General Astronomy ASTR 2310
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Date Created: 10/27/15
Astr 2310 Thurs Jan 21 2009 Today s Topics Ancient Astronomy Babylonians and early culture Greeks Aristarchus Hipparcos Ptolemy Origin of Modern Astronomy and Celestial Mechanics Copernicus Tyco Brahe Kepler Galileo Newton Penumbra Screen close Screen far to tack from tack Light source From onrtext Horizons by Seeds Both the Earth and the Moon will cast shadows If the Sun Earth and Moon are all lined up then the shadow from one can fall on the other Because the Earth is 4 times bigger it will cast a shadow 4 times bigger Umbra Portion of shadow where it is completely dark for a person in the shadow the light bulb would be completely blocked out Penumbra Portion of shadow where it is only partially dark for a person in the shadow the light bulb would be partially blocked out To remember the names think of ultimate and penultimate Types of eclipses Lunar Eclipse Solar Eclipse Class secuon ul Earlh39s mum Sunlight om almann lolalocllpse 7 H 7 Paih of total eclipse Max In Real We View the illuminating object the Sun and see it blocked out We View the illuminat object and watch it go dark Only a few people are in Everyone on one Slde 0f the right place to be in the the Earth can see the shadow Moon so a glven lunar eclipse is Visible to many It is coincidence that the people umbra just barely reaches earth Palh oi oxal eclipse A Yaw Sula Eclipse the risk a ma moan glu uany was me dxsk a m Sun sunugm beams From our text Horizons by Seeds Solar eclipses If you are outside the penumbra you see the Whole sun If you are in the penumbra you see only part of the sun If you are in the umbra you cannot see any of the sun The fact that the moon is just barely big enough to block out the sun results from a coincidence The sun is 400 times bigger than the moon but also almost exactly 400 times further away The orbit of the moon is elliptical At perigee it can block out the full sun At apogee it isn t quite big enough giving an annular eclipse Eclipse Facts Longest possible total eclipse is only 75 minutes Average is only 23 minutes Shadow sweeps across Earth 1000 mph Birds will go to roost in a total eclipse The temperature noticeably drops Totally predictable even in ancient times eg the Saros Cycle eclipse pattern repeats every 65853 days or 18 years 11 13 days due to precessional period of Moon s orbit Eclipses and Nodes 2mm Brook Col Publishing 7 3 mm mums Lmrning Fun moon Earth lew moon Plane oi moon39s orbit Favorabie for eclipse Plane 0 Earlh39s orbit Uniavorable or eclipse Line 0 nodes Line at nodes Uniavorabie or eclipse Favorable for ecllpsa e 2002 auxh Cale Fuhlixhlnggt a division nn39iiomann Learning From our textbook Horizons by Seeds Variations in Solar Eclipses Elliptical orbits mean angular size variation DiamondRing Effect Annular Edipse Phases of the Moon and its orbit around the Earth 1 1 Everything almost in the solar As seen from Earth Q a a system rotates or orbits New Waxing First Waxing Full Waning Third Waning counterclockwise as seen from the crescent quarter gibbous gibbous quarter crescent North Firstquane39 39 2 The illumination of the Earth and Waxing gt the moon will be almost the same 39bb f o 939 OHS D mmquot smce the sun is so far away that both receive light from almost the Sunset same direction Nonh 3 It takes 4 weeks for the moon to complete an orbit of the earth Pole V Full Midnight Noon i E g 522 V 4 The moon is phaselocked In other words we always see the same face 9 although the illumination pattern Sunrise Waning 9mm we see changes How long is a Thirdquarter lunar From our text Horizons by Seeds Phases of the Moon and its orbit around the Earth 2 As seen from Earth Waxing Full Waning gibbous gibbous D New Waxing First crescent quarter First qua er Waxing gibbous D Sunset North Pole V Midnight Noon Earihfs rotation Sunrise Full Waning gibbous Third quarter From our text Horizons by Seeds Third quarter Waning crescent Suppose you are asked when the rst quarter moon will rise when it will be overhead and when it will set Which side will be illuminated If it is rst quarter it has moved 1 revolution around from the new moon position so it is at the top of the diagram For a person standing on the earth the moon would rise at noon be overhead at 6 pm and would set at midnight It has to be the side towards the sun which is illuminated Imagine yourself lying on the ground at 6 pm head north right arm towards the west That west right arm points towards the sun That must be the side which is illuminated Chapter 1 The Origin of Modern Astronomy The development of modern science The Aristotelian Universe The Copernican Revolution The rules of modern science References The Beginnings of Western Science by David Lindberg Galileo s Daughter by Dava Sobel Coming of Age in the Milky Way by Timothy Ferris The Historical Setting 1543 99 years of astronomy 1642 1 500 1 550 1 600 1 650 1700 1 750 1 1 1666 London 1 G wrge wash39quotgt quot 1 1 1 1 Black Plague 1 Sidereal Messenger Dialogues 39 0 1 1510 1632 39 American War Of independence gt 1 1 V 1 Telegcope lm rggged Edward Tea h Napoleon Tycho s nova invented Blackbeard Luther 1 572 1 gegrge m 1 4 r 1 1 20 yrs at Hveen 212493 wunam Penn I 1 1 A o 1 v 1 1 Magelian39s i 1 French and 1 1 1 Indian War 1 around the Tycho Law ill Principia 1 world hires 161 9 1687 1 John Marshall Ke Ier 1 h 1 1 6 1 Benjamin Franklin Michelangelo j 1 Destruction of he1 Voyage of 1 Klte Leonardo Spanish Armada 1 the Mayflower 1 1 da Vinoi r 1 Shakespeare 1 1 Columbus Eiizabeth 1 Milton 7 1 139 39Voltaire 1 Bacon 1 1 1 G F k 1 so Bach Mcizalt Liquot aw es 1 V 1 1 y i i R mbi dt i 7 1 1 Beethoven 1 1 1 l The Renaissance The European Discovery of the New World The Reformation From our text Horizons by Seeds Reniassance Astronomers Nicolaus Copernicus 1473 1543 Heliocentric model Explanation of retrograde motion Tycho Brahe 1546 1601 Observations of changes in sky Accurate planet positions Johannes Kepler 1571 1630 Mathematical description of planetary orbits Galileo Galilei 1564 1642 Observations using telescope supporting Copernican model Isaac Newton 1642 1727 Physics to explain Kepler s orbits Planetary Configurations The standard planetary configurations Note that the terms describe the position of the planet relative to the Earth and Sun as if the Earth weren t moving Eastward congg l on Eastward Su erim P anea Superior Conjunction full Figure 12 Heliocentric planetary con gurations Ar rows indicate the direction of orbital motion as well as the rotational direction of the Earth The phases of the planets illumination viewed from the Sun are also shown Copernicus 1473 1543 Proposed heliocentric model Apparentpamoniars as seen from Earth Circular orbits and uniform motion Less accurate for predicting positions but more physically realistic Simple explanation for retrograde motion De Revolutionibus Orbium Coelestium published in 1543 Computed the scale of the Solar System relative to Earth s orbit ie in AU From Horizons by Seeds Copernicus continued Copernicus also claimed Planets were all round worlds like the Earth Earth was just another planet Copernicus model was just an alternative model It was simpler and elegant but there was no physical evidence Proof came 100 years after his death Copernicus and Scale of the Solar System Inferior Planets Angle of Greatest Elongation gives Orbital Radius Copernicus and Scale of the Solar System Determining the Siderial Period of a Planet S synodic period viewed from Earth P siderial period f planet E siderial period of Ea h 6 SE360E S360P With deg daysdegday Figure 1 4 Synodic and sidereal periods in a heliocen tn39c model As the Earth 39orbiis the Sun at an angular speed of 360 E degrees per day a superior planet moves at 360 P degrees per day as seen from the Sun The Earth moves from position 1 to position 2 after one orbit and has 5 E days to reach the next opposition at position 3 During this time the superior planet has moved from position 1 to position 3 S E360E 8360P Simplfying further SE360 EE360 SP360 SE 1 SP Dividing by 8 yields 1E 18 1P valid for superior planet For an Inferior planetjust switch E amp P 1P 18 1E Or 1P 1E 18 valid for inferior planet Copernicus and Scale of the Solar System Copernicus used relative geometry of the Eatrh Sun and planet to determine the radius of all the planet s orbits Inferior Planets Use angle of greatest elongation Superior Planets Measure position of Planet at two successive siderial periods planet in the same place Figure 1 5 Distance determinations in a heliocentric model A When an inferior planet reaches greatest elongation P we know angle SEP and can nd 1 because an gle SPE is a right angle B A superior planet is at P at the start and end of one sidereal period at these times the Earth is at E and E Angles PBS and PE S are ob served they are the elongations of the planet from the Sun Tycho Brahe 1546 1601 1563 Conjunction Jupiter and Saturn show problems with Ptolemaic predictions of positions 1572 Tycho s supernova challenges ideas of unchanging nature of the heavens Lack of parallax shows it was at least as far away as the moon 1576 1596 Most precise observations of positions of the planets 1596 Moves to Prague hires Johannes Kepler as assistant Brahe advocated a combination of heliocentric and geocentric model for the Solar System 1601 Collapses requests Kepler be appointed his replacement then dies Johannes Kepler 1571 1630 The nature of planetary orbits Problem Copericus heliocentric model just wouldn t fit the precise data from Brahe Realized Mars orbit must be elliptical not circular Everything now fit 1 The orbits of all Kepler s Laws 1 and 2 1609 Published two laws showing 1 Planets orbit the sun in ellipses with the Sun at one focus 2 Motion is faster when they are near the Sun in such a way that a lIne from the planet to the sun sweeps out equal areas in equal times Filllll 410 The geometry of elliptical orbits 3 Drawing an ellipse with two tacks and a loop of string b The semimajor axis a is half of the longest diameter c Kepler s second law is demonstrated by a planet that moves from A to B in 1 month and from A to B in the same amount of time The two blue segments have the same area A t From our text Horizons by Seeds Properties of Ellipses Ellipse defined by two constants semimajor axis eccentricity a 12 length of major axis 0circe1 line Two ellipses with the same a but different e e Same focus at the sun Kepler s Laws 3 1619 Publishes third law showing that there is a relationship orbital period and semimajor axis Exact relationship is P2 cc a3 Outer planets orbit more slowly than inner ones Example Earth P 365 days a 100 AU Mars p 687 days a 1524 AU 687 days2 1524AU3 188215243 354 354 365 days 1000 AU Orbital Period of some asteroid with a 9 AU 2 3 Iaasteroid aasteroid P Earth aEaIth 3 2 PEarth j 1yeargtlt932 33 27 years Earth PA steroid Figure 16 Kepler s laws of ch to 4 The radius vector to the planet SP sweeps out the same area A during these times C For all major plan ets this log log plot of semi major axes 1 versus sidereal periods P falls very close to a straight line of slope 32 con rming Kepler s third law gt 10 poms2 T i E m J 01 I 1 I g 01 10 100 1000 10 Sidereal Period P Years gt C Kepler s Laws Continued Form P2 Ka3 of the law results from gravity so it is valid for any orbit Units used determine K K 1 if a is in AU and P is in years Solar System units For other units K must be computed Moon and artificial satellites around the Earth Satellites around other planets Stars orbiting each other Stars orbiting the Galaxy Galileo Galilei 1564 1642 Galileo s earlier work Invented Physics Developed concept of inertia and force 1590 Masses fall at same rate heavier do not fall faster unless affected by air resistance 1604 Observes a supernova Kepler s no parallax must be beyond the Moon Telescopes 1609 Hears of invention of telescope which at that point just use eyeglass lenses Works out details of better lenses and lens placement builds improved ones himself Galileo First telescopic observations Sidereus Nuncius The Starry Messenger published in 1610 reporting Moon isn t perfect violating Aristotelian principles for heavens Shows mountains and valleys Uses shadows to estimate heights Milky Way made up of myriad faint stars Doesn t directly violate Aristotelian principles but suggests that a few simple phenomena can explain many features of the heavens Discovers 4 moons Galilean Satellites orbiting Jupiter Violates idea that all motion is centered on the Earth Shows that orbiting objects can follow a moving body 4 moons will also be seen to follow Kepler s 3lrd law P2 oca3 but with a different proportionality constant i321 i Q iii a 3 Detects sunspots and the rotation of the Sun Further evidence of the imperfect heavens Detects the phases of Venus Phases show that Venus must orbit the Sun Full Venus when it is on far side of Sun Crescent Venus when it is on near side of Sun Ptolemaic universe Copernican universe enter of e picycie Galileo s critical observations Jupiter s moons show orbits which are not earth centered Venus phases show it must circle the Sun Several objects Moon Sun show imperfections which are not supposed to be present in the heavens Galileo s observations clearly support Copernican model but so far his printed work has mostly been reporting what he sees rather than directly arguing for Copernican model Galileo and the Dialog Written as a debate between 3 people Salviati Copernican advocate really Galileo Sagredo Intelligent but uninformed Simplicio Aristotelian philosopher not very bright Hoped to avoid earlier ruling by not directly advocating Copernican model Actually made things worse by convincing accusers they were Simplicio 1633 Inquisition condemns him for violating 1616 order Something like modern contempt of court ruling Proceeding not a reargument of Copernican vs Aristotelian debate But forced to recant admitting errors Sentenced to life imprisonment actually house arrest Dies in 1642 Pope John Paul II finally makes some amends 350 years later Newton 16421727 Principia published in 1687 3 Law of motion 1 A body continues at rest or in uniform motion in a straight line unless acted upon by some force 2 A body s change of motion is proportional to the force acting on it and is in the direction of the force 3 When one body exerts a Enigma second body the second body exerts an equal and opposite force back on the first body Universal gravitation There is an attractive force between all bodies proportional to their mass and inversely proportional to the square of their distance Mm G 2 G 667 x 10 11 m3 s2 kg 739 Explanation for Kepler s Laws Momentum keeps the planets moving you do not need some force to do this Gravity provides the force which makes orbits curve Gravity of Sun curves orbits of Planets Gravity of Earth curves orbit of moon and also makes objects on earth fall downward Conservation of Angular Momentum explains why motion is faster when closer to the sun The inverse square law of gravity explains P2 o a3 and the details of why the orbits are ellipses Circular Orbits Limiting case of an ellipse Centripetal acceleration v2lr caused by Gravity mv2 Mm GM G 2 v r r r Period found by distance 23W 23W 231 32 r velocity v GM JGM r Period Kepler s 3i Law just comes from this 2 4J3917 3 P2 r GM From our text Horizons by Seeds Given P and a and G we can find the mass of a planet or star Geometric Properties of Ellipses Figure 1 7 An ellipse Important properties labeled here are AP perihelion distance A F aphelion distance a semimajor axis b semiminor axis and c center FF 2ae definition of e Consider triangle BcF b2 a2e2 r2 a2 rr 2a so b2 a2 a2e2 a21e2 b a1e2 2 relationship between b amp a Furthermore Rmin a ae a1e Rmax a ae a1e distances at perihelion aphelion Applying law of cosines to F PF gives r 2 r2 2ae2 2r2aecos9 But since r 2a r we have 4a2 4ar r2 r2 4a2e2 4raecos0 a rae2 recose a ae2 r recosE a1e2 r1e cose so r a1e21e cose equ for ellipse in polar coordinates What about the velocity Kepler s 2nOI law 12 r2 d6dt constant must hold for entire penod 12r2 deldt nabP areaperiod Since b a1e212 erBdt 2naPa1e212 Or deldt 2nPar21e212 Recall s r6 so dsdt r deldt V6 Velocity contin ued 0 V9 r dBIdt r2 lPa2lr21e21 2 2mPa21e212a1e21ecosq So finally VB 2naP1ecos1e212 Since 1e2 1e1e so we consider 2 cases Perihelion velocity 0 0 voeri 21alP1e1e21 2 Aphelion velocity 0 180 Vaph ZuaP1e1eZ12 Nicolaus Copernicus 1473 1543 Tycho Brahe Johannes Kepler Galileo Galilei Isaac Newton 1546 1601 1571 1630 1564 1642 1642 1727 Heliocentric model Explanation of retrograde motion Observations of changes in sky Accurate planet positions Mathematical description of planetary orbits Observations using telescope supporting Copernican model Physics to explain Kepler s orbits Astr 2310 Thurs Jan 29 2009 Today s Topics Celestial Mechanics cont Newtonian Derivation of Kepler s Laws Newton s Test of Universal Gravitation The TwoBody Problem Least Energy Orbits Example of LeastEnergy Orbit to Mars Chapter 2 Solar System Overview Constituents Discovery of Outer Planets Fundamental Characteristics Mass and Radius Surface Temperature and Black Body Radiation Planetary Atmospheres and Composition Radioactivity and HalfLife Nuclear Physics see The Making of the Atomic Bomb by R Rhodes Age Dating of Solar System Newtonian Derivation of Kepler s Laws 1 The general form of a planetary orbit is an ellipseconic section Extensive derivation requiring calculus see Mechanics 2 A planet in orbit about the Sun sweeps out equal areas in equal amounts of time Recall that the area of a sector is given by Area Gr22 E in radians Consider the motion of a planet between points 1 amp 2 and between points 3 amp 4 The orbital path length is given by 81 and the angular difference is given by 6 and a given time interval At t2 t1 u g The conservation of angular momentum requires mv1r1 mv2r2 mv3r3 mv4r4 so V1r1 v3r3 and multiplying by At gives Atv1r1 Atvgr3 but since distance velocity x time we have S12r1 834r3 but 812 r1 612 and 834 r3634 so 912 r12 634r32 dividing by 2 gives 912 r12 2 634r322 area of sectors 2 nd law results from conserv of ang mom 3 The square of the orbital period is proportional to the cube of the semimajor axis of it s orbit Consider a circular orbit for simplicity Equate the centripital and gravitational forces FC Fg Mpr2r GMSMpr2 dividing by MID and 1r sz GMpr but the circular velocity is VID 2nrP where P is the orbital period so 2ru2r2P2 GMpr and solving for p we have P2 4n2GMSr3 but the circle is just a special case of an ellipse so P2 k a3 or P2 a3M P is in years a in AU and M is in solar masses Newton s Test of Universal Gravitation Recall the form of Newton s Gravitational Law Fg GMmr2 so ag Fgm GMr2 a apple 9807 ms2 at RE Since RE 6378 km and clm 3844 x 105 km REdm 6027 so the acceleration at clm should be am ag6O272 ag3632 But what is it am Vm2 clm Vm 2ndmP 1023 x 103 ms So am 2723 x 10393 ms2 ag 3632 2698 x 103 ms2 within 1 TwoBody Problem Newton s form for Kepler s 3039 Law Center of Mass location where Fg 0 and lies along the line connecting the two masses Each mass must have the same orbital period P1 27r1N1 P2 2ner2 so r1v1 r2v2 r1r2 v1v2 Newton s 3rOI law means F1 F2 so m1v12r1 m2v22r2 substituting for V gives m147u2r12r1p2 m24n2r22r2p2 or m1r1 er2 thus r1r2 m2m1 v1v Now we define a relative orbit where the more massive object ie the Sun lies near the center of mass Let a r1r2andvv1v2 TwoBody Problem Continued Since r1 r2 M2M1 gt r1 r2 m2r2m1 r2 and a r21 m2m1 The displacement is small for planets Note r2 am1m1 m2m1 and r2 m1am1 m2 combining gives r1 m2am1m2 note the symmetry Recall that Fg FC gravity centripital force F1 m1v12r1 Gm1m2r1r22 substituting for V1circular orbit 4712m1r1P2 4n2m1m2aP2m1m2 Gm1m2a2 Thus P2 4712Gm1m2a3 Chapter 2 Homework 6 7 9 11 12 15 19 Due Thursday February 5 Astronomy 2310 General Astronomy Michael Pierce Of ce Physical Sciences 111 Phone 7666102 EMail moierceuwvoedu Course Webpage httpphysicsuwyoedumpierce Of ce Hour Tues 130 330 PM Also by Appointment Lab Instructors Jesse Runnoe Astr 2310 Tues Jan 13 2009 Today s Topics Class Overview How to do well in this class Syllabus Schedule Introductions Who are you Who am 1 Course Prologue Astronomy amp Astrophysics as a science Tour of the Universe Today s Topics Continued Celestial Sphere Concepts and Nomenclature Rising and Setting of Celestial Objects Effects of Latitude Preview of Lab this Week Homework none this week Reading for Next Time How to Do Well in this Class Come to class Read textbook chapters before class Printout and read online notes add to them Ask questions in class Turn in homework on time Turn in labs on time Highlights of the Syllabus Course Content a quantitative survey of Astronomy Prerequisites Trig CalculusI and PhysicsI Lectures Reading done in advance notes on the web Two chapters covered each week Laboratory Starts THIS week Attendance Required Homework Typically AssignedDue on Wednesdays Exams 2 exams nal both inclass and takehome parts Grading Exams 50 Homework Labs 50 Who are You Introductions Please ll out the questionaire I can make adjustments depending on math background Why are you taking the class What do you want to learn from it Who am I Background PhD University of Hawaii Measured expansion of the Universe 0 Inferred Existence of Dark Energy Plaskett Fellow Herzberg Institute for Astrophysics Victoria BC Research Fellow Kitt Peak National Obs Tucson AZ Indiana University University of Wyoming Research Interests 0 Evolution of Galaxies Cosmology Astronomical Instrumentation Come by and talk if you want to hear more Prologue amp a Tour of the Universe Astronomy the study of the Universe Discovery amp application of physical laws to understand how the universe works and came to be Study of the solar system understand the Earth as a planet and its context Study of largerscale properties understand the origin of the Sun other stars and the Universe The Scale of the Cosmos Space is big Really big You just won39t believe how vastly hugely mindbogglingly big it is I mean you may think it39s a long way down the road to the chemist but that39s just peanuts to space Douglas Adams The Hitchhiker 39s Guide to the Galaxy 1979 Sizescales vary by gt 40 orders of magnitude 1040 Space is REALLY Transparent We can see very far only because space is incredibly transparent We can see 10 Billion Light Years Earth s atmosphere seems pretty transparent How far could we see if space were only as transparent as the Earth s atmosphere The Age of the Universe is Finite The Universe is very old but not in nitely 01d about 15 Billion years old The speed of light is very large but not in nite 186000 milessec 300000 kmsec So as we look over increasingly larger distances we look back into the past We can study the history of the Universe The lookback time light travel time What if the Universe were in nitely 01d Scientific Method Assume that the natural world has order and not designed to trick us chaos doesn t rule Expect that science produces change Revision is expected Math provides a highprecision language and cuts down on the BS hard to fake Procedure is formalized to make it ef cient Hypothesis gt Experiment ModelTheory Scientific Method Continued We don t waste time on mundane ideas The Sun rises everyday Why test it Instead study the cuttingedge of science Search for Universal IdeasLaws Universal Law of Gravity Conservation Laws in Physics Assume laboratory physics is same as space physics Astronomy is a Passive Science Few real experiments observations instead Science isn t Perfect but Highly Successful Brief Tour of the Universe Earth 13000 km in diameter Dearth Moon distance d 30 X Dearth 1 1 1001 1 N 1 Dmoon A Dearth Sun d un 400 dmoon 1 AU 150 X 106 km 8 light minj Jupiter dJ 78 X 108 km 52 AU DJ 143000 km 11 Dealth Pluto dP 59 X 109 km 40 AU Nearest Star a Centauri 12 X 1012 km 300000 AU 43 light years Tour Continued Milky Way Galaxy 100000 ly across center 25000 ly from Earth contains 1010 stars Andromeda Galaxy 2 X 106 ly away Virgo Cluster Cluster of 1000 galaxies 50 X 106 ly away Most Distant Galaxies 1010 ly away Edge of Visible Universe 14 X 109 ly away Zoom outward in steps of 100 Enargnd In shnw valallva slze 16000 km 1600000 km From our Text Hon39zons by Seeds The Scale of the Cosmos Zoom outward in steps of 100 Fluln n mum 19st 160000000 km 11 astronomical units 110 AU 11000 AU 1700001y 17 1100000 AU 17 lightyears The Scale of the Cosmos Zoom outward in steps of 100 lanky le Gunny r 17000 ly 1700000 ly 170000000 ly It has taken twelve steps of 100 to go from human scale to the scale of the cosmos How do we quantify this Appropriate units In ordinary life we use inches for small things miles for large Astronomers use meters for small things AU for planets light years for stars Use scienti c notation 10 101 100 102 1000 103 01 10 1 001 10 2 It makes it possible to easily express large and small numbers It also makes dividing and multiplying them easier Powers of Ten Movie Original Powers of Ten Movie imitated but never duplicated Cosmic Voyages video narrated by Morgan Freeman ImaX version at Smithsonian Institute First ve minutes of the 1997 lm Contact Movie Time I Zenith South quot1 celestial pole Celestial Sphere Concepts Reference points Horizon Zenith amp Meridian North and South Celestial Poles Celestial Equator Effects of Latitude Height of Celestial Pole Circumpolar Stars Effects of Earth s Rotation Rising and Setting of Celestial Obects Time and Time Zones Ecliptic 21 I Zenith South quot1 celestial pole Nomenclature HORIZON The horizontal circle which separates the part of the sky visible to you and the part of the sky hidden by the earth Half the Celestial Sphere is visible at any given time but the visible portion depends on latitude and time of day and year ZENITH The point on the sky directly overhead MERIDIAN The circle which starts on the northern horizon runs through the zenith continuing on to the southern horizon It separates the eastern half of the sky from the western half CELESTIAL POLES The points where the extension of the rotation axis of the earth would intersect the celestial sphere The NCP is the North Celestial Pole and the SCP is the South Celestial Pole CELESTIAL EQUATOR The circle around the sky corresponding to the projection of the earth s equator The Celestial Equator divides the Northern Sky from the Southern Sky 23 Effects of Latitude Zenith Altitude of pole Norm North latitude of celestial celestial Zenith the observer I pole I pi e I J North 39 celestial pole At North Pole At Equator At intermediate latitude From Voyages through the Universe by Fraknoi a a1 At the Earth s north pole looking overhead all stars appear to circle around the north celestial pole At the equator Stars on the celestial equator rise in the east move overhead then set in the west The N and S celestial poles are just on your N and S horizons and stars near those points still circle around them But those stars are only visible for the upper half of their circles 24 quot14 Altitude of pole Norm Iatitu e 0 celestial celestlal Zenlth he observer Pole celestial pole At North Pole A Equator At intermediate latitude M Height of the Celestial Pole is your latitude Stars close enough to the north celestial pole are always above the horizon and just circle the pole star CIRCUMPOLAR STARS Stars on the celestial equator rise in the east move higher along a slanted path which crosses the meridian to the south of the zenith then descend and set due west Stars far enough to the south never make it above the horizon K celestial anr x V y v Look39ng norm Looking 933 26 Astronomical Coordinates Vernal equinox Righl ascension 0quot 0m Zenith North 4 th equator The location of an astronomical object can be speci ed via Right Ascension RA and Declination Dec left or in realtime Via Altitude Alt and Azimuth AZ right 27 Lab this Week Celestial Sphere amp Planetarium Visit Understand the geocentric perspective Horizon Zenith amp Meridian Celestial Pole Celestial Equator Effect of Latitude Circumpolar Stars Rotation of the Earth Time and Time Zones Rising and Setting of Celestial Objects Understand Seasonal Motions Origin of Seasons Annual Drift of Stars 28 Homework this Week No Homework this week 29 Reading this Week By Next Thursday Review Math Appendix 9 pg A20 A31 Review Celestial Sphere Appendix 10 pg A32 A36 httpenwikipediaorgWikiCelestial sphere History of Astronomy httpenwikipediaorgwikiHistoryofastronomy By Next Tuesday Chapter 1 Celestial Mechanics At the end of each chapter study the Key Equations amp Concepts 3O
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