Astronomy: Principles and Practice PDF
Preview Astronomy: Principles and Practice
Chapter 1 Naked eye observations 1.1 Introduction Theetymologyoftheword‘Astronomy’impliesthatitwasthe disciplineinvolvedin ‘thearranging of the stars’. Today we might say that astronomy is our attempt to study and understand celestial phenomena, part of the never-ending urge to discover order in nature. We do not know who were thefirstastronomers—whatwedoknowisthatthescienceofastronomywaswelladvancedinparts of Europe by the middle of the third millennium BC and that the Chinese people had astronomical schoolsasearlyas2000BC. Inallages, fromthe burgeoningof man’sintelligence,therehavebeen people fascinated by the heavensand their changingaspect and these people, as far as their cultural environmenthasallowedthem,havetriedtoformulatecosmologies.Wearenodifferenttoday. Nowadays,the word‘Astrophysics’isalso usedtodescribethe studyofthecelestialbodies. In fact, many astronomers use both terms quite generally and it is not infrequent to find Departments of Astronomyand Astrophysicswithin educationalestablishments. Thequestion maywell be asked ‘What is the difference between Astronomy and Astrophysics?’ Very loosely, Astronomy might be definedasthe subjectof the‘where andwhen’ relatedto the descriptionof a celestialbodywith the ‘whyandhow’beingcoveredmorebyAstrophysics.Ratherthantryingtoprovideahardandfastrule fortheterminology,wewillsimplyuseAstronomytocoverallaspectsofthedescriptionoftheskies andtheUniverse. IfourcurrenttheoriesoftheUniversearenearerthetruth,itisprobablynotthatourintelligence hasincreasedinthepastsixmillennia.Itismorelikelythatthemainfactorhasbeenthediscoveryand developmentofthe‘scientificmethod’,whichhasledtoourpresentcivilizationbasedonthefloodof technologicaladvantagesprovidedbythismethod. Thishasenabledscientistsinfargreaternumbers than ever before to devote their lives to the study of the heavens, assisted by telescopes, computers, space vehicles and a multitude of other equipment. Their attempts to interpret and understand the wealthofnewinformationprovidedbythesenewinstrumentshavebeenaidedbyalliedsciencessuch asphysics,chemistry,geology,mathematicsandsoon. We must remember, however, that for more than nine-tenths of the last five thousand years of our study of the heavens, we have had to rely on the unaided eye. The Mediterranean people who set the constellations in the sky, the Babylonians, Egyptians and Greeks, the Arabian astronomers whoflourishedduringtheDarkAgesofPost-RomanEurope,theChinese,theMayanandotherearly Americanastronomers,allbuilttheirtheoriesoftheUniverseonnakedeyeobservations. Andsowe beginby followingin their footstepsand seeing whatthey saw as they observedovera few minutes (see section1.2),overafewhours(seesection1.3),overa month(see section1.4)oroveratleast a year(seesection1.5).Inthisway,wewillfinditeasiertounderstandwhytheircosmologicaltheories wereformulatedintheirparticularways. 3 4 Nakedeyeobservations 1.2 Instantaneous phenomena 1.2.1 Day Duringthedayavarietyofphenomenamaybeseen. InaparticulardirectionliestheSun,sobrightit isimpossible(anddangerous)tolookdirectlyatit. Ingeneral,theskybackgroundisblue. TheMoon mayalsobevisible,havingadistinctshapethoughcertainlynotcircular. IftheSunhasjustsetorif dawnisnotfaraway,thereissufficientdaylighttoseeclearly.Wecallthisconditiontwilight. On the horizon opposite to the twilight glow, a dark purple band is sometimes seen. This area correspondstoazoneontheskywhichiscutofffromthedirectsunlightbytheEarthandisreceiving verylittlelightbyscatteringfromtheatomsandmoleculesintheatmosphere. Itcorresponds,infact, totheshadowoftheEarthinthesky. Itspresencetellsusoftheextremepurityandlowhumidityof thelocalatmosphere.Needlesstosay,itisveryrarelyseeninBritain. To the ancients, clouds, wind, rain, hail and other atmospheric phenomena were inadequately distinguished from what we term celestial events. Our civilization includesthem in meteorology, a sciencequitedistinctfromastronomy,sothatweneednotconsiderthemfurther,excepttoremarkthat astronomers’observationshave,untilrecently,beendependententirelyupongoodweatherconditions being available. With the developmentof radio telescopes and the fact that other equipmentcan be placedinartificialsatellitesandoperatedabovetheEarth’satmosphere,thisdependenceisnolonger complete. 1.2.2 Night If seeing conditions are favourable, a view of the night sky providesa far wider variety of celestial phenomena.IftheMoonisvisible,itsbrightnesswilldominatethatofallotherobjects. Itsshapewill becrescentorgibbousorevencircular.Atthelastcondition,itsapparentdiameterisveryclosetothat oftheSun.Toanyonewithreasonableeyesight,itssurfacewillnotbeevenlybright.Areasdarkerthan theirsurroundingswillbenoticed,sothatthefancyofprimitivemancouldseea‘ManintheMoon’,a ‘BeautifulLady’ora‘Rabbit’,sketchedoutbythesefeatures. InadditiontotheMoon,sometwotothreethousandtiny,twinklingpointsoflight—thestars—are seen,ranginginbrightnessfromoneseasilyvisiblejustaftersunsettoonesjustvisiblewhentheMoon is below the horizonand the sky backgroundis darkest. Carefulcomparisonof one brightstar with another shows that stars have differentcolours; for example, in the star pattern of Orion, one of the manyconstellations,BetelgeuseisaredstarincontrasttotheblueofRigel. Theapparentdistribution ofstarsacrossthevaultofheavenseemsrandom. Withtheeyesbecomingaccustomedtothedarkness,afaintbandoflight,theMilkyWay,catches the observer’s attention. Modern astronomers, with the aid of telescopes, know that this luminous region stretching from horizonto horizonacross the sky in a great circle is made up of a myriad of starstoofainttoberesolvedwiththenakedeye.Totheancientobserver,itspresenceinspiredallkinds ofspeculations,noneofthemverifiable. Oneortwoofthetinypointsoflightmaydrawacloserscrutiny. Theyshinesteadily,incontrast to the twinklingof the starsandtheyare amongthe brightestofthe star-like objects. Theremustbe somereasonwhytheyaredifferent.Ifourobserverisgoingtowatchforafewhours,attentionwillbe returnedtotheseobjects. 1.3 A few hours 1.3.1 Day Theheavensareneverstatic. The slowly-movingshadowcastbyan uprightrodora boulderortree reveals the Sun’s movementacross the sky. If observation is kept up throughoutthe day, the Sun is Amonth 5 seentoriseabovetheeasternhorizon,climbuptheskyinacircleinclinedatsomeangletotheplane definedbythehorizonandculminate,i.e.reachamaximumaltitudeabovethelinejoiningthenorth tothesouthpoints,thendescendinamirrorimageofitsforenoonpathtosetonthewesternhorizon. IftheMoonisseenduringthatday,itwillappeartoimitatetheSun’sbehaviourinrisingandsetting. 1.3.2 Night Asdarknessfalls,thefirststarsbecomevisibleabovetheeasternhorizon. Withtheendingoftwilight the fainter stars can be seen and, as the hours pass, the stellar groupsrise from the eastern horizon, reachtheir maximumaltitudelike the Sun, thenset orbecomedim andinvisibleas daylightreturns. The impression of being on a flat plane surmountedby a darkrevolvingbowl to which the stars are attachedisstrong,especiallywhenitisseenthattherearemanystarsinaparticularregionofthesky thatrevolve,neverrising,neversetting,aboutahuborpivot. Thesestarsaresaidtobecircumpolar. Itis then clear thatthose otherstars thatrise andset do so simply becausetheir circularpathsabout thispolearesobigthattheyintersectthehorizon. TheMoonalsorevolvesacrossthisupturnedbowl.AlthoughtheMoonappearstohaveanangular motionacrossthe skysimilar to thatof thestars, carefulobservationovera few hoursrevealsthatit movesslightlyeastwardsrelativetothestarbackground. Occasionally a brightobject, called a meteor, shootsacross the sky in a second, lookinglike a fast-movingor ‘falling star’. It may be too that faintly luminous sheets are seen, hangingdown the bowloftheheavenslikegreatcurtains. ThesearetheauroraeW1.1. Ifourobserveriswatchingatanytime afterOctober4, 1957,it isquitelikelythatoneormore faintspecksoflightwillbeseentocrossthesky,takingafewminutestodoso,theirpresencegiving reminderthatman-madesatellitesarenowinorbitabouttheEarth.Indeed,oneofthelatestsatellites— theInternationalSpaceStationW1.2—isexceedinglybright—asbrightasthebrightestplanetVenus— andbearstestamenttothecontinualdevelopmentofmannedorbitinglaboratories. 1.4 A month Themonthisthenextperiodofanysignificancetoourwatcher. Duringthistime,theideasaboutthe heavensand their movementschange. It will be noted that after a few nightsthe first groupof stars seen above the eastern horizon just after sunset is markedly higher at first sight, with other groups underitbecomingthefirststarstoappear.Indeed,afteramonth,thefirstgroupisaboutthirtydegrees abovetheeasternhorizonwhenthefirststarsareseenaftersunset.ItisthenapparentthattheSunmust shiftitspositionagainstthestellarbackgroundastimepasses. Therateisslow(aboutonedegreeper day—orabouttwoapparentsolardiameters)comparedwithitsdaily,ordiurnal,movementaboutthe Earth. The Sun is not the only object to move independently of the stellar patterns. A few nights’ observationsoftheMoon’spositionagainstthestars(itssiderealposition)showthatittoomovesbut atamuchfasterrate,aboutthirteendegreesperday,sothatitisseentomakeonecompleterevolution of the stellar background in twenty-seven and one-third days, returning to the same constellation it occupiedat the beginningof the month. In addition, its shape changes. From a thin crescent, like a reversed ‘C’, seen in the west just after sunset, it progresses to the phase we call first quarter about seven dayslater. At this phase, the Moon’sterminatoris seen to be almost a straightline. Fourteen daysafternewmoon,itisfullandatitsbrightest,appearingatitshighestintheskyaboutmidnight. Seven days later it has dwindled to third quarter and rises before the Sun, a pale thin crescent once more,amirrorimageofitsphasejustafternewmoon.Twenty-nineandone-halfdaysafternewmoon, itisnewoncemore. ItwasafairlyeasymatterfortheancientstoascertainthattheMoonwasnearertheEarththanthe stars. FrequentlytheMoonwasseentoblotoutastar,occultingituntilitreappearedattheotheredge 6 Nakedeyeobservations Figure1.1.Thechangeinlengthofashadowaccordingtothetimeofdayandthetimeofyear. oftheMoon’sdisc. AndoccasionallytheMoonwaseclipsed,theEarthprogressivelyblockingoffthe sunlightuntilthesatellite’sbrightnesshaddiminishedtoadull,copperyhue. Anevenmorealarming, butrarer,occurrencetookplaceattimesduringdaylight: theMoonrevealeditsunseenpresencenear theSunbyeclipsingthesolardisc,turningdayintonight,causingbirdstoseektheirnestsandcreating superstitiousfearinthemindofprimitiveman. Theobserverwhostudiesthenightskyforamonthorsoalsodiscoverssomethingnewaboutthe oneortwostar-likeobjectsnotedthatdonottwinkle. Carefulmarkingoftheirpositionswithrespect to neighbouringstarsshowsthattheytooare movingagainstthe stellar background. Theredoesnot seemtobemuchsystem,however,aboutthesemovements. Inthecourseofamonth,onemaymove inthedirectiontheMoontravelsin,whileasecondobject,inanotherpartofthesky,maymoveinthe oppositedirection.Indeed,towardstheendofthismonth’sobservingsessions,eitherobjectmaycease tomove,seemalmosttochangeitsmindandbegintoretraceitsstepsonthecelestialsphere. These wanderers, or planets (‘planet’ is a Greek word meaning ‘wanderer’), are obviously of a different naturefromthatofthefixed,twinklingstars. 1.5 A year A year’spatientobserving,bydayandnight,providesthewatcherwithnewconcepts. Forexample, theSun’sdailybehaviour,movingeasterlybitbybit,islinkedtotheseasonalchanges. Eachday,formostobservers,theSunrises,increasesaltitudeuntilitculminatesonthemeridian atapparentnoon,thenfallsdowntheskyuntilitsetsonthewesternhorizon. We haveseenthatthis progresscanbestudiedbynotingthechangesindirectionandlengthoftheshadowcastbyavertical rodstuckintheground(seefigure1.1). As the days pass, the minimum daily length of shadow (at apparent noon) is seen to change, becoming longest during winter and shortest during summer. This behaviour is also linked with changes in the rising and setting directions of the Sun. Six months after the Sun has risen between north and east and setting between north and west, it is rising between south and east and setting Ayear 7 betweensouthandwest. Anothersixmonthshastopassbeforethesolarcycleiscompleted,withthe Sunoncemorerisingbetweennorthandeastandsettingbetweennorthandwest. All this could be explained by supposing that the Sun not only revolved with the stars on the celestialsphereaboutthe Earthin oneday(itsdiurnalmovement)butthatitalso movedmuchmore slowly along the path among the stars on the celestial sphere, making one revolution in one year, returningtoitsoriginalpositionwithrespecttothestarsinthatperiodoftime. Wehavealreadyseen thattheobserverwhonotesoveramonthwhatgroupofstarsisfirstvisibleabovetheeasternhorizon aftersunsetwillhavealreadycometotheconclusionthattheSunmovesrelativetothestars. Nowit isseenthatthereisaregularsecularprogressionrightroundthestellarbackgroundandthatwhenthe Sunhasreturnedtoitsoriginalstellarposition,theseasonalcycleisalsocompleted. The Sun’s stellar route was called the ecliptic by the ancients. The groups of stars intersected by this path were called the housesof the Zodiac. The ecliptic is foundto be a greatcircle inclined atabout231 degreestotheequator,thegreatcircleontheskycorrespondingtotheprojectionofthe 2 Earth’sequator,intersectingitattwopoints,thevernalandautumnalequinoxes,180degreesapart. Itwasquitenatural,then, fortheancientstoworshiptheSun. Notonlydiditprovidelightand warmth by day against the evils of the night but, in addition, its yearly progression was intimately linkedtotheseasonsandsoalsotoseedtimeandharvest.Itwas,therefore,necessarytokeeptrackof progresstouseitasaclockandacalendar.Tothisend,thescienceofsundial-makingbegan,ramifying from simple obelisks that throw shadows on a fan of lines radiating from their bases, to extremely ingeniousand complicatederectionsin stone and metal. Up to the 19thcentury, these constructions rivalledmostpocket-watchesinaccuracyastimekeepers. For calendrical purposes, lines of standing stones could be set up, pointing to the midsummer, midwinterandequinoctialrisingandsettingpointsoftheSun. Inthe British Isles, therestill remain hundredsofsuchsolarobservatories,witnessestoourforefathers’preoccupationwiththeSun-god. Theobserverwhowatchesthenightskythroughoutayearcountsaboutthirteenrevolutionsofthe stellarbackgroundbytheMooninthattime.Overthatperiodoftime,itisnotapparentthatanysimple relationshipexistsbetweenthesiderealperiodofrevolutionoftheMoon,theperiodofitsphasesand the year (the time it takes the Sun to performone complete circuit of the ecliptic). That knowledge comesaftermuchmoreextendedobservation,certainlymeasuredindecades. Itwouldbe noticed, however,thatthe Moon’ssiderealpath is verylittle inclinedto the ecliptic (aboutfivedegrees)andifrecordswerekeptofthepointsoftheeclipticcrossedbytheMoon,itmight be realizedthatthese pointswere slippingwestwardsata rate ofabouttwenty degreesperyear (see figure1.2). More information, too, would be acquired about the star-like objects that do not twinkle and whichhavebeenfoundinthe courseofamonthto havea slowmovementwithrespecttothestellar background.Theseplanets,liketheMoon,wouldneverbeseenmorethanafewdegreesfromtheplane oftheecliptic,yetmonthaftermonththeywouldjourneythroughconstellationafterconstellation. In thecaseofoneortwo,theirpathswouldincludenarrowloops,thoughonlyoneloopwouldbeobserved foreachoftheseplanetsinthecourseoftheyear. The year’s observations would not add much to the observer’s knowledge of the stars, except to confirmthattheirpositionsand brightnessesrelativeto each otherdidnotalterand thateachstar, unliketheSun,haditsownfixedrisingandsettingdirection,unlessitwascircumpolar. Itispossible, however,thatinayear,theextra-carefulwatchermighthavecausetowonderiftheconclusionsabout stars were withoutexceptionfor, byregularcomparisonof the brightnessof onestar with respectto that of neighbouringones, it might be discovered that a few stars were variable in brightness. This wascertainlyknowntotheArabianastronomersoftheMiddleAges. Theappearanceofanovamight even be observed, i.e. a star appearingin a position where one had not been previously noted. This occurrencemightwellleadto doubtaboutthe knowledgeofthe nowfamiliarconstellations—inany eventitcouldbringaboutthedecisiontomakeastarmapforfutureuseifthephenomenonhappened again. Itisalsopossiblethatinthecourseofayeartheobservermightseeacomet,astar-likeobject 8 Nakedeyeobservations ◦ Figure1.2.TheMoon’ssiderealpathcrossestheecliptictwiceeachmonthatanangleofabout5 .Forsuccessive ◦ lunationsthecrossingpointsmovewestward,coveringabout20 overayear. TheConstellationofLeoisshown togiveanindicationofthescaleofthemovement. withalongluminoustail. Thedevelopmentofthetailandthemovementofthecometheadcouldbe detectedfromnighttonight. Our observer by now must have come to tentative conclusions concerning the heavenly phenomena studied and noted. The interpretations, and the use made of the world-picture, will be constrainedby thecultureof the time. A manof Neolithictimesand a GreekofAthens’ goldenera woulddevelopentirelydifferentcosmologiesfromidenticalobservations. Andahunterorfarmerhas differentneeds,astronomicallyspeaking,fromasailor. Chapter 2 Ancient world models Firsttheorieswerenecessarilysimple.TheEarthwasaflatplanewithrivers,hills,seasandland,fixed, eternal.Theheavenlybodiesrevolved,passingfromeasttowest.Butifthelandcontinuedindefinitely, howcouldtheSunthatsetinthewestbethesameSunthatroseintheeastthenextmorning?Perhaps, theBabyloniansreasoned,theEarthwasflatbutfinitewitha circleofoceanbeyondwhicha ringof mountainssupportedtheheavens,thefirmament.Then,ifdoorswereprovidedinthebaseofthisgreat solidhalf-sphereontheeasternandwesternsides,thecelestialbodieswouldbeabletoslipthroughthe westerndoorsonsettingandbetransportedinsomemiraculouswaytotheeasttoreappearasordained. TheBabylonianswereskilledastronomersthoughtheirworld-picturewasna¨ıve. Theyobserved the positions of the Sun, Moon, planets and stars for many centuries with great accuracy. They found that they could predict eclipses. Their observations were motivated by their belief that the future of human beings could be predicted from celestial configurationsand events such as eclipses or the appearanceof comets. Because of this, kings kept courtastrologers and the wealthy paid for horoscopes. This belief in astrology, foundin all nations, should have withered away with alchemy and the search for the philosopher’s stone but even today there are many who set great faith in this pseudo-science.Itisperhapsneedlesstosaythatmodernastronomydemonstrateshowludicroussuch beliefsare. The Egyptians, astronomers almost as skilled as the Babylonians, had equally simple world- pictures. They noticed that the yearly inundation of the Nile valley coincided with the days when the star Sirius could be seen best in the morning twilight. This linking of celestial and earthly eventsspurredontheirdevelopmentofastrologyandbroughtreligionintothe picture. TheSun-god descendedatnight,passingbeneaththeEarthtovisitthedead. Farming people were more interested in the solar cycle since it was linked with seed time and harvest. SeafaringpeopleslikethePhoeniciansandtheMinoansusedtherisingandsettingdirections ofthestarsasnavigationalaids.Itmaywellhavebeenasanaidtomemorythatthestarsweregrouped inconstellations,embodyingmythscurrentatthattime. As is to be expected, the ancient Chinese civilizations produced schools of astronomy and cosmologicaltheories. SeriousChineseastronomyprobablybeganpriorto2000BCalthoughdetails of events in that era are largely legendary. The story of the two Chinese astronomers, Ho and Hi, executedforfailingtopredictaneclipseoftheSunin2137BCispossiblyapocryphalandmayrefer to two astronomicalcollegesof a muchlater date destroyedin civil strife. Reliable historicaldetails beginabout1000BC.Afarmingpeoplerequiredacalendarandsothelengthsofmonthandyearwere quicklyascertained.Ayearof3651 dayswascertainlyusedby350BC. 4 By that date, the Chinese constellation figures, 122 in number and quite different from those handeddowntousbytheGreeks,hadbeenmappedout,theSun’spath—theecliptic—beingdivided into 12 regions. The size ofa regionwas notonlyconnectedwith the heavenlyarc inhabitedby the Sun each month but also with the yearly journeyof the planet Jupiter. The other planetary motions 9 10 Ancientworldmodels werealsostudied. Asinthewest,apseudo-scienceofastrologydevelopedfromsuchstudies. China wasthecentreorhuboftheflatEarthwithheavenlyandhumaneventsincloseharmony:notonlydid celestialeventsguideand controlmen, in particulartheEmperorandhis courtbutthe decisionsand actionsofsuchpowerfulrulersinfluencedthestateofHeaven. As mathematical knowledge grew and more accurate astronomical instruments for measuring altitudes and angles were developed in succeeding centuries, the movements of the Sun, Moon and planets were systematized in remarkably accurate tables for prediction purposes. Cometary appearanceswerenoted, amongthemseveralapparitionsofHalley’scomet, andbythe 14thcentury ADthestateofChineseastronomycomparedfavourablywiththatoftheArabsintheWest. Invariousotherplaceswhereacivilizationhaddeveloped,astronomicalschoolsflourished. The ravagesoftimeandbarbarismhavesadlydestroyedmostoftheworksofsuchschools,thoughhappily some tracesremainto tellusof theheightsof thoughttheirpractitionersachieved. Forexample, we shallseelaterhowingeniouswerethestepsmegalithicmantooktokeeptrackoftheSunandMoon. ThisremarkablecivilizationflourishedinWesternEuropeinthethirdandsecondmillenniaBC. Observations of eclipses were also recorded by early American Indians as, for example, by Mayans. A sundial remaining in the ‘lost city’, Macchu Piccu, provides us with evidence that the Incasof Peruused solar observationsto some purpose. The‘Puerta delSol’ atTiahuanaco,Bolivia, tellsusofsolarobservationspriortotheIncas. However, very few of the ideas and notions of astronomy and cosmology from any of these civilizations have had an influence on the development of our understanding of the astronomical Universe.OurstartingpointsfindtheiroriginsmainlyinancientGreece. Acompletelynewdepartureinmankind’scontemplationandinterpretationoftheheavenscame with the flowering of Greek civilization. Many of their thinkers had extraordinarilyoriginal minds, were mentally courageous and devoted to rational thought. They were not afraid of questioning cherishedbeliefsandoffollowingunsettling,disturbingtrainsofthought. Many of them dismissed the ‘common-sense’ picture of solid, flat Earth and god-controlled Heaven. They saw that a spherical Earth poised in space solved a lot of problems. Those stars and planets not seen during the night were simply on the other side of the Earth. Stars were not seen duringthedaybecausethedazzlingbrightSunblottedouttheirfeeblelight. TheMooncausedsolar eclipses. Pythagoras,inthe6thcenturyBC,taughtthatthemovementsofalltheheavenlybodieswere compoundedofoneormorecircularmovements. In the next century, Philolaus, a follower of Pythagoras, suggested the bold idea that the Earth wasnotthecentreoftheUniverseand,indeed,thatitmoved. AtthecentreoftheUniversetherewas agiganticfire. AroundthisfirerevolvedtheEarth,Moon,Sunandplanetsinthatorder,incirclesof varioussizes. HealsopostulatedabodycalledtheAnti-Earthtobringthetotalofmovingbodiesup to the sacred numberof ten. This Anti-Earth revolved aboutthe centralfire within the Earth’s orbit andwasneverseenfromtheEarthbecausetheEarthfacedoutwardstowardsthehomeofthegods— Olympus—situatedbeyondthesphereofthefixedstars. PhilolausalsobelievedthattheSunwasnot self-luminousbutshonebythelightitabsorbedfromOlympusandthecentralfire. In contrastto this, Anaxagorastaughtthat the Sun was a mass of glowingmetalcomparablein sizewithGreeceitself. Aristarchus,inthe3rdcenturyBC,agreedwithPhilolausthattheEarthmoved andtaughtthatitrotatedonitsaxis,thusexplainingthediurnalmotionoftheheavens. Moreover,he said,theSunisastarandtheEarthrevolvesroundit,allotherstarsbeingverymuchfartheraway. Aristarchus, like Anaxagoras, had ideas about the relative sizes of Sun, Moon and Earth. The Sun’sdiameterhad to be aboutseventimesthe diameterof the Earth, a figurefar removedfromthe modernonebutembodyingtherightidea,namelythattheEarthismuchsmallerthantheSun. Eratosthenes of Alexandria, living about 230 BC, used solar observations and a knowledge of geometryand geographyto calculate the circumferenceof the Earth, obtaininga value within a few percentoftoday’sacceptedfigure. HeknewthatatthesummersolsticetheSunpassedthroughthezenithatSyeneinUpperEgypt,
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