Solution Manual for Understanding Our Universe, 3rd Edition

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’S MANUALUnderstanding Our UniverseT H I R D E D I T I O NStacy Palen, Laura Kay, and George BlumenthalAna LarsonU N I V E R S I T YO FW A S H I N G T O N

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Learning Astronomy by Doing Astronomy: CollaborativeLecture Activities▶This section introduces activities from theLearningAstronomy by Doing Astronomyworkbook that arerelevant to the chapter. The textbook reference ofthe associated topic is noted.Interactive Simulations▶Textbook author Stacy Palen has created sevenInteractive Simulations that pair with selected Explo-ration activities. This section briefly describes eachInteractive Simulation associated with the chapter.Check Your Understanding Solutions▶This section provides answers and supportinginformation for all of the in-chapter Check YourUnderstanding questions.End-of-Chapter Solutions▶This section provides worked solutions to Evaluat-ing the News and all of the end-of-chapter questionsand problems (Test Your Understanding, Thinkingabout the Concepts, and Applying the Concepts).Exploration▶This section briefly describes the Exploration activ-ity and provides worked solutions to each question.For adopters ofThe Norton Starry Night Workbook,the answers to the exercises are included at the end ofthe manual.We hope that you will find the information in this man-ual useful. We welcome your comments, questions, andsuggestions (contact your local Norton representative:http://books.wwnorton.com/books/find-your-rep/).Finally, we would like to thank Ethan Dolle of NorthernArizona University and Sean Hendrick of Millersville Uni-versity, whose careful review improved the accuracy andusefulness of this manual.Additional resources:Norton Interactive’s Guide (IIG)iig.wwnorton.com/unduniv3PrefaceFor each chapter of the textbook, you will find a corre-sponding chapter in the’s Manualthat contains allor most of the following sections:Notes▶This section provides a brief overview of the chapterand a list of major topics discussed. It often includescommon misconceptions to address and recommen-dations for additional resources.Discussion Points▶This section suggests important discussion topicsand activities. The chapter Learning Goal associatedwith each item is noted.Teaching Chapter-Opening Learning Figure▶This section discusses the Active Learning Figureand how you might use the experiment with stu-dents. We also have questions in Smartwork5 thatrelate to the figure.AstroTour Animations▶The AstroTour animations are narrated, conceptualoverviews with a consistent structure of Introduction—Explanation—Conclusion. This section of the’s Manualbriefly describes each AstroTouranimation associated with the chapter and notes thecorresponding section of the textbook.Astronomy in Action Videos▶The Astronomy in Action Videos are a series ofmini-lectures and demos done by textbook authorStacy Palen. This section of the’s Manualbriefly describes each Astronomy in Action Videoassociated with the chapter and notes the corre-sponding section of the textbook as well as thelength of the video.Teaching Reading Astronomy News▶This section provides an alternate article to the onepresented in the textbook. The Evaluating the Newsquestions for that article and suggested answers arealso included.vii

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viii◆FrontmatterPrefaceThis new and searchable online resource is designedto help instructors prepare for lecture in real time. All ofthe content in this’s Manual, and more, is locatedon the IIG. In addition to this manual’s content, you willfind: theTest Bank, AstroTour animations, Astronomy inAction videos, Interactive Simulations, Lecture Power-Point slides, all of the textbook’s art, photos, and tables, andLearning Management System Coursepacks (available inBlackboard, Canvas, Desire2Learn, and Moodle formats).Smartwork5 Online Activities and Assessmentdigital.wwnorton.com/universe3More than 1,500 questions supportUnderstanding OurUniverse, Third Edition—all with answer-specific feedback,hints, and ebook links. Norton offers pre-made assignmentsfor each chapter of the text to make it easy to get started, butSmartwork5 is also fully customizable.Questionsincluderanking,labeling,andsortingexercises based on book and NASA art, selected end-of-chapter questions, versions of the Explorations (basedon AstroTours and new Simulations), and questions thataccompany the Reading Astronomy News feature in eachtextbook chapter. Astronomy in Action video questionsfocus on overcoming common misconceptions, whileProcess of Science guided-inquiry assignments take stu-dents through the steps of a discovery and ask them toparticipate in the decision-making process that led to thediscovery.

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PA RT I :’s Manualix

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PA RT I I :Answers to Starry NightWorkbook Exercises133

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134students are surprised that the rotation period is not a full24 hours. A number of the exercises forStarry Nightrequirethat the students observe in intervals that are multiples of1 sidereal day, so it is important that the students learn thisconcept.ANSWER KEYActivity 1: Circumpolar Constellations1.From typical latitudes in the continental United States,the circumpolar stars are in the constellations ofCamelopardalis, Cassiopeia, Cepheus, Draco, UrsaMajor, and Ursa Minor. You might want to point outto students that all the constellations in the NorthernHemisphere are circumpolar as seen from the NorthPole. This fact was demonstrated in the exercise on thecelestial sphere.Activity 2: Rising and Setting Constellations2.The answer will depend on the constellation se-lected. Small constellations take about an hour to rise,whereas larger ones (Orion, Pegasus) may take 3 hoursor more.Activity 3: Earth’s Rotation Period3.The students are asked to determine the intervalbetween meridian crossings a few times and averagethe answer to smooth out any inaccuracies in theirmeasurements.4.The length of the sidereal day is 23 hours 56 minutes4 seconds.5.The average amount by which stars cross the meridianearlier each day is 24 hours minus the length of thesidereal day, or 3 minutes 56 seconds.6.A star that crosses the meridian at midnight tonightwould cross 4 minutes earlier tomorrow night, at11:56 p.m. Thirty days later, the star would cross themeridian 120 minutes earlier (3034), at 10 p.m. Thisimplies that any particular star will continue to transitearlier and earlier until it is eventually only above thehorizon during the day. But also, the star would againEXERCISE 1: THE CELESTIAL SPHEREThis exercise illustrates the daily motion of the celestialsphere. It animates the apparent motion of the sky as seenfrom Earth’s North and South poles.Students will learn the most basic operations ofStarryNight: selecting objects to view, changing the orientation oftheir gaze, and altering the flow of time.ANSWER KEYActivity 1: Directions on the Sky1.In this view, west is toward the right, and east is towardthe left.2.From the North Pole, the apparent motion is parallelto the horizon.Activity 2: Direction of Rotation3.From the North Pole, the apparent motion of the sky iscounterclockwise.4.Polaris is located in the constellation of Ursa Minor.Activity 3: View from the South Pole5.From the South Pole, the apparent motion of the sky isclockwise.6.The south celestial pole is in the constellation Octans.7.Stars at the North and South poles appear to move inopposite directions. This is because the point of viewof the observer is inverted, so that a counterclockwisemotion as seen at the North Pole appears clockwise asseen at the South Pole.EXERCISE 2: EARTH’S ROTATION PERIODHere, the students will become familiar with the appear-ance of the celestial sphere from an intermediate latitude.The instructor may wish to direct the students to pick aparticular viewing location for this exercise.The students will determine Earth’s rotation period byfinding the average time between meridian crossings for astar. The exact value of Earth’s rotation period (23 hours56 minutes 4 seconds), is called the sidereal day. ManyThe Norton Starry Night Workbook: ExerciseSummaries and Activity Answers

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The Norton Starry Night Workbook: Exercise Summaries and Activity Answers◆135continue to transit earlier until a year later, when itwould again transit at midnight.EXERCISE 3: MOTION OF THE SUN ALONGTHE ECLIPTICThis exercise demonstrates that the Sun moves eastwardalong the ecliptic each day, and asks the students to notewhich constellation the Sun appears in at different timesof the year. The exercise reinforces the concept of Earth’schanging position in its orbit around the Sun, causingconstant changes in the apparent position of the Sun in thecelestial sphere as viewed from Earth.Most students know something of popular astrology, ifonly their birth sign. The students will compare the actualdirection of the Sun with the locations listed on many cal-endars and see that the dates of the astrological signs havetheir origins more than 2,000 years ago.ANSWER KEYActivity 1: The Sun and the Zodiac1.Dates on which the Sun entered the modern constella-tion boundaries:ConstellationDate Sun EntersDays SpentGemini6/22/200729Cancer7/21/200721Leo8/11/200737Virgo9/17/200745Libra11/01/200722Scorpius11/23/20077Ophiuchus11/30/200719Sagittarius12/19/200732Capricornus1/20/200828Aquarius2/17/200824Pisces3/12/200838Aires4/19/200825Taurus5/14/200838Gemini6/21/2008—Allow61 day for the student estimates.Activity 2: Astrological Dates2.Students will notice that (a) the current constella-tion boundaries mean that the Sun spends differentintervals in the various constellations; (b) there is adifference of about 1 month between the traditionaldates and the current dates; and (c) the Sun spendsalmost 3 weeks in Ophiuchus, which is not one ofthe traditional zodiacal constellations.Activity 3: Dates in the Distant Past3.The approximate year that the Sun entered Gemini onMay 21 is 900 BC (allow ±1 century).4.The Sun only appears to pass through the zodiac con-stellations because the ecliptic plane of Earth’s orbitaround the Sun lines up with these constellations. TheSun never passes through Ursa Major because thatconstellation is not in the ecliptic plane.EXERCISE 4: MOTION OF THE MOONThis exercise asks the students to measure the synodic andsidereal periods of the Moon and to compare their mea-surements to the values quoted in the reading.The instructor may wish to stress that any set of mea-surements will be accurate only to a particular level. Thestudents should be encouraged to be honest about theirmeasurements and not to try to land on the stated periods.By comparing their values to the actual ones, the studentswill get a feel for the accuracy of their measurements. Thereare more accurate ways of measuring the synodic and side-real periods usingStarry Night, but this exercise is designedto produce answers accurate only to about a quarter of a day.ANSWER KEYActivity 1: Time of Moonrise on Successive Nights1.The exact times will depend on the viewing location.The instructor may wish to specify a particular view-ing location so that all students come up with the sametimes.2.The average time interval will be about 50 minutes.Activity 2: The Moon’s Sidereal Period3.The students should derive numbers between 27 and28 days. In the exercise, they work in steps of 1 day,so the fraction of a day over 27 that they derive willdepend on how they interpolate between positions ofthe Moon on successive nights.4.The length of the sidereal month is 27.3 days.Activity 3: The Moon’s Synodic Period5.As in answer 3, the exact value will depend on how thestudents interpolate.6.The length of the synodic month is 29.5 days.7.The difference between the Moon’s sidereal and syn-odic periods is about a little more than 2 days. Thesynodic period is longer because as the Moon orbitsEarth, the Earth-Moon system is moving around the

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136◆The Norton Starry Night Workbook: Exercise Summaries and Activity AnswersSun. It takes 27.32 days for the Moon to completeone orbit around Earth (sidereal period), but in thattime, Earth has moved to a different position in itsorbit around the Sun. The Moon must therefore movea little farther in its orbit to line up with the Sun again,making this synodic period 29.5 days.EXERCISE 5: EARTH AND MOON PHASESThis exercise explores the relationship between the phasesof the Moon as seen from Earth and the phases (shading)of Earth as seen from the Moon. Students will predictDate and TimeMoon Phase(shadow = dark)Phase DescriptionEarth Shading(shadow = dark)Shading DescriptionJan. 9, 201622:21:49 UT1ANew Moon1BFull EarthJan. 13, 201622:06:06 UT2AWaxingCrescent Moon2BWaningGibbous EarthJan. 16, 201621:54:18 UT3A1stQuarter Moon3BLast/3rdQuarter EarthJan. 19, 201621:42:30 UT4AWaxingGibbous Moon4BWaningCrescent EarthJan. 23, 201621:26:47 UT5AFull Moon5BNew EarthJan. 27, 201621:11:03 UT6AWaningGibbous Moon6BWaxingCrescent EarthJan. 31, 201620:55:19 UT7ALast/3rdQuarter Moon7B1stQuarter EarthFeb. 4, 201620:39:36 UT8AWaningCrescent Moon8BWaxingGibbous Earththe best conditions to observe phases of the Earth fromthe Moon.ANSWER KEYActivity 1: Moon PhasesActivity 2: Earth Phases1-3.4.The shading (phases) of Earth appears to be opposite orthe reverse of the Moon phase shading. A New Moon is afull Earth for the same date and time. Similarly, a waxing

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The Norton Starry Night Workbook: Exercise Summaries and Activity Answers◆137crescent Moon phase is accompanied by a complemen-tary waning gibbous Earth phase. The first quarter Moonfeatures a last/third quarter Earth. A waning crescentMoon is opposed by a waxing gibbous Earth, and so on.5.To see Earth completely, it should be in its full phase,which corresponds to the new Moon phase.6.It depends on how well the observers can be protectedfrom the extreme cold on the surface of the Moon, inthe total darkness of a new Moon. Observing might notbe practical during the extreme cold of the new Moonphase. Since there is no atmosphere on the Moon,heat is conducted only by radiation and conduction.Furthermore, Bruce Crater is near the lunar equator, sothe surface experiences the most extreme high temper-atures during the lunar day time such as when there arewaxing and waning as phases. The temperature can rise toalmost 390K (water boils at 373K) during the daytime,and sink to as low as 95K (water freezes at 273K) in thenighttime. Selecting a phase when the most moderatetemperatures occur, around dawn as the Sun first risesfor the lunar day, which is a little over 27 Earth days long,might be the best time to observe. This procedure wasused during the Apollo lunar landings from 1969 to 1972.7.Date and TimeMoon Phase(shadow = dark)Phase DescriptionEarth Shading(shadow = dark)Shading DescriptionJan. 9, 201622:21:49 UT1ANew Moon1BFull EarthJan. 13, 201622:06:06 UT2AWaxingCrescent Moon2BWaningGibbous EarthJan. 16, 201621:54:18 UT3A1stQuarter Moon3BLast/3rdQuarter EarthJan. 19, 201621:42:30 UT4AWaxingGibbous Moon4BWaningCrescent EarthJan. 23, 201621:26:47 UT5AFull Moon5BNew EarthJan. 27, 201621:11:03 UT6AWaningGibbous Moon6BWaxingCrescent EarthJan. 31, 201620:55:19 UT7ALast/3rdQuarter Moon7B1stQuarter EarthFeb. 4, 201620:39:36 UT8AWaningCrescent Moon8BWaxingGibbous Earth

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138◆The Norton Starry Night Workbook: Exercise Summaries and Activity AnswersEXERCISE 6: SUNRISE ON MARSIn this exercise, students will observe and document sun-rises and sunsets along with related objects from the surfaceof mars. Students will also predict the seasons based on theshifting location of the sun along the Martian horizon.ANSWER KEYActivity 1: Sunrises from MarsSunrise Table:Observation step/DateSunrise timeList other objects observednear the Sun along thesunrise path to the horizonSketch of Sun and any objects at sunrise(show and label horizon with directions)Stopped time1/9/13/20159/14/201522:0:47/0:05:03 UTEarthVenusMercury30˚10˚90˚80˚60˚75˚SunEEVMeMe100˚0˚2/3/13/201618:06:30 UT/20:06:57 UTMercuryVenus30˚10˚90˚80˚60˚65˚E100˚0˚3/9/13/201616:59:37/19:04:38 UTEarthMercuryVenus30˚10˚108˚120˚80˚90˚E100˚0˚4/3/13/201714:23:27/16:25:18 UTJupiterEarthVenusSaturnSE30˚10˚120˚100˚103˚140˚0˚5/9/13/201710:48:36/12:52:17 UTJupiterSaturnMercuryVenusE30˚10˚80˚90˚60˚ 65˚100˚0˚

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The Norton Starry Night Workbook: Exercise Summaries and Activity Answers◆1391.They are the planets rising or setting. The names ofthese may be seen by rolling the cursor over the ob-jects or by turning on the planet labels.Sunset Table:Observation step/DateSunset timeList other objects observednear the Sun along thesunset path to the horizonSketch of Sun and any objects at sunrise(show and label horizon with directions)Stopped time1/9/13/20159/14/201510:31:17/12:31:29VenusEarthMercury30˚10˚288˚320˚280˚ MeNWEV300˚0˚2/3/13/20167:28:26/9:29:02 UTEarthMercuryVenus30˚10˚292˚320˚280˚NW300˚0˚3/9/13/201604:39:16/6:34:30 UTEarthJupiterMercury30˚10˚252˚270˚ 280˚240˚W260˚0˚4/3/14/172:13:29/4:12:50 UTVenusEarth30˚10˚252˚270˚ 280˚240˚W260˚0˚5/9/14/170:12:27/2:28:05 UTVenusMercuryEarthVMe30˚10˚293˚280˚NWE300˚320˚0˚

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140◆The Norton Starry Night Workbook: Exercise Summaries and Activity AnswersActivity 2: Predicting Seasons fromSunrise/-Set Data2.Differencea.Summer Solstice1/3/2016-------------------b.Autumnal Equinox7/4/20166 months, 1 dayc.Winter Solstice11/28/20164 months, 24 daysd.Spring Equinox5/5/20175 months, 7 dayse.Summer Solstice11/20/20176 months, 15 daysTotal22.6 months3.Northern Hemisphere.4.The greater eccentricity of the orbit of Mars causes theseasons to be unequal.EXERCISE 7: PRECESSIONHere we focus on the precession of Earth’s rotation axis.The students will measure the angular separation betweenthe north celestial pole (NCP) and Polaris at differentepochs and will see that the current separation is close tothe smallest possible value.The text emphasizes the effect of precession on the timesof the spring and fall equinoxes; we touch on that conceptin Exercise 3, on the motion of the Sun along the ecliptic.ANSWER KEYActivity 1: The Distance Between Polarisand the North Celestial Pole1.The separation in 2007 is about 0 degrees 42 minutes(or 0° 429). Allow an error of a few minutes, as the stu-dents may land on slightly different positions near thenorth celestial pole.Activity 2: When Polaris is Closest to the Ncp2.The minimum separation will occur about the year2100 and will be approximately 0° 289.3.This is about 67 percent of the current value.Activity 3: The Separation in the Past4.In the year AD 1, the separation was almost 12° (about11° 459)!5.The following table shows a few bright stars that werecloser than Polaris to the north celestial pole in theyear AD 1. The last column displays the separation indegrees and minutes. If they ignore the instructions toexamine the stars in the stick figures for Ursa Minorand Draco, some students may zoom in and identifyfaint stars that are much closer to the NCP.ConstellationStarSeparationUrsa MinorKochab8° 209Zeta Ursae Minoris8° 329DracoKappa Draconis9° 1096.Though Polaris was about the same distance from theNCP as Kochab at this time, Polaris is the brighter star.7.The change in the position of the north celestial poleaffects all stars, not just Polaris. The stars stay in thesame positions relative to each other, so the constel-lation patterns themselves are not affected, but if theNCP moves away from Polaris, it must move closer toother stars.EXERCISE 8: KEPLER’S LAWSThis exercise reinforces a student’s knowledge of Kepler’slaws by creating an asteroid with a semimajor axis of 1 AU,but with a very elongated orbit. In the first part, the stu-dents will calculate the orbital period and then verify it byinspection. They will see that the period is independent ofthe eccentricity.The elongated orbit for the asteroid makes Kepler’ssecond law more apparent than it would be for the orbits ofthe major planets, which are nearly circular.This exercise views the orbits of Earth and the asteroidfrom a position above Earth’s ecliptic pole. This helps illus-trate that Earth’s distance from the Sun does not vary muchduring the year. Many students get the opposite impressionfrom figures that show Earth’s orbit from the side, whichmake it appear much more eccentric, thereby causing con-fusion when they learn the causes of the seasons.ANSWER KEYActivity 1: Kepler’s Third Law1.The length of the semimajor axis isa= 1 AU. FromKepler’s harmonic law,P2=a3, soP= 1 year.2.The orbital period is independent of the eccentricitye.This sometimes surprises students because a circularorbit looks so different from a highly elongated orbit.3.Witha= 4 AU,a3= 64, soP= 8 years.Activity 2: The Period of X’s Orbit4.The period determined by measurement should bevery close to 1 year, in agreement with the value fromKepler’s harmonic law.

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