Solution Manual for Astronomy: A Beginner's Guide to the Universe, 8th Edition

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Chapter 0: Charting the HeavensThe Foundations of AstronomyOutline0.1The“Obvious”View0.2Earth’sOrbital Motion0.3The Motion of the Moon0.4The Measurement of Distance0.5Science and the Scientific MethodSummaryThis chapter covers the view from Earth, including constellations, the celestial sphere, and the apparentmotions of the Sun and stars. The actual motions of Earth that give rise to those apparent motions are thendiscussed. The motion and appearance of the Moon are addressed in the third section. This chapterconcludes with distance determinations and a discussion of the scientific method.Major ConceptsThe view from EarthConstellationsThe celestial sphereEarth’sorbital motionRotationRevolutionAngular measurementPrecessionMotion of the MoonLunar phasesEclipsesMeasuring distanceTriangulationParallaxScientific theory and the scientific methodObservationTheoryPredictionTeaching Suggestions and DemonstrationsOne of the challenges in studying astronomy is developing the ability to view the universe from differentperspectives, primarily the perspective we have from Earth, where we see the Sun and stars rise in the eastand set in the west, and the perspective from outside, where we see Earth spinning on its axis and orbitingthe Sun. Use plenty of models and diagrams in teaching this introductory material in order to help yourstudents practice shifting viewpoints. Lots of new vocabulary is introduced in this chapter; take the timeto define new terms.

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Chapter 0: Charting the Heavens9There has been an emphasis among the astronomy educational research community that teachingapproaches in college astronomy classes should be more learner-centered. An easy way to start toincorporate this approach is the bookLecture-Tutorials for Introductory Astronomy3/E by Prather, Slater,Adams, and Brissenden. This book contains many in-class exercises that students may work on in smallgroups. There are exercises on positionalastronomy,solar vs. sidereal day,seasonal stars, theecliptic,andphases of the Moonas well as additional topics that will be mentioned throughout this book. It takesa lot of consideration to decide how to use such materials, but research shows that it will benefit moststudents for the classroom to be more learner-centered.Section 0.1Your students will all have heard ofconstellationsand will probably be able to name at least a few.Emphasize that the stars in a given constellation are probably not physically close to each other inspace; they just appear close to each other as seen from Earth. The stars in each constellation weregrouped together by observers in ancient times, and we continue to use nearly the same groupingstoday. You can pass out or project a sky chart without constellations drawn in and challenge students tomake up their own.Asking students what their zodiacal sign is can be a good way for the students to feel connected to thesky, even though very few might actually follow astrology. Consider usingStarry Night Collegetodemonstrate how the zodiacal constellations lie across or near the ecliptic line. Show how the sky viewwill change during the year. Be sure to let students know that their zodiacal constellation is associatedwith where the Sun was located when they were born, but it is about a month off due to precession of theequinoxes. This is illustrated in Figure 0.8.Itisalsointerestingtocomparenamesofnorthernandsouthernconstellations.Thenorthernconstellations are typically named for animals and mythological characters. The Southern Hemispheresky includes constellations such as the telescope, the microscope, and the octant. Ask your students ifthey can explain the difference. Theconstellation nameswe have inherited today derive from northernobservers. The northern constellation names, therefore, date from ancient times, but the southern onesdate from the early travels made by northern explorers to the Southern Hemisphere.If you have time, explain a few of themythsthat involve whole families of constellations. The story ofOrion, Taurus, and the Pleiades is a good one, as is the story of Cassiopeia, Cepheus, Andromeda, Cetus,and Perseus. These are all constellations that students can find in the night sky, depending on the time ofyear you are teaching the course. Provide star charts and encourage your students to find majorconstellations in the night sky throughout the course.The concept of thecelestial sphereis an important one. We are missingdepth perceptionwhen we lookout at the night sky. If you have one, bring in a transparent model of the celestial sphere with Earth insideand point out thenorth and south celestial polesandthe celestial equator. This is a good time todiscuss Polaris and clear up any misconceptions; often, introductory astronomy students believe the NorthStar must be the brightest star in the sky.Introduce students toright ascensionanddeclinationby comparing these to latitude and longitude.Emphasize that the celestial coordinates are attached to the sky. Over the course of a night, stars movefrom 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. Ask students to compare thetwo different methods of describing star locations, by coordinates and by constellation, and discuss theadvantages of each.

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10Chaisson/McMillan,Astronomy, Eighth EditionSection 0.2Students usually know the termsrotationandrevolutionbut often confuse them, so take a few momentsto define these terms. Considerusing the word “orbit” instead of “revolution”to help avoid confusion.Students will also probably know that Earth takes a day to turn on its axis and a year to orbit the Sun, butwill not know the difference between asolar dayand asidereal day, or atropical yearand asiderealyear. Use lots of diagrams, such as Figure 0.7, to help explain. Models also help. Demonstrate rotationand revolution with globes, or bring students to the front of the class to modelEarth’smotions. Forinstance, one student can spin around (slowly) while also orbiting another. Ask the class to concentrate onone point on the Earth, say, the spinningstudent’snose, and imagine when it is lit and when it is dark.Use this model to explain day and night, sidereal vs. solar days, and why different constellations arevisible in the night sky during different months.Figure 0.9 is also an important one. Make sure students understand that it shows theapparentpath of theSunon the celestial sphere. Use models of Earth and the Sun (or just two spheres) to help explain howEarth’stilt changes the position of the Sun in the sky as Earth orbits the Sun. Emphasize that the termssolsticeandequinoxcan each refer to both a point in timeanda point in space. The summer solstice, forinstance, is the point on the ecliptic where the Sun is at its northernmost position, but we also use the termto refer to the time and day when the Sun is at that point. Students will be most familiar with the lattermeaning, and know that the summer solstice occurs around June 21.Begin your discussion ofseasonswith an informal, multiple-choice pre-quiz.If you’dlike to make thispre-assessment a bit more formal, author Paul Green discusses more ideas in his bookPeer Instructionfor Astronomystarting on page 11. He also includes“concept tests”for theseasonsas well as thecelestial sphereandtime conventionsused in astronomy that can be used throughout the lecture. Thesecan be used in conjunction with additional“clicker questions”that are provided with the instructormaterials. During your lecture, ask students what causes the seasons, and include in the answer choicesboth the correct response, namely,Earth’stilt, and a common misconception, the distance from Earth tothe Sun. If significant numbers of students choose the distance answer, make sure you address thismisconception and explain why the different distances from Earth to the Sun do not affect the seasons.Many students are surprised to find that, in fact, the Earth isfarthestfrom the Sun during the NorthernHemisphere summer. Bring in a flashlight and shine it directly down on a tabletop or on the floor, andthen shine it at an angle to show how the angle of theSun’srays affects solar heating. Go back to yourmodel of Earth orbiting the Sun to show how the length of time the Sun is up in the sky also changes asthe seasons change.A gyroscope or top makes a good demonstration ofprecession. Find Vega on a star chart and point it outto students to help them get a sense of the scale of the change. Precession is also responsible for the factthat the zodiac constellations no longer correspond to their astrological dates. The heliacal rising of Sirius,in the constellation Canis Major, was an important date in the ancient agricultural calendar, but this nolonger occurs on the same date today.Angular measureis very important to astronomy. DiscussMore Precisely 0–1carefully. Demonstrateangular measure by holding up a penny. At a distance of about 1 meter, a penny subtends an angle ofabout 1 degree. Students can hold up a penny and see what objects at different distances in the classroomhave an angular size of about 1 degree. Also have students try this at night and estimate the angular sizeof the Moon, half a degree. Go over angular measurements and then try several examples. Many problemsthroughout the text use the equations in this section, so it is worth spending some time with them toensure student understanding.

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Chapter 0: Charting the Heavens11Section 0.3Demonstrate theMoon’sphasesby shining a flashlight on a ball. You can also paint one half of aPing-Pong ball black and have students hold it atarm’slength with different amounts of the black sidefacing them. For different positions of the Moon, ask students how much of the surface of the Moon islit, and how much of the lit surface can be seen from Earth. Emphasize that half of the surface isalways receiving light, but we just do not see it all. Before showing Figure 0.13, demonstrate anddiscuss with students when one particular phase, first quarter, say, will rise and set. Then ask them topredict rising and setting times of the other phases. This exercise provides an excellent opportunity forstudents to practice changing viewpoints as discussed in the previous sections. For best results, youshould do this demo in a very dark room. Even with all the lights turned out, there will still be a lot oflight reflected from the walls. It’s best to use a classroom with darkwalls, but this might be a difficulttask. You should always try out a demo in the room whereyou’ll be teaching before you do the demoin front of a class.Consider assigning students a project to track theMoon’sphases. For instance, you can ask them to lookfor the Moon each (clear) night for a month, sketch its shape, and note the time and position in the sky. Atthe end of the month, they can compare this view from Earth with a diagram showing the perspectivefrom outside the Earth.Once your students have a good grasp of phases, they should have no trouble understanding the causes ofeclipses. Some points that you may need to clarify include why we do not have a solar eclipse every newMoon and a lunar eclipse every full Moon, and why a lunar eclipse lasts a while and can be seen fromabout halfEarth’ssurface, but a solar eclipse can be seen only from a narrow band and lasts only a shorttime for any particular observer. A scale model using two spheres (for Earth and the Moon) and a stronglight source (for the Sun) can help clarify points about lunar eclipses. Show pictures of the Sun during asolar eclipse and try to convey some of the excitement and awe inspired by eclipses. In addition to beingspectacular events to watch, solar eclipses provide Earth-bound astronomers a rare opportunity to studytheSun’scorona.Section 0.4Figure 0.21 illustrates an excellent demonstration ofparallaxthat you can have your students try in class.Instruct them to hold up a finger (or pencil), close one eye, and line their finger up with some object onthe far wall of the classroom. When they sight on their finger with theothereye open instead, it lines upat a different position. Ask students to try the exercise several times with their finger at different distancesfrom their eyes to determine the relationship between the distance and the amount of shift. Figure 0.20shows this method applied to astronomy usingEarth’sdiameter as a baseline. Challenge students to comeup with a method where observers restricted to the surface of Earth can create an even longer baseline inorder to measure parallaxes of more distant stars. (Observations can be made at different points inEarth’sorbit around the Sun.) Even with the diameter ofEarth’sorbit as a baseline, the parallax method onlyworks for the stars in the solar neighborhood.Section 0.5Since many of your students are likely to have had minimal exposure to science, this section is worthwhilefocusing on for class discussions. In introducing thescientific method, refer to Figure 0.22 now as well asthroughout the semester. Remind the students that science is a cyclic process rather than some fixed set ofideas or laws. This is aSTRENGTH, not a weakness. Sometimes those that might challenge the validityof science using non–scientific arguments often try to exploit the tentative nature of science. The strength

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12Chaisson/McMillan,Astronomy, Eighth Editionof science rests on the fact that it does not rely on the authority of political or religious systems nor on theinterpretation of texts, ancient or otherwise. Ask the students to provide examples of ideas in their ownminds that have changed once additional data or knowledge had become known to them. In my ownopinion, I think science is a way that we (as humans) can sense the world around us and make predictionsthat can be tested and verified. At the heart of this process is the fact that the universe is inherentlyknowable. When discussing the nature of science, it is easy to fall into the philosophy of science. This canbecome a very exhaustive discussion, so make sure to have certain specific goals in mind so that you canmove on to othertopics when you’ve completed them.Student Writing Questions1.What was the tiniest object you have ever seen? The largest? The longest distance you have evertraveled? What is the largest number of objects you have ever knowingly encountered? (You mayencounter lots of bacteria but not knowingly.) What was the longest you ever spent doing oneactivity? How do the largest and the smallest of these compare? How do the distances compare tothe size of Earth? To the distance to the Moon? How does your time spent in one class compare toyour lifetime?2.Describe in metric units the room in which you do most of your studying. How big is it? What is thesize of your desk? The TV or radio? How heavy are your books? The dimensions of your bed?Choose objects that have a range in sizes.3.Test your horoscope. Each day, write two or three sentences about the most significant events thatoccurred to you that day. Cut out or copy your horoscope for that day and save. Continue this dailyfor about three weeks and make sure you write down your daily events before you read thehoroscope. After three weeks, check what you wrote and your horoscope for each day to see whetherthere is a match. Count the number of hits and misses. Discuss the results and whether there is anysignificance to the number of hits. Are horoscopes truly predictive?4.Find a location to view the night sky with as little interference as possible. Do this on as clear anight 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 yousee on its surface?5.What would it be like to live with only one functional eye? How would this change your perceptionof everything around you? What would pose the greatest difficulty to you? The least? You mightactually try this first and then write about it. Did you get used to not having both eyes? Is parallaxthe only effect you miss with only one eye?6.Describe an ordinary situation in which people regularly apply the scientific method, even thoughthey are not aware they are doing so. Relate the situation to the three basic steps in the scientificmethod: gather data, form theory, and test theory.7.Compare and contrast science as a way of knowing with some other way of knowing, such associal science, art, philosophy, or religion. How do these disciplines differ, and how might they besimilar?

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Chapter 0: Charting the Heavens13Answers to End of Chapter ExercisesReview and Discussion1.The Earth’s diameter is about 110th that of the Sun. The Earth is about 1014times smaller than theMilky Way Galaxy and about 1018times smaller than the Universe.2.A constellation is a pattern of stars that appear together in the sky although they are generally notclose together in space. Many constellations are named after mythological figures or animals. Eachconstellation covers a specific area on the celestial sphere, and stars are designated by theconstellation to which they belong.3.Earth’srotation makes the Sun, the Moon, and the stars appear to rise in the east and set in the west.4.A solar day (measured by the Sun) is about 3.9 minutes longer than a sidereal day (measured by thestars). As Earth rotates on its axis, it also moves forward in its orbit so it has to rotate a little fartherthan one full turn to bring the Sun back to the same position in the sky.5.One orbit of the Sun corresponds to 1 year, so aperson’sage in years equals the number of times heor she has orbited the Sun.6.As Earth revolves around the Sun,Earth’sdark side (away from the Sun) faces a different directionat different times inEarth’sorbit. The stars visible in the winter night sky are behind the Sun in thesummer and therefore not visible.7.Seasons are caused by the tilt ofEarth’saxis with respect to the plane of its orbit. The hemispheretilted toward the Sun has summer, because the Sun appears higher in the sky and therefore the Sun isup longer and its rays are more direct. Both the length of time the Sun is in the sky and the angle ofthe rays contribute to increased heating.8.Precession is the slow shift in the orientation ofEarth’srotation axis. It is caused by the combinedgravitational pulls of the Moon and the Sun.9.Only a portion of the hemisphere of the Moon that is lit by the Sun may be facing Earth. Forinstance, during a full Moon, the entire lit portion faces Earth, but during a new Moon, the entire lithemisphere is facing away from Earth, so we see none of it.10.A lunar eclipse occurs whenEarth’sshadow falls on the Moon. A solar eclipse occurs when theMoon passes directly in front of the Sun, blocking its light so that shadow of the Moon falls onEarth. TheMoon’sorbit is slightly inclined with respect to the ecliptic, so Earth, the Moon, and theSun are not precisely lined up every full and new Moon.11.Since neither Mercury nor Venus has moons, it would have to be Mars or other outer planets.However, the moons of Mars are too small to cover the solar disc as seen from the surface of Mars,as shown in Problem #10 of Chapter 6. Eclipses as seen from the cloud tops of Jupiter is the topicfor Problem #5 in Chapter 8.12.Parallax is the apparent shift in position of a foreground object with respect to the background as theobserver’sposition changes. For example, as you drive down the road, a telephone pole along theroad will line up with different points in the distant landscape.

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14Chaisson/McMillan,Astronomy, Eighth Edition13.When using triangulation, the longer the baseline, the greater the shift in position, or the greater theparallax angle. Objects in space are so far away that their shifts are very small. A long baseline willincrease the chance that the shift will at least be measurable.14.The diameter of an object can be determined if both the distance to the object and its angulardiameter are known.15.The scientific method obtains truths that rely on empirical data obtained in a naturalistic way usingour senses. Religion, on the other hand, relies on truths that are divinely revealed.Conceptual Self-TestTrue or False?1. F; 2. F; 3. T; 4. F; 5. T; 6. T; 7. FMultiple Choice8. b; 9. b; 10. c; 11. a; 12. c; 13. d; 14. b; 15. aProblems1.The year 10,000 A.D. is about 8000 years from now, which is about 0.3 of the total precessionalperiod of 26,000 years. Because there are 12 constellations in the zodiac, this corresponds to about3½ constellations. If the vernal equinox is just now entering Aquarius, then it will be in the latterhalf of Scorpio in 10,000 A.D. (See Figure 0.8.)2.The distance Earth moves in a year is the circumference of its orbit:882πr2π(1.510km)9.4210km.CA day is 1/365 of a year, so the distance Earth moves in a day is869.4210km/3652.5810km.An hour is 1/24 of this, so the distance Earth moves in an hour is652.5810km/241.0810km.Finally, in a second, the Earth moves:51.0810km/360029.9 km.3.The sidereal day would be the same, but the solar day would change in length because the Earth is stillorbiting the Sun at roughly 1 degree per day. Normally the Earth must rotate an extra 1 degree after itreaches an entire sidereal day as shown in Figure 0.7. This means that it takes about 3.9 extra minutesfor the Earth to reach the position for a solar day, so a solar day is 3.9 minutes longer than a siderealday. If the direction of rotation is changed, then it will take ~3.9 minutes less to reach a solar day thanit would a sidereal day. In this case, the solar day will be ~3.9 minutes shorter than the sidereal day,which remains the same. The difference in the solar day would be:3.9 min28min.4.Let’s assume that theMoon is in a circular orbit with an orbital period of 27.3, which is the siderealperiod. We’ll assume that it moves through 360 degrees in these 27.3 days. Convert 27.3 days toseconds: 27.3 days = 2,358,720 seconds. The calculations should be done using ratios:(a)3600.533'/hour2,358,720 sec3600 secXX

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Chapter 0: Charting the Heavens15(b)3600.010.55'33''/ min2,358,720 sec60 secXX(c)3600.000150.01'0.55''/ sec2,358,720 sec1secXX3600.53276sec55min/ 0.52,358,720 secsecTT.5.Calculate the circumference of the lunar orbit, then divide it by the sidereal period (27.3 days)converted to seconds. 27.3 days = 2358720 seconds:3.142384,000 km1.0 km/s2,358,720 sec.6.Sidereal month = 27.32 days27.30.986° = 26.92° (the Moon must travel this extra angle for a synodic month)synodic month386.921.07527.3229.4 days (synodic month)27.32 d360.7.tan 60° =distance100 m(drawing the triangle to scale will result in a similar answer)173 m =d.8.Use the relationship(360 /2π).distbaselineparallax(a)(360 /2π).1000 km57,300 km1dist(b)6(360 /2π).1000 km3.4410km(1/ 60)dist(c)8(360 /2π).1000 km2.0610km.(1 / 3600)dist9.Angle = 360°780 km100,000 km= 2.8°.10.UsingDiscovery 0–1,if the Earth was flat, the angle with respect to the shaft of the well wouldalways be zero, as long as the Sun is far enough way so that the Sun’s rays are parallel when theyreach the Earth. InDiscovery 0-1,the angle is caused by the roundness of the Earth.

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16Chaisson/McMillan,Astronomy, Eighth EditionResource InformationMastering Astronomy Media ResourcesSelf-Guided Tutorials for StudentsPhases of the MoonStellar ParallaxAnimations/VideosSummer SolsticeWinter SolsticeThe EquinoxesSolar Eclipse in IndianaInteractive FiguresFigure 0.2 Constellation OrionFigure 0.4 The Celestial SphereFigure 0.5 The Northern SkyFigure 0.8 The ZodiacFigure 0.10 SeasonsFigure 0.12 PrecessionFigure 0.14 Lunar EclipseFigure 0.16 Solar Eclipse TypesFigure 0.20 ParallaxMaterialsSome basic materials helpful for demonstrations in this chapter include a globe (showing the tilt ofEarth’saxis), a strong flashlight, a gyroscope, and at least two different-size balls. (Styrofoam balls workwell; you can use toothpicks stuck in the poles to show the axes.)“Star wheels”or“star finders”are adjustable circular star charts that enable you to show the stars for anyparticular night and time. These are very helpful for explaining the apparent motions of the stars duringthe course of a night or the course of a year because you can rotate the wheel to represent passing time.Edmund Scientific has inexpensive cardboard ones sold in bulk packs.Starry Night Prosoftware is very helpful for illustrating positions and motions of objects on the celestialsphere.Suggested ReadingsAllen, Richard Hinckley.Star Names: Their Lore and Meaning.Dover Publications, New York. Areprinting (with corrections) of a work first published in 1899. It has fascinating information and moredetail than you will ever need to know.Berman, Bob.“Five-five-uh-oh.”Astronomy(5 May 2000). p. 93. Discusses the effects of the planetaryalignment of May 2000, and provides arguments against astrology.

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Chapter 0: Charting the Heavens17Brown, Ronald A. and Kumar, Alok. “A new perspective on Eratosthenes’measurement of the Earth.”The Physics Teacher(Oct 2011). p. 445. Further discussion of the experiment described in theDiscoverybox in Section 0.5.Byrd, Deborah.“The starry sky: Libra.”Astronomy(May 1995). p. 63. A short article about theconstellation Libra, which is home to the autumnal equinox.Camino, Nestor and Gangui, Alejandro.“Diurnalastronomy:Usingsticks and threads to find our latitudeon Earth.”The Physics Teacher(Jan 2012). p.40. Describes an experiment students can perform todetermine latitude.Cordell, John. “Non-mathematical explanation of precession.”The Physics Teacher(Dec 2011). p. 572.Good conceptual explanation of a motion that is often hard for students to understand.Dunlop, S. and Tirion, W.How to Identify the Night Sky.Collins, 2004. I particularly like this referencebecause the star maps include an adjacent star field image which is good for practicing constellationidentification.Gangui, Alejandro. “Whither does the sun rove?”The Physics Teacher(Feb 2011). p. 91. A study on therising and setting locations of the Sun from different locations in the world.Gurshtein, Alexander A.“In search of the first constellations.”Sky & Telescope(June 1997). p. 46.A fairly detailed discussion of the origin and history of constellations.Hobby, David.“Portrait of the shortest day.”Sky & Telescope(6 June 1998). p. 46. Displays anddiscusses making a photograph of the Sun’s path across the sky on the winter solstice.Kanipe, Jeff.“Tilt-a-whirl astronomy: The seasons explained.”Astronomy(Mar 1996). p. 50. Describesthe apparent daily and annual motions of the Sun across our sky.Krupp, E. C.“Slithering toward solstice.”Sky & Telescope(6 June 2000). p. 86. Discusses the symbolismof snakes, serpents, and solstices.Krupp, E. C.“Springing down the banister: Vernal equinox festival at Chichen Itza pyramid, Mexico.”Sky & Telescope(Mar 1996). p. 59. A fun description of a vernal equinox festival held at Chichen Itza.Kuhn, T. S.The Structure of Scientific Revolutions. 3rd edition.University of Chicago Press, Chicago,1996. This is a reprinting of the classic 1962 work which discusses the philosophy and nature of science.This is a must for those who want to delve deeper into the philosophy of science.MacRobert, Alan M.“Understanding celestial coordinates.”Sky & Telescope(Sep 1995). p. 38. Describesthe celestial coordinate system.Panek, Richard.“That sneaky solstice.”Natural History(5 June 2000). p. 20. Describes the meaning ofthe solstice, and discusses why the earliest sunrise does not happen on the solstice.Ratcliffe,Martin,andShaffer,Rick.“Firstviews:Oldsolcelebratesthesolstice.”Astronomy(25 Dec 1997). p. 71. Discusses the analemma and how it demonstrates the offset between dates ofearliest/latest rising/setting of the sun and the solstices.

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18Chaisson/McMillan,Astronomy, Eighth EditionRey, H. A.The Stars: A New Way to See Them.Houghton Mifflin, Boston, 1962. One of my favoritebooks for introducing constellations. Rey uses diagrams that make the groupings of stars actually looklike what they are supposed to represent!Ryan, Jay.“SkyWise: Equinox.”Sky & Telescope(3 Mar 2000). p. 114.Comic strip drawing illustratingthe equinoxes.Ryan, Jay.“SkyWise: Latest sunrise earliest sunset.”Sky & Telescope(6 Dec 1998). p. 124. Cartoon stripillustrating why the date of the earliest sunset is not exactly the winter solstice.Schaaf, Fred. “Celebrating the longest night.”Sky & Telescope(Dec 2002). p. 90. Addresses the wintersolstice and sidereal time.Schaff, Fred. “A constellation not like Orion.”Sky & Telescope(Jul 2007). p. 42. Compares and contraststhe constellation Ophiuchus with Orion.Schulz, Teresa M. “Mask of the black god: The Pleiades in Navajo cosmology.”Journal of CollegeScience Teaching(Oct. 2005). p. 30. Describes a case study in which students learn about the role of aconstellation in Navajo cosmology and also practice their observational and star map skills.Trefil, James.“Architects of time.”Astronomy(9 Sep 1999). p. 48. Discusses history of astronomicaltimekeeping, from Stonehenge to pulsars.Notes and IdeasClass time spent on material: Estimated:Actual:Demonstration and activity materials:Notes for next time:

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Chapter 1: The Copernican RevolutionThe Birth of Modern ScienceOutline1.1The Motions of the Planets1.2The Birth of Modern Astronomy1.3The Laws of Planetary Motion1.4Newton’s LawsSummaryChapter 1 continues the view from Earth begun in Chapter 0 by discussing the apparent motions of theplanets. The historical development of astronomy from Copernicus through Newton is considered next.This chapter ends with a thorough discussion of Kepler’s laws of planetary motion and Newton’s laws ofmotion and gravity. The development of models of the universe from Ptolemy through Newton isdiscussed as an example of the scientific method at work.Major Concepts•The planets’ motionsWanderers among the starsRetrograde motion•Geocentric models of the universeAristotlePtolemy•History of modern astronomy and heliocentric modelsCopernicusBraheGalileoKepler•Kepler’s laws of planetary motion•Isaac NewtonLaws of motionGravityTeaching Suggestions and DemonstrationsAt the beginning of this chapter, give your students a copy of a current star chart showing positions of anyvisible planets. Encourage them to observe the planets over the course of the semester and the Moon overthe course of a month and notice how these move with respect to the stars.Sections 1.1 and 1.2Humans have looked at the sky and tried to unravel the motions of the stars and planets since early times.Discovery 1-1on ancient astronomy describes several intriguing examples of artifacts and structures withastronomical significance that have survived from ancient societies. The evolution of our understandingof the structure of the universe is a remarkable story ofscientific process, where each successive model

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20Chaisson/McMillan,Astronomy, Eighth Editiontook care of some problem of the previous model. Ptolemy, for instance, introduced epicycles to accountfor retrograde motion that could not be explained by the Aristotelian universe. Kepler changed the shapeof the orbits from circles, as shown in Copernicus’ model, to ellipses.Starry Night Collegecan be used to demonstrate theretrograde motionof the superior planets. Marswill be the best planet to use because the retrograde motion happens over just a few months. Jupiter andSaturn will both work since they are visible as they move through the constellations. The trick with thissimulation is that you should center on the planet and then change the time intervals to multiple days.It takes some practice, but will make for a good demo in class and will likely be more effective thanshowing a static image. You should have the students mark the relative positions of both Earth and Marsin their orbits during the retrograde interval. Students should understand that the retrograde motion isassociated with the Earth overtaking Mars in its orbit.Students accept theheliocentric modelwithout question, and they tend to forget just how hard it was forpeople to give up thegeocentric model. The reason is obvious; go outside at night and observe the skyover a period of time. It surelookslike the stars are going around Earth, and it certainly does notfeellikeEarth is moving! Reluctance to demote Earth from its position at the center of the universe resulted inPtolemy’s complicated and intricate model, which still failed after a long time to accurately predict thepositions of the planets. Moving to a heliocentric system and changing the orbits from circles to ellipsesgreatly simplified the model. As discussed in the text, simplicity is a desirable characteristic in scientificmodels; ask students to think of other examples of scientific advancement where successive modelsincreased simplicity.Tycho Braheactually had a model of his own that combined aspects of the heliocentric model withgeocentrism. He kept Earth in its central position, but placed the other planets in orbit around the Sun,which itself orbited Earth. Brahe’s model was largely ignored, and he is remembered today for hiscontributions in the form of vast quantities of observational data (that predated the telescope), which laidthe foundation for Kepler’s work. Interestingly, Brahe’s main argument for keeping Earth at the centerwas the lack of observed stellar parallax. Brahe had a good point; he just could not conceive of stellardistances so great that the corresponding parallaxes would be too small to be observed without preciseinstruments. In fact, the first successful parallax measurements were made in 1838 by Wilhelm Bessel.Before discussingGalileo’s observations with the telescope, go over the prevailing worldview of histime and emphasize some of its major characteristics. This background will just help students understandhow dramatic Galileo’s discoveries were. The Aristotelian view maintained not only that all astronomicalobjects orbited Earth but also that they did so in perfect circles. Earth was flawed, but heavenly objectswere perfect, unblemished, and unchanging. Further, Aristotle’s view had been inextricably linked withChristianity through “medieval scholasticism,” so contradicting Aristotle was extremely serious as it wasequivalent to contradicting the Roman Catholic Church. Galileo’s discoveries provided evidence thatobjects not only orbited something other than Earth (Jupiter’s moons, phases of Venus) but also thatheavenly bodies were not unblemished (sunspots, mountains on the Moon). Galileo’s experiments withfalling bodies also directly contradicted the Aristotelian view, which maintained that heavier objects fallfaster than do lighter ones.If Jupiter is visible at night when you are teaching the course, encourage your students to view Jupiterthrough binoculars from a reasonably dark site. The fourGalilean moonsare visible in binoculars, andstudents can follow their motions over the course of a week or so to recreate Galileo’s observations. Theorbital motion of the Galilean moons can be demonstrated usingStarry Night Pro. You will need tozoom in on Jupiter until the moons are visible. Then you can advance through time and watch the moonsorbit. When you initially see the moons it is not necessarily apparent which moon is which, soStarryNight Procan be used to identify them.

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Chapter 1: The Copernican Revolution21It will probably surprise students that Galileo andKeplerwere contemporaries. In terms of conceptualdevelopment, it seems that Galileo built upon and provided evidence for Copernicus’ heliocentric model,and then Kepler refined the heliocentric theory with details about the orbits of the planets. In fact, Galileoand Kepler were working at the same time. Galileo was placed under house arrest for promoting theheliocentric model and was forced to declare that it was useful as a mathematical tool only, not as adescription of reality. Meanwhile, at the same time, Kepler was not only assuming that the planets orbitthe Sun, but he was also describing their actual paths and speeds in those orbits. Point out to students thedifferences in societies at the time that resulted in these very different climates for debate and discussion.Throughout your discussion of thehistorical developmentand final acceptance of the Copernicansystem, sprinkle in interesting details of the lives of the people involved. Copernicus’ theory was not evenpublished until he lay on his deathbed. Brahe wore metal noses after he had his nose cut off in a duel.Galileo was a flamboyant character who loved to engage in debate. He published in Italian and oftenexpressed his ideas in dialogue form, to make them accessible to both the common man and the scholar.Sections 1.3 and 1.4Begin your discussion ofKepler’s laws of planetary motionby drawing an ellipse on the board oroverhead using the method shown in Figure 1.11. Define the various parts of an ellipse and show how acircle is the special case of an ellipse with an eccentricity of 0. Have students draw ellipses with the sameeccentricities as the planets and point out that most of the planetary orbits are nearly circular. (See Table 1.1for data.) Extend Kepler’s second law to comets, and ask students to describe the relative speeds of a cometwith a very elliptical orbit when it is close to the Sun and when it is far away.Finally, for Kepler’s third law, pick one or two planets and use the semimajor axes given in Table 1.1 tocalculate the periods. Compare the periods given in the Appendix on planetary orbital properties. Reviewthe mathematical meaning of “squaring” and “cubing.” Many students will confusea3with 3a. The moremathematically aware students are often concerned that the units of the third law do not work out correctly.When it is said that the constant of proportionality is one, it does not imply that there are no unitsassociated with the constant. In fact, the constant is 1 yr2/AU3, but for convenience we rarely show it.Todemonstrateorbitalmotion,whirlaballaroundonastringinahorizontalcircle.Inthedemonstration, 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”;demonstrate by letting go of the string. Note that if you shorten the string then the period will alsoshorten, much likeKepler’s third law. For instructors that might be skilled with a yo-yo, the trick“around the world” can be used instead of the ball and string for this demo. To shorten the string, simplyhave a second yo-yo that already has a shorter string prepared.Try using “Observing Retrograde Motion” from the bookLecture-Tutorials for Introductory Astronomy.This exercise is particularly good and helps to reinforce material that you have covered in lecture. Be sureto consider how much time to devote to this exercise because it normally takes more class time than youwould estimate.Newton’s laws of motionare extremely important and not necessarily intuitive. Give plenty of examplesof each. For instance, ask students to imagine an airplane trip on a beautiful day with no turbulence.If you throw a peanut up in the air, does it hit the person behind you or fall back in your lap? Alsoconsider 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 of the notion of inertia when he argued against the geocentricview and used ships at sea as an example.) Emphasize to students that Newton’s laws divide objects intothe two categories ofacceleratingandnonacceleratinginstead ofmovingandnot moving. An object

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22Chaisson/McMillan,Astronomy, Eighth Editionmoving at a constant velocity (that is, in a straight line and at a constant speed) is like an object at rest inthat both have no net force acting on them.Defineaccelerationcarefully and calculate an acceleration with which students are familiar, such as theacceleration of a car merging onto the highway. You can use first units that make sense, such as miles perhour per second, and then convert to the more standard meters per second squared to help students gain afeel for the acceleration due to Earth’s gravity. Students often confuse acceleration and velocity, so besure to distinguish between the two carefully. You can demonstrate Newton’s third law and the role ofmass by attaching a rope to a rolling chair and asking a student to pull it across the floor. Then sit in thechair and repeat. Ask the student to compare (qualitatively) the force used to accelerate the empty chairwith the force applied to the chair with occupant.Use an air track with carts or an air hockey table with pucks to demonstrateNewton’s laws, if possible.Seeing the behavior of objects in a nearlyfrictionless environment willhelp students overcomeAristotelian misconceptions about motion.Gravitational force is an extremely important concept in astronomy so it is worth spending some time onNewton’s law of gravity. Refer to the explanation in the text as well as to Figure 1.18, which gives botha mathematical expression of the law and a graph depicting its inverse-square nature. Ask students whatwould happen to the force of gravity between Earth and the Sun if the mass of Earth doubled or if thedistance between them doubled. Students often confuse the force of gravity with acceleration due togravity. Derive the expression for acceleration due to gravity and show that it is consistent with Galileo’sexperiments regarding the motion of falling bodies. Also emphasize that Earth alone does not “have”gravity; gravity is a forcebetweentwo objects. For instance, the weight of an object is the force betweenit and Earth when the two are in contact. Calculate the weight of a 70-kg person on Earth and on theMoon and compare. It is important to distinguish the difference between weight and mass of an object.The mass of an object is expressed in kilograms, but the weight is a force and is calculated by the masstimes the acceleration due to gravity. The weight of a 70-kg person is 686 N (or kg×m/s2). The weightvaries from planet to planet because the acceleration due to gravity is a function of the mass and size ofthe planet. Use Figure 1.19 to help explain how gravity is responsible for objects falling as well as objectsorbiting. Ask your students to picture the Moon as constantly falling toward the Earth and missing!The final section of this chapter refers back to the scientific method introduction in Chapter 0. Use thedevelopment of ever-improving models of the universe as an illustration of the cyclic nature of thescientific process.Student Writing Questions1.Try to identify at least one star that you can see at night. Look up information on it such as itsdistance and how its properties compare to the Sun. What would it be like to live on a planet orbitingthis star?2.Mars is a planet with several similarities to Earth: its day is about the same length and it is tilted in away that causes seasons to occur. But its orbital period is significantly longer. Imagine people bornand raised on Mars. They might use the Martian year rather than an Earth year to measure time.How long are the seasons on Mars, as measured in Earth units? How old would you currently be inMartian years? Do you think time would actually pass differently for you if you lived on Mars?There are 669.5 Martian days in a Martian year. What kind of calendar would you design? Howwould you define months and weeks and how many would you want to make?

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