motions ofthe 7 visible “planets,” which included the Moon and the Sun.Scholars clung to this model for reasons thathad nothing to do with religion or needing a “special place in the Universe.” They had two very rationalreasons for thinking the Earth was stationary at the center. First, there was no sensation of motion, no“wind” as the Earth moved through space. Second, there wasno observed change in position of the stars(parallax) as the Earth moved around the Sun. This change in position occurs, but it was not measurableuntil the mid-1800s.3.The most obvious flaw in the Ptolemaic model is in its basic premise, since the Earth is not at the center ofthe solar system, let alone the entire universe. The unquestioned acceptance of perfectly circular orbits isanother problem. However, a deeper flaw is that the Ptolemaic model did not attempt to explain why themotions are the way the model depicts them. The model maydescribethe motions, but it does notexplainthem. Today we would require any such explanation to be based on fundamental physical laws.4.Copernicus revived the idea that a Sun-centered (heliocentric) model could explain the complex motions ofthe bodies of the solar system in a simpler way than a geocentric model. However, it was still flawed in thatCopernicus clung uncritically to the idea that the orbits of the planets around the Sun had to be “perfectcircles.”5.A theory is a framework of ideas and assumptions that represents our best possible explanation for thingsthat happen in the real world, backed up by hard data. A good theory can be used to make predictions aboutfuture events, in addition to explaining things we already know. Theories are always subject to challenge,and thus can never be proven to be true. They can, however, be proven to be false, meaning they no longerexplain the phenomenon adequately. It is notable that theories are refuted by data, not by other theories. Aslong as a theory survives any attempts at disproving it, it will likely continue to be accepted.6.Galileo discovered that the planet Venus exhibits phases that would be impossible in Ptolemy’s geocentricmodel. In addition, the phases of Venus also changed size, indicating that Venus was closer to Earth when a“crescent,” and farther away when close to “full.” This could be most simply explained by saying that Earthand Venus were both orbiting the Sun, with Venus’ orbit entirely inside the Earth’s. In addition, the moonsof Jupiter demonstrated that objects could move around a body other than the Earth, that there was morethan one “center” of motion.7.Through years of meticulous observations of the motions of the planets among the stars, Tycho Braheprovided the huge amount of data that was later analyzed by Kepler to produce the laws of planetarymotion.8.First law: The orbits of the planets, including the Earth, are in the shape of an ellipse with the Sun at onefocus.Second law: A line connecting the Sun and a planet sweeps out equal areas in equal intervals of time; thus,a planet’s orbital speed is greatest when it is closest to the Sun.Third law: The square of a planet’s orbital period (in years) is proportional to the cubeof the semi-majoraxis of its orbit (in astronomical units).

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science109.The astronomical unit, defined as the average distance between the Earth and the Sun, was used to providean estimate of the distances between the planets long before its actual numerical value was known. Byreflecting radar waves off the planet Venus and timing how long it takes them to return, we can determinethe distance from Venus to Earth in kilometers. Comparing this to the distance from Venus to Earth in AU,the size of the AU in kilometers could be determined, and with it, the distance between the Earth and theSun.10.While Kepler’s laws do an excellent job of describing how the solar system is structured, they do notexplain why the planets move as they do. They are justified purely by observational data with noexplanation of basic causes. Explanations would have to wait for Newton’s laws.11.First law of motion: Every object continues in a state of rest or in a state of uniform motion (constantmotion in a straight line) unless it is compelled to change that state of motion by an unbalanced force actingon it.Second law of motion: When an unbalanced force (F) acts on a body of mass (m), the body experiences anacceleration (a) equal to the force divided by the mass. Thus,a=F/m, orF=ma.Third law of motion: To every action there is reaction equal in size and opposite in direction to the originalaction.Law of gravity: Every particle of matter in the Universe attracts every other particle with a force that isdirectly proportional to the product of the masses of the particles and inversely proportional to the square ofthe distance between their centers.12.Newton explained Kepler’s First Law by saying that a planet and the Sun have an attraction for each other.They do not crash into each other because they have been moving from the beginning. You can say that theEarth is indeed “falling” toward the Sun, but keeps missing the Sun due to its motion. Alternatively, youcan say that the Earth wants to go flying off in a straight line(Newton’s First Law) but its motion ischanged by the unbalanced force of the Sun’s gravity (Newton’s Second Law). Kepler’s Second Law can beexplained as follows: as a planet approaches the Sun from aphelion to perihelion, it is moving in thedirection of the force of gravity (toward the Sun) and thus it speeds up. From perihelion to aphelion, theplanet is moving away from the Sun, in the opposite direction of the gravitational force, and the planetslows down. Kepler’s Third Law is a relationship betweenthe average distance of a planet from the Sun,and the amount of time for the planet to orbit the Sun. Distance from the Sun is an important factordetermining the strength of the gravitational force between a planet and the Sun, which in turn controlsorbital speed.13.Earth does move in response to the baseball, but its motion is too small to be noticed, or even measured.The Earth and the baseball pull on each other with equal gravitational force, but because of its greater mass,Earth is harder to accelerate. Thus, by Newton’s second law, the acceleration of the baseball toward Earth ismuch greater than the acceleration of Earth toward the baseball.14.The Moon is “falling” toward Earth because of the attractive force of gravity between the two bodies.However, because the Moon has a sufficiently large velocity tangential to that gravitational pull, the twobodies will never collide. The Moon keeps “missing” Earth.By measuring the speed the Moon is travelingto maintain its orbit, we can calculate the strength of the gravitational pull between the Moon and Earth, andthen find the Earth’s mass.15.The escape speed is the speed you must be traveling to get far away enough from a planet or other largeobject so that its gravitational influence on you becomes too small to matter. As you rise higher above the

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science11surface of the body, its gravitational pull gets weaker. If you are traveling at the escape speed when youleave the surface, gravity cannot reduce the speed quickly enough to stop you. Therefore, you will not fallback down to the object.CONCEPTUAL SELF-TEST1.A2.D3.B4.C5.C6.A7.C8.B9.C10. APROBLEMS1.We use the equation for angular size here, with the angular size set to 1/60 of a degree.actual diameter0.016757.3distance distanceactual diameter0.016757.3(a) For the Moon, distance = 384,000 km, so diameter = 110 km.(b) For the Sun, distance = 150,000,000 km, so diameter = 44,000 km.(c) Saturn is 9.5 AU from the Sun, and so is 8.5 AU at its closest distance to Earth. This gives a diameter of370,000 km. Since that is bigger than Saturn itself is, Saturn just looks like a point to the unaided eye.2.We can use Kepler’s third law to calculate the semi-major axis from the period. 762=a3, soa= 17.9 AU.We double this to get the length of the major axis (35.9 AU) and then subtract the perihelion distance to getthe aphelion distance of 35.3 AU, beyond the orbits of all the major planets.3.The satellite’s perihelion distance will be 0.72 AU and the aphelion distance will be 1 AU. The semi-majoraxis will be the average of these two values, or 0.86 AU. Using Kepler’s thirdlaw,P2=a3= (0.86)3, we getan orbital period for this satellite of 0.798 years, or 291 days. The satellite will travel from aphelion (Earth)to perihelion (Venus) in half this time, or 146 days.4.Since 1 AU is about 150 million kilometers, 0.7 AU is 105 million kilometers. The round trip of the radarsignal would be 1.4 AU = 210,000,000 km, traveling at the speed of light. Therefore, the travel time is:210,000,000kmtime700 seconds = 11.7 minutes300,000 km/s

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science125.During a transit, Mercury is between Earth and the Sun. The aphelion distance of Mercury from the Sun is0.47 AU, and the perihelion distance of Earth is 0.98 AU. Thus, during transit, the closest Mercury can beto Earth is 0.51 AU, or 76,500,000 km. Using the equation for parallax in Chapter 1 yields:baseline3000 kmparallax = 57.357.30.0022distance76,500,000 kmThis is about 8.1 arc seconds6.The formula for the acceleration due to gravity is2GMar. The mass of Earth is 5.97 × 1024kg, so theonly thing that varies isr,the distance of the object from the Earth’s center.(a)r= 6,500,000 m, soa= 9.43 m/s2.(b)r= 7,400,000 m, soa= 7.28 m/s2.(c)r= 16,400,000 m, soa= 1.48 m/s27.The speed of the spacecraft in a circular orbit is given byGMvr= 1700 m/s, or 1.7 km/s for the MoonAs stated in the text, the escape velocity is the square root of two (1.41) times this, or 2.4 km/s.8.Assuming a mass of 55 kg for the person, a mass for Earth of 5.97 × 1024kg, and a radius for Earth of6,400,000 m, the law of gravity givesF= 535 N, or 120 pounds. This force is simply your weight.Suggested ReadingsWeb Resourceshttp://www.jpl.nasa.gov/video/index.cfm?id=888NASAvideo on the discovery of Jupiter’s moons.The site alsooffers current information about making observations of Jupiter’s moons.https://solarsystem.nasa.gov/basics/index.php.A series of videos from NASA that can help students betterunderstand the force of gravity and orbits.http://www.wam.umd.edu/~tlaloc/archastro. The Center for Archaeoastronomy.The “Crash Course” channel onYouTube has a series about astronomy:https://www.youtube.com/playlist?list=PL8dPuuaLjXtPAJr1ysd5yGIyiSFuh0mILVideo # 7 is especially relevant to this chapterYoucan purchase a modern replica of Galileo’s telescope athttp://galileoscope.org/.BooksA number of excellent books are available about the history of astronomy. Here is a sampling:

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science13Aveni, A.,Sky Watchers of Ancient Mexico. Austin: University of Texas Press, 1980. A discussion of astronomyin ancient Mesoamerica.Aveni, A.Between the Lines.Austin: University of Texas Press, 2000. Although the Andean Nazca Lines aregenerally regarded as having no astronomical significance, they are still an interesting study in moderninterpretations of ancient monuments.Gribbin, J.The Scientists.New York: Random House, 2002. A 500-year-plus tour of the history of science,featuring many prominent astronomers, to whet the appetite for deeper study.Hadingham, E.Early Man and the Cosmos.Norman: University of Oklahoma Press, 1985. An interesting treatiseabout ancient astronomy in Britain, Mexico, and southwest America.Hawking, S., ed.On the Shoulders of Giants: The Great Works of Physics and Astronomy.Philadelphia: RunningPress, 2002. This immense omnibus features the seminal works of Copernicus, Galileo, Kepler, Newton, andEinstein, with commentary by Dr. Hawking.Johnson, A.Solving Stonehenge.London: Thames and Hudson, Ltd., 2008. A recent attempt to reconstruct thevarious stages of the construction of Stonehenge, and gain insight as to the site’s intended purpose.Koestler, A.The Sleepwalkers: A History of Man’s Changing Vision of the Universe.New York: Penguin Books,1990. More information than you will ever need about Copernicus, Brahe, Kepler, Galileo, and Newton. Anexhaustive work.Kolb, R.Blind Watchers of the Sky.Reading, MA: Addison Wesley, 1999. A lively historical narrative. The firstchapter deals with Renaissance astronomy. The title comes from a remark Tycho Brahe made about his detractors.North, J.Stonehenge: A New Interpretation of Prehistoric Man and the Cosmos.New York: The Free Press,1996. Further investigation of the ancient megalithic site and its environs.Panek, R.Seeing and Believing: How the Telescope Opened Our Eyes and Minds to the Heavens.New York:Penguin Books, 1999. A brief book, but packed with information about a number of astronomers, includingGalileo and Kepler.Walker, C., ed.Astronomy before the Telescope.New York: St. Martin’s Press, 1997. A series of essays onastronomy from ancient times to the early Renaissance.Magazine ArticlesBerman, B. “The Outsider.”Astronomy(October 2003). p. 48. Illuminating article about a modern astronomer.Helpful when discussing the scientific method with students and a good reminder that science is a humanendeavor/activity. Relevant to this chapter and to Chapter 1.Falk, D. “Therise and fall of Tycho Brahe.”Astronomy(December 2003). p. 52. A nice overview of TychoBrahe, his observatories, and details of his eccentric life.Falk, D. “Did ancient astronomers build Stonehenge?”Astronomy(July 2009). Proposes that the astronomicaluses of Stonehenge were not its primary function.

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Astronomy Today, 9th Edition Instructor GuideChapter 2: The Copernican RevolutionThe Birth of Modern Science14Falk, D. “Who was Thomas Harriot?”Astronomy(April 2010). The career of one of the early users of thetelescope.Gettrust, E. “Anextraordinary demonstration of Newton’s Third Law.”The Physics Teacher(October 2001). p.392. A description of an apparatus using magnets and force probes to demonstrate that the action and reactionforces are equal in magnitude.Gingerich, O. “The great Martian catastrophe and how Kepler fixed it.”Physics Today64:9 (2011). p. 50. HowKepler dealt with the problems resulting from Mars’ eccentric orbit.Harwit, M. “Thegrowth of astrophysical understanding.”Physics Today(November 2003). p. 38. A historicalreview of almost 3000 years of inquiry about the universe.Hudon, D. “How Johannes Kepler revolutionized astronomy.”Astronomy(January 2009). A summary of theGerman astronomer’s outstanding body of work.Kemp, Martin. “Kepler’scosmos.”Nature(May 14, 1998). p.123. Describes ancient cultures’ image of thecosmos.Kemp, M. “Maculatemoons: Galileo and the lunar mountains.”Nature(Sept. 9, 1999). p. 116. DiscussesGalileo’s observations of features on the Moon.Krupp, E. C. “Designatedauthority.”Sky & Telescope(May 1997). p.66. Discusses the role of the “official”astronomer in ancient cultures.Krupp, E. C. “Fromhere to eternity: Egyptian astronomy and monuments.”Sky & Telescope(February 2000). p.87. Discusses the depiction of the stars and sky in ancient Egyptian monuments.Krupp, E. C. “Stairway to thestars: The Jantar Mantar, or ‘House of Instruments,’ in Jaipur, India.”Sky &Telescope(September 1995). p. 56. Describes an 18thcentury Indian monument that was used to track themotions of the Sun.Nadis, S. “Bigscience.”Astronomy(May 2003). p. 46. Explores the trend toward fewer, but larger researchprojects and the hope for a trend reversal. This is a good contrast when discussing the projects that occupiedBrahe/Kepler and Galileo.Panek, R. “Venusiantestimony.”Natural History(June 1999). p.68. Discusses Galileo’s observations of thephases of Venus.Quinn, J. “Stargazing with Galileo.”Night Sky(May/June 2006). p.44. A guide to reproducing Galileo’sobservations with a backyard telescope.Ruiz, M. “Kepler’s Third Law without acalculator.”The Physics Teacher(December 2004). p. 530. Describes asimple activity for introducing students to Kepler’s third law.Schilling, G.“Gravitational waves hit prime time.”Sky & Telescope(December 2015). p. 26. Recent potentialdetections of gravitational waves may change the way we view gravity.Sherwood, S. “Science controversies past and present.”Physics Today64:10 (2011). p. 39. A comparisonbetween the heliocentric controversy and the modern controversy of global warming.

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