TheThe TransitTransit ofof VenusVenus
JohnJohn S.S. ReidReid
CruickshankCruickshank LecturerLecturer inin AstronomyAstronomy DepartmentDepartment ofof PhysicsPhysics
UniversityUniversity ofof AberdeenAberdeen PublicPublic interestinterest
VenusVenus crossingcrossing thethe Telescopic view by US faceface ofof thethe SunSun Naval Observatory of 1882 transit AA rarerare phenomenonphenomenon ¾ Last seen in 1882 ¾ Visible without a telescope ¾ An annular eclipse of the Sun by Venus
Courtesy: www.williams.edu/astronomy/ eclipse/transits/ AstronomicalAstronomical interestinterest
RefineRefine elementselements ofof Venus’sVenus’s orbitorbit usingusing observedobserved timingtiming ¾ 1717th centurycentury resultresult DetermineDetermine thethe absoluteabsolute scalescale ofof thethe solarsolar systemsystem ¾ 1818th centurycentury resultresult FindFind anan accurateaccurate valuevalue forfor 11 AUAU ¾ 1919th centurycentury interestinterest ¾ 11 AUAU isis thethe metremetre--stickstick forfor thethe UniverseUniverse SolarSolar systemsystem andand Kepler’sKepler’s lawslaws
TheThe relativerelative sizessizes ofof thethe orbitsorbits inin thethe solarsolar systemsystem Average areare givengiven byby Kepler’sKepler’s 33rd distance a Sun lawlaw ¾ a3 ∝ (planetary year)2 WhatWhat isis thethe absoluteabsolute sizesize?? Planet a ¾ 1 AU is average distance Mercury 0.387 between Earth and Sun between Earth and Sun Venus 0.723 Earth 1.00 Mars 1.524 Jupiter 5.203 ParallaxParallax ofof aa planetplanet
YouYou cancan findfind thethe distancedistance ofof aa planet,planet, P,P, ifif youyou cancan measuremeasure itsits parallaxparallax angleangle fromfrom separatedseparated points,points, AA andand B,B, onon thethe EarthEarth
Parallax angle B P
Distance A Earth
Definition: Parallax angle = AB/Distance Hence: Distance = AB/Parallax angle MethodMethod waswas triedtried forfor MarsMars
ObserveObserve positionposition ofof MarsMars againstagainst thethe fixedfixed backgroundbackground ofof starsstars
Mars
Earth ¾ DifficultDifficult ¾ ParallaxParallax fromfrom 11 EarthEarth radiusradius isis 2020"" atat bestbest ¾ CanCan useuse EarthEarth’’ss rotationrotation andand observeobserve changechange inin MarsMars’’ positionposition fromfrom eveningevening toto prepre--dawndawn EnterEnter VenusVenus
VenusVenus isis closestclosest planetplanet toto EarthEarth andand inin principleprinciple bestbest forfor parallaxparallax ¾ ClosestClosest isis typicallytypically 0.280.28 AUAU MeasureMeasure parallaxparallax againstagainst backgroundbackground ofof Sun’sSun’s diskdisk ¾ WhenWhen atat greatestgreatest elongationelongation Venus orbit fromfrom SunSun (46(46ºº)),, VenusVenus 46º V ~2.5~2.5 timestimes furtherfurther fromfrom EarthEarth E Sun 0.28 AU TheThe mastermaster planplan
UseUse thethe Sun’sSun’s diskdisk asas aa calibratedcalibrated screenscreen ObserveObserve thethe transittransit fromfrom differentdifferent locationslocations onon EarthEarth MeasureMeasure thethe parallaxparallax ofof VenusVenus
Observed ScaleScale thethe solarsolar systemsystem andand hencehence from determinedetermine 11 AUAU inin termsterms ofof metresmetres St Helena
Observed from Aberdeen
Venus Earth Side view Sun’s disk TheThe refinementrefinement
UseUse thethe curvedcurved edgeedge ofof thethe SunSun andand timetime thethe ingressingress andand egressegress ofof VenusVenus toto deducededuce whichwhich chordchord VenusVenus travelledtravelled onon ¾ ClocksClocks areare moremore accurateaccurate thanthan telescopetelescope anglesangles
Sun AlignmentsAlignments ofof Earth,Earth, VenusVenus && SunSun
TheThe Earth,Earth, VenusVenus && SunSun areare inin aa lineline lookinglooking downdown onon thethe solarsolar systemsystem everyevery 583.9583.9 daysdays (1.6(1.6 yearsyears == 8/58/5 years)years) ¾ VenusVenus orbitsorbits 2+2+ timestimes
¾ EarthEarth orbitsorbits 1+1+ timetime 2
4 E V S
5 3 Earth year: 365.25630 days Venus year: 224.70078 days TheThe problemproblem
Venus’sVenus’s orbitorbit isis tiltedtilted atat 3.393.39ºº withwith respectrespect toto thethe EarthEarth’’ss orbitorbit InIn reality,reality, onlyonly 22 pointspoints inin VenusVenus’’ss orbitorbit areare inin thethe planeplane ofof thethe EarthEarth’’ss orbitorbit ¾ DescendingDescending nodenode NN View from ¾ AscendingAscending nodenode N'N' Earth to N' Venus E V S N 3.39º Plane of Earth’s orbit Line of nodes TheThe opticsoptics
EarthEarth mustmust bebe inin thethe centralcentral shadowshadow conecone ofof VenusVenus toto seesee VenusVenus inin frontfront ofof thethe SunSun
Sun V E
Shadow cone Line of sight to Venus and Sun
SomeSome ofof shadowshadow conecone mustmust bebe inin thethe planeplane ofof Earth’sEarth’s orbitorbit forfor transittransit toto bebe seenseen TheThe transittransit seasonseason
2004 TheThe transittransit seasonseason lastslasts ~3.5~3.5 daysdays
Plane of Venus’s Shadow orbit cone What would be N seen E
Earth’s orbit
~1 day for shadow cone 1.8 days for Earth TheThe alignmentsalignments
SupposeSuppose aa transittransit occursoccurs inin oneone year,year, howhow longlong beforebefore thethe nextnext one?one? EarthEarth--VenusVenus--SunSun alignmentalignment shiftsshifts 2.42.4 daysdays (earlier)(earlier) afterafter 88 yearsyears 2012 ¾ HenceHence afterafter 88 yearsyears aa secondsecond transittransit willwill occuroccur onon thethe otherother sideside ofof thethe nodenode
What would be N seen
Earth’s orbit E
~2.4 days ThenThen what?what?
ThereThere areare nono transitstransits forfor aa longlong timetime ¾ WhenWhen thethe EarthEarth passespasses throughthrough thethe lineline ofof nodes,nodes, VenusVenus hashas alreadyalready beenbeen therethere TheThe ~8~8 yearyear alignmentsalignments occuroccur progressivelyprogressively earlier,earlier, beforebefore thethe EarthEarth reachesreaches thethe nodenode TheThe alignmentalignment ‘spokes’‘spokes’ retreatretreat clockwiseclockwise
2.4° per 8 2 E years V 44 2 E S NN' 3 5 3 5 243243 yearsyears betweenbetween repeatrepeat pairspairs
AlignmentAlignment directionsdirections everyevery 88 yearsyears lessless 2.42.4 daysdays 2, alignment after 1.6 years Alignment 153 ≡ 243 years 32
62 153 Sun N N' 72
123 alignment 72 ≡ 113.5 years 93 V 63 E 33 3, alignment after 3.2 years TheThe ascendingascending nodenode transitstransits
7171 transitstransits (113.5(113.5 years)years) afterafter thethe firstfirst one,one, thethe shadowshadow conecone passespasses closeclose toto thethe 1874 ascendingascending nodenode NN'' & 2117 ¾ AnotherAnother pairpair ofof transitstransits willwill bebe seenseen
What would be N' seen Earth’s orbit
E Venus moving shadow cone SeriesSeries ofof transitstransits everyevery 243243 yearsyears
AscendingAscending nodenode seriesseries ReturnReturn toto 20042004 transittransit
(2012 transit occurs 2.4 days earlier, mainly during our night) ExpectedExpected sightsight
CloudsClouds allowing!allowing!
Courtesy: http://www.eso.org/outreach/press- rel/pr-2004/images/vt-anim.gif Venus’Venus’ tracktrack acrossacross thethe SunSun
WhyWhy isis Venus’Venus’ tracktrack 8.78.7ºº toto thethe ecliptic?ecliptic?
→ 29.78 km s-1 E N → 48.55 km s-1 ↓ 2.87 km s-1 0.52×106 km VenusVenus tracktrack acrossacross thethe SunSun isis thethe EarthEarth’’ss tracktrack acrossacross thethe shadowshadow conecone ¾ VelocityVelocity ofof EarthEarth relativerelative toto shadowshadow conecone ¾ MaxMax durationduration ~7.6~7.6 hrhr 19 km s-1 8.7º ¾ 20042004 transittransit ~~ ¾¾ maxmax ~~ 55½½ hrhr Illustrating the Earth & central parallax in transits shadow cone to experienced at Parallax effects scale different latitudes on Earth Aberdeen (57ºN)
St Helena (15ºS)
Each point in the shadow Equatorial cone corresponds rotational speed to Venus 0.46 km s-1 appearing at a different place on the Sun’s disk DetailsDetails ofof JuneJune 88thth transittransit
Sun Approximate BST timings shown for Aberdeen Ecliptic
0640 BST 7 8 9 10 11 12 ObservingObserving thethe SpectacleSpectacle
DirectlyDirectly –– useuse eclipseeclipse glassesglasses ¾ VenusVenus willwill bebe aa veryvery smallsmall dotdot
ProjectProject usingusing binoculars/telescopebinoculars/telescope PhotographPhotograph withwith ~200~200 mmmm telephototelephoto lens,lens, oror longerlonger ¾ rememberremember thethe solarsolar filter!filter! JeremiahJeremiah HorrocksHorrocks (1619(1619 –– 1641)1641)
Horrocks predicted the 1639 transit and observed it, as did his friend Wm Crabtree Horrocks deduced improved orbital parameters for Venus
William Crabtree, Horrock’s friend 24th Nov 1639 Old-style calendar JamesJames GregoryGregory (1638(1638 –– 1675)1675)
BrilliantBrilliant mathematicianmathematician && astronomerastronomer fromfrom DrumoakDrumoak FirstFirst suggestedsuggested thatthat observationobservation ofof thethe transittransit ofof VenusVenus couldcould determinedetermine thethe scalescale ofof thethe solarsolar systemsystem
Courtesy: University of Aberdeen EdmondEdmond HalleyHalley (1656(1656 –– 1742)1742)
St Helena Halley observed the transit of Mercury and worked out the details of finding the solar distance from the Transit of Venus observations
Plantation house 1812 66thth JuneJune 17611761 transittransit
AA bigbig internationalinternational CharlesCharles MasonMason (1730(1730 -- efforteffort 1786)1786) JeremiahJeremiah DixonDixon (1733(1733 -- 1779)1779)
Transit of Venus from ceiling of the Paris Observatory Nevil Maskelyne (1732 – 1811) unsuccessful at St Helena
http://www.bdl.fr/Granpub/Promenade/ pages6/608.html 33rdrd JuneJune 17691769 TransitTransit
CharlesCharles Green’sGreen’s && JamesJames Cook’sCook’s James Cook observationsobservations fromfrom TahitiTahiti werewere successfulsuccessful
Pictures courtesy: http://www.transitofvenus.org/historic.htm
Venus Point DavidDavid GillGill (1843(1843 –– 1914)1914)
SirSir DavidDavid GillGill KCB,KCB, FRS,FRS, PRAS,PRAS, etc.etc. OneOne ofof thethe 1919th century’scentury’s foremostforemost observationalobservational astronomersastronomers HerHer Majesty’sMajesty’s astronomerastronomer atat thethe CapeCape ofof GoodGood HopeHope EnterEnter LordLord LindsayLindsay
FounderFounder ofof thethe DunDun EchtEcht observatoryobservatory ¾ ~15~15 kmkm WestWest ofof AberdeenAberdeen ThisThis observatoryobservatory waswas amongamong thethe bestbest equippedequipped inin thethe world,world, turningturning outout highlyhighly professionalprofessional astronomyastronomy Heliometer dome ↓
DavidDavid GillGill atat thethe CapeCape ObservatoryObservatory ResultsResults
1761:1761: “solar“solar parallax”parallax” 8.288.28"" toto 10.20"10.20" ¾ Equivalent solar distances (159 – 129)×106 km 1769:1769: “solar“solar parallax”parallax” 8.438.43"" toto 8.80"8.80" ¾ Equivalent solar distances (156 – 149)×106 km 1919th centurycentury rere--analysisanalysis ¾ Encke (1825): 8.577" z Widely used but later discredited EndEnd 1919th century:century: “solar“solar parallax”parallax” 8.788.78"" ModernModern value:value: “solar“solar parallax”parallax” 8.7941488.794148"" ¾ Equivalent solar distances 149.598×106 km ReferencesReferences
David Sellers The Transit of Venus [Maga Velda Press, Leeds, 2001] Eli Maor June 8 2004: Venus in transit [Princeton Univ. Press, 2000]
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit4/venussun.html http://www.transitofvenus.org/historic.htm http://www.venus-transit.de/links.html library of refs
VT-2004 international observing programme seeking active participation of amateurs from around the globe ¾ http://www.vt-2004.org/ PhotographicPhotographic animationanimation ofof thethe 18821882 transittransit
http://skyandtelescope.com/observing/objects/sun/article_1187_1.asp