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38 Winter2011-2012 21stCenturyScience&Technology
Butconsiderewel,thatIneusurpenattohavefoundethiswerkofmylabourorofmynengin.InambutalewdcompilatourofthelabourofoldeAstrologiens,andhavehittranslatedinmynEnglishonlyforthydoctrine;&withthisswerdshalIsleenenvye.
—Chaucer,TreatiseontheAstrolabeca.1391
IntroductiontotheAstrolabeThere is a tale, both apocryphal and
scatological, thatClaudiusPtolemy, theAlexandrian astronomer (ca. 90 A.D.-168A.D.)whoseideasdominatedastro-nomicalthoughtforwelloveramillen-nium (Figure 1), got the idea for theplanispheric astrolabe while riding adonkey.Thearmillaryspherehewascar-ryingfellandwasflattenedbythedon-key’s hoof into a pile of fresh donkeydung.Uponinspectingtheresultingim-pression, a candle ignited in hismind,leadingtothecreationofanastronomical instrument souseful,thatitoutlastedPtolemaicastrono-myitself.
Becausethefirstpreservedastro-labesaremadeofbrassanddatedsincethetimeofMuhammad,andthefirstknowntreatiseontheastro-labe was written well before Mu-hammad,itisunknownwhenandwhere the astrolabe was born—surely not full-grown and fullyadorned,likeAthenafromtheheadof Zeus. Early astrolabes probablylong predated the technology foraccurately rendering the requisitelines and arcs onto brass. Paper,cloth,andwoodweremore likelythemediaforthefirstastrolabes.
TheMuslimsattribute theastro-labe to the Greeks, and certainlyGreekgeometryinformeditsdevel-opment. As Greeks moved East,conquering and occupying areas
suchasBactria,andareas in IndiaduringandafterthereignofAlexan-dertheGreat,theytookGreekcul-tureandtechnologywiththem,andthey maintained contact with theMediterraneanGreeks.
However,whentheRomanscon-queredtheGreeksduringtheThirdPunicWar,itseemsasifasemi-per-meablemembranewereappliedbe-tweentheEasternGreekareassuchas Bactria, and the Roman strong-holdstotheWest.MuchGreeksci-ence,especiallynewdevelopments,could not penetrate back into thatarea,butflowedfreelyintopartsofIndiaandmuchofAsiaMinorandNorthAfrica.
Thesenewdevelopments,aswellasolderknowledgedestroyedintheWest, became the heritage of thepeoplewhowould fallunder the influ-enceoftheMuslims.Whetherbecauseof
RomanindifferenceorGreekreluctance,suchdiscoveriesas theplanisphericas-
trolabeneverpenetratedbackintotheRomanEmpireintheWest,buthadtoawait theMuslimconquestofSpainathousandyearslatertobere-introducedintoEurope.
During thatmillennium, the as-trolabe and countless other trea-sures of Greek culture exclusivelyenrichedtheEast.Itwastherethattheplanisphericastrolabereacheditsmaturityasanastronomical in-strument(Figure2).
AnAnalogComputerThe planispheric astrolabe is a
two-dimensional analog computerforsolvingproblemsrelatedtoce-lestial movements: time, the sea-sons,andstarpositions.Itisalsoanobserving instrument; the back oftheastrolabeissetup,amongotherthings,tomeasurealtitudesofstarsandplanets,includingthedaytimeSun.Theastrolabepacksalotofin-formationintoaverysmallspace—even more than an adventurer’s
Figure1PTOLEMYWITHANARMILLARY
SPHEREThispaintingofPtolemywithaarmillaryspheremodelisbyJoosvanGhentandPe-droBerruguete,ca.1476.
ASTRONOMY REPORT
HowtoConstructanAstrolabe,UsingYourPCbyChristineCraig
Figure2PLANISPHERICASTROLABE
A planispheric astrolabe of Persian origin, ca.1590,ondisplayat thePutnamGallery in theHarvardUniversityScienceCenter.
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21stCenturyScience&Technology Winter2011-2012 39ASTRONOMYREPORT
wristwatch(althoughatleastonemanu-facturer—Ulysse-Nardin—madeawrist-watchinthe1980sthatwasafunctional,automated astrolabe.You can buy oneforonly$27,500online).
TheplanisphericastrolabeisreallyjustastereographicprojectionofallobjectsofinterestontheCelestialSphere(onelikePtolemy’sarmillarysphere,completewitheclipticandusefulstars)toaplanecoinci-dent with the Equator of the CelestialSphere. (However,aglanceat theworkon theastrolabeof the9thCenturyPer-sian astronomer al Farghani shows hisplanetangenttotheNorthPoleoftheCe-lestialSphere).TheEquatoroftheEarthisunderstood to be coincident with thatplaneaswell.Theoriginpointforthepro-jectionistheSouthPoleoftheCelestialSphere,aconventionconvenientforthoseresidingnorthoftheEquatoronEarth.
Thestereographicprojectionwasdis-covered by the ancient Greeks, and isusuallyattributedtoHipparchus(ca.190B.C.-120 B.C.), although Apollonius ofPerga(ca.262B.C.-190B.C.)couldwellhavedeveloped it. It isausefulway tomaptheheavensontoaflatsurfacewhilepreserving both circles and angles be-tweenobjects,asmeasuredonthethree-dimensionalsphere.
The astrolabe is made up of severalmoving parts securely attached to themater,whichholdsandprotectstheoth-erparts,andalsocontainsessentialde-greeandtimeorotherscalesontheouterraceorlimbofboththefrontandback.
Thebackof theastrolabematercon-tains degree, calendar, and zodiacalscales(Figure3).Astrolabemakersoftenaddedmanyusefultablesforsolvingas-tronomical, time, and trigonometricproblems.Thebackalsocontainsamov-ablepointer,thealidade,attachedtothecenter,withsightsforobservingaceles-tialobjecttofinditsaltitude.
Todothis,onewouldhangtheastro-labe on the thumb with the arm heldabove the eye.Ancient astrolabes con-tainedringsattachedtoatoppiececalledthethroneforhangingthedeviceonthethumb.Thealtitudeoftheobjectinviewcouldthenbereadfromascalealongthelimboftheback.
Thefrontoftheastrolabemater(Figure4) contains the limb with scales in de-grees and hours, and a central circularcavitycapableofholdingseveralclimateplates,overlainwithamovablerete(pro-
Figure3ASTROLABEMATER(BACK)
Figure4ASTROLABEMATER(FRONT)
40 Winter2011-2012 21stCenturyScience&Technology ASTRONOMYREPORT
nouncedreetee),theeclipticcirclewith CLIMATE PLATEusefulstarslocatedonit.Finally,thereisa movable graduated pointer called arule,forreadingoffdeclinationsfromtheplate,ordegreesorhoursfromthelimb.
Thewholedeviceisheldtogetherwithanaxleandlinchpindevice(Figure5).
Existingancientastrolabesweremadefromdurableengravedbrass,butitstandsto reason that most astrolabes weredrawnonpaper,wood,orsimilarmateri-als,whichwerecheaperandmoreread-ilyavailable.Unfortunately,thoseinstru-mentsdidnotsurvivetheravagesoftimeandhumanevents.
Your instrument will suffer the samefate,unlessyouplantoengraveoretchyour astrolabemarkings intobrass.Butluckilyforyou,youcanpreservethetem-platesforyourastrolabeonyourcomput-ertobereprintedontocardstockinthefuture, in case of the tragic demise ofyourpresentastrolabe.
WhyBuildanAstrolabe?AlmosteveryoneseemstohaveaPC
thesedays,withMicrosoftOfficeon it.Mostly it is used for e-mail and simpledocumentproduction,andtheexpensivesoftwarejustgoestowaste.Constructingourastrolabewillpushthelimitsofoneof the applications of Microsoft Officethat few people take seriously: Power-Point.PowerPointmightjustbetheper-
Figure6
Figure5ANASTROLABEDISASSEMBLED
An18thCenturyastrolabefromNorthAfrica,show-ingitsvariousparts.Theaxleandlinchpindeviceareintheforeground.
Figure7CLIMATECIRCLES
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fect vehicle to introduce people to thepower and beauty of an ancient astro-nomicalinstrumentwithrelevanceeventoday:theplanisphericastrolabe.
UsingPowerPoint toconstructanas-trolabeisasclosetoconstructingtheas-trolabewithstraightedge,compass,andprotractorasyoucangetonacomputer.IfyoucandoitwithPowerPoint,youcandoitoncardstock.
ButPowerPointhasmanyadvantagesover pencil and paper in adjustability,erasability, and transferability of linesandcircles.Further, thewholeprocess,frombeginningtoend,canbesavedonslidestoillustrateyourprogressforpos-terity.
Myaimistoconvincepeopletolearnmoreaboutastronomyanditshistorybyconstructinganastronomicalinstrumentsousefulthatitmayhavepredated,andcertainlyoutlasted,thePtolemaicastro-nomicalsystem.Becausethesubjectisalargeone, thisarticlewill focusmainlyontheconstructionofoneimportantpartoftheastrolabe:theclimateplate.
ElementsoftheClimatePlateTheheartofthemateristheclimate,or
latitudeplate,which,asitsnamesimply,is different for different latitudes of theEarth(Figure6).Theclimateplateisalat-itude-specificcircularslideruleforcal-culating solutions to problems dealingwithtime,season,theSun,thefixedstars,andeventheplanetsandtheMoon,giv-en an ephemeris to locate the planetsupontheplate for thetimeanddateofinterest.
Theotherpartsoftheastrolabecanbeusedanywhere,buttheclimateplatemustbeconstructedspecificallyforthelatitudeof theobserver. In the timeofClaudiusPtolemy, theEarthwasdivided intoCli-matesbasedonmaximumhoursofsun-light/darkness,withtheEquatorbeingXII,andtheNorthPolebeingXXIV.Sixorsev-en climate plates would serve for theknownNorthernWorldofPtolemy.
Nowadays,wemeasureEarth’slatitudebydegrees,withtheEquatorbeing0de-grees,and theNorthPolebeing90de-grees.Areasonablecompromisebetweenaccuracyandexpediencywouldbealat-itudeplateforeach5degreesoflatitudewhereoneexpectedtousetheplate.
Theclimateplateismadeupofseveraltypesofcirclesandarcs,whicharenec-essaryforitsfunctionalityasameasuringinstrument.Thethreemaintypesarethe
climatecircles,thealmucantars,andtheazimutharcs.
Theclimatecircles (Figure7)arecir-clesrepresentingtheTropicofCapricorn,theEquator,andtheTropicofCancer,asviewedbystereographicprojectionfromthe South Celestial Pole.TheTropic ofCapricornisthelargestcircle,whiletheTropicofCanceristhesmallestone.TheNorth Pole would be represented by apointinthecenterofthethreeconcentriccircles.
Thealmucantars(Figure8)areaseriesofnestedbutnon-concentriccirclesradi-atingoutwardfromtheZenith(apointat90degreesfromtheHorizon).Theyrep-resentthealtitude,indegrees,ofobjectsof interestabove theHorizon,which isthelargestcircle,at0degrees.Thelarger
almucantarcirclesarecutoffbytheout-eredgeoftheclimateplate—theTropicofCapricorncircle.
TheNorthPoleisaholeatthecenteroftheplatewheretheclimateplateisat-tached to the mater, and would corre-spondtothelatitudeofyourlocationonEarth.
Thethirdmajorcurvesontheclimateplate are called azimuth circles (Figure9),althoughtheyaretruncatedintoarcsbytheedgeoftheplate.Thesearcs,inter-sectingattheZenith,representdivisionsoftheclimateplateintodegree-segmentsfrom East through South throughWest,andbacktoEast,withEastandWestdes-ignated as 0 degrees, and South andNorthdesignatedas90degrees(thisvar-iedamongastrolabemakers).
Figure8ALMUCANTARS
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BuildingtheClimatePlateWe shall now focus on constructing
suchaplate for40degreesNorthLati-tude. Such a plate would be usablethroughoutawide swathof theUnitedStates,includingmanyofthelargestcit-ies, from San Francisco to the Oregonborder,St.LouisuptoDetroit,andWash-ington,D.C.,uptoBoston.
The first step in constructing the cli-mateplateistodeterminethesizeoftheEquatorcircle,forthatwilldeterminetheoverallsizeoftheplate.Theradiusofthiscirclewillbeusedincalculatingthesiz-esoftheTropicofCancerradiusandtheTropicofCapricorn radius.The limbofthemater,withitsmarkings,mustlieout-side theTropicofCapricorncircle.TheEclipticcircleof the retewill cycleec-centricallybetween theTropicsofCan-cer and Capricorn circles in its diurnalandseasonalmotions(Figure10).
WewillchoosetheradiusoftheEqua-tortobe2inchesforourpurposes,givingusanoveralldimensionfortheastrolabeoflessthan7.5inches.
Next we must draw this circle on ablankPowerPoint slidebyselecting thecircleobject, clicking itonto the slide,and right-clickingon it to bringup themenutoFormatShape.Choosesizeas4(diameter), after checking the Lock as-pectratiobox.ChoosetheFillasclear.NoShadow.Linecolorandthicknessofyourchoice.Centerthecircleinthecen-teroftheslide.SelectalineobjectfromtheObjectPalette.Clickitontotheslideatthecenterofthecircle,anddrawitouttotheedgesoftheslidehorizontally,bi-sectingthecircle.
Youmaydothesamewithaverticalline.YounowhaveacrosssectionoftheCelestial Sphere, with the North/SouthaxisandtheEquatorialaxisdisplayed.Ifyouwish,youmaycolorthetwolinestodifferentiate them from new lines youwilldrawonyourworkingslide.
NowduplicatethatslideusingtheIn-sert menu/Duplicate Slide. I note herethatitisimportanttocontinuallydupli-cateslidestopreservepartsofyourworkwhileyouareconstructingyourclimateplate.SelectalineobjectfromtheOb-jectPalette.Clickitontothefirstslideatthecenterofthecircle,anddrawitouttothecircumferenceontheright-handhor-izontalradiusofthecircle.
Next,copyandpastethatlineontothesameslidetogiveyouasecondlineto
Figure9AZIMUTHS
Figure10RETE
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Figure11CLIMATECIRCLEPROJECTION
Figure12CONSTRUCTINGTHECANCERCIRCLE
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work with. Now right-clickthat second line to bring upFormatShape,andgoto theSizesubmenu.Addthepres-entanglefor theobliquityoftheEcliptictotheexistingan-gle in the Angle field, andmoveitsoitextendsfromthecentertothecircumference.
Then, using the first hori-zontal line, again copy andpaste the line,andnext sub-tracttheangleoftheobliquityoftheEclipticfromwhateverangle is in the Angle field.Move that line so it extendsfromthecentertothecircum-ference.
Because the present angleoftheobliquityisabout23.44degrees, and PowerPoint ac-ceptsonlyintegerangles,youare left with the contrivanceofproducing thin linesat23degrees,24degrees,andmi-nus23and24degrees, thensplittingthedifferenceathighZoom in the next operation.Onceyouhavetheanglesofthe obliquity marked on thecircumference above and below theEquator,selectanewline,click itontotheSouthPolepoint,anddrawituptotheTropicofCancerpoint.
TakeanotherlineanddrawitfromtheSouthPole,throughtheTropicofCapri-corn point, and onto the Equator line.WhereeachoftheselinesintersectstheEquatorline,marksthelengthofthera-diusofeachcirclefromthecenter.Tofindthelengthofthoseradii,youcanextendaline to each point from the center, andfindthelengthintheSizefield.Multiplyby2togetthediameterofeachcircle.
NowselectandformatcirclesofthosesizesfromtheObjectPalette,andcenterthemconcentricwiththeEquatorcircleonyourduplicateslide(Figure11).Alter-natively,youcanfigureoutthetwotropiccirclesmorepreciselyusingtrigonomet-ric ratios: Rcan=ReqTan((90– )/2) (Fig-ure12)andRcap=ReqTan((90+)/2)(Fig-ure13).Multiplyby2togetthediametersandplacethemaroundtheequatorcircleintheduplicatedslide.ConstructionoftheAlmucantarCircles
Thenextstepistodrawthealmucantar(altitude)circles.Allofthiscanbedoneon the same slide,but itwouldget in-
Figure13CONSTRUCTINGTHECAPRICORNCIRCLE
Figure14NORTH-SOUTH-EQUATORCROSSHAIRS
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crediblyclutteredandhardtoplacethelines.Also,someof thealmucantarcir-cles, especially the Horizon circle, arevery large,so it isbest tocreateanewslide using the same-size circle as theEquatorcircle,butmovingittotheleftofcenterby2.5inches.
Divide the circle vertically and hori-zontally by selecting line objects andclickingthemintoplace(asinFigure14).The vertical diameter represents theNorth/SouthPolesoftheCelestialSphere.Thehorizontal lineshouldbeextendedtothelimitsoftheslide.Itisacrosssec-tion of the plane of projection at theEquator of the Celestial Sphere. It alsorepresentstheMeridianoftheastrolabeunder construction, with South to therightandNorthontheprojectionpointoftheCelestialNorthPole(atthecircle’sor-igin). Create a duplicate slide at thispoint.
Nowpasteanewlinefromtheoriginofthecircletothetop,ontopoftheverti-cal diameter line. Copy and paste thatlineontotheslidesoyouhavetwowork-inglinestousenext.Rightclickthenew-lypastedverticallineandgototheSizewindow.Whatevertheanglesaysfortheverticalline,add40degreestoitanden-terthatintherotationfield.
Moveyourlinetotheoriginsothatitisaradiuspointing40degreestotheleftofvertical, and extend it to the circle cir-cumference in both directions, makingsureitpassesthroughthecenter.ThislineisyourHorizonlineforalatitudeof40degrees.TheCelestialNorthPole is 40degreesclockwisefromtheNorthHori-zon.
Nowcopyandpasteyouroriginalver-ticallineagain,thistimesubtracting50degreesfromit.Putitattheorigin,andextend it to thecirclecircumference inboth directions, making sure it passesthroughthecenter.ThislineistheZenith/Nadirline.Itis90degreesfromtheNorthHorizon.
SelectanewlinefromtheObjectPal-etteandclickitontotheSouthPoleofthe Celestial Sphere. Extend it to theNorth Horizon point on the circle cir-cumference.Where this linemeets theEquator line is the projection of theNorthHorizonpointontotheastrolabeplate.
Repeat,byextendinglinestotheSouthHorizonpoint,theZenithpoint,andtheNorthPolepoint(projectedtotheoriginofthecircle).Marktheprojectionpointsfor theZenithandNorthPolewithtinycolored circles. The distance from the
North Horizon projection point to theSouth Horizon projection point (Figure15)givesthediameterandlocationoftheHorizoncircletobecreatedonthecli-mateplate.
Createacircleofthisdiameterjustliketheearliercircles,andpositionitsothattheNorthandSouthHorizonprojectionpoints are on the circumference of thecircle—if youwereusing compass andstraightedge, you would bisect the linebetween theprojectionpoints,andusethe compass to draw the circle (Figure16).Now,selectthatcircleandcopyandpasteitontoyourduplicateslide.
YoumayalternativelyfigureoutyourHorizon circle diameter using trigono-metricratios(Figure17).
Therestofthealmucantarcirclescanbeconstructedthesameway(seeFigure18),byfindingtheanglesforeachaltitudeupto90degrees(theZenith),projectingfrom theSouthCelestialPole to get thenorth and southdiameterpoints for thenecessarycircle,andplacingthecircleontheslide.Theconstruction,movedtotheclimate circles, and including the Hori-zoncircleand thealmucantarcircle for50degrees,isshowninFigure19.
Note that while the 50-degree circlewillbeacircleinthefinalplate,theHo-
Figure15CONSTRUCTINGTHEHORIZONCIRCLE
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Figure16THECONSTRUCTEDHORIZONCIRCLE
Figure17THETRIGONOMETRYOFTHEHORIZONCIRCLE
21stCenturyScience&Technology Winter2011-2012 47
rizoncirclewillbeanarccutoffbytheTropic of Capricorn circle. Figure 20showsallofthealmucantarcirclesin3-degreeintervalsfrom0degreesto60de-grees,andin5-degreeintervalsfrom60degreesto80degrees.
The50-degree circle from theprevi-ousslideissuperimposedinredtoillus-tratewhereitfallsontheplate.YouwillfinditvaluabletoZoominandoutdur-ing the construction of the almucantarcircles.
ConstructingtheAzimuthCirclesAfterconstructingthealmucantarcir-
cles,thenextphaseistoconstructtheaz-imuth circles. If the almucantar circlesare viewed as dividing the heavens upintoequalaltitudezonesfromtheHori-zontotheZenith,theazimuthcirclesdi-vide the heavens from Zenith to NadirintoequalanglezonesfromEastthroughSouthtoWesttoNorth,thenbacktotheEast, like the segments of an orange.Whenprojectedontotheclimateplate,eachazimuthcirclehasboththeZenithandtheNadiraspointsonitscircumfer-
ence, but each has a different originrangedoutonalinewhichistheperpen-dicular bisector of the line connectingtheprojectionpointsof theZenithandNadir.
If you create a circle connecting theZenithandNadirprojectionpointsasadiameter,theperpendiculardiameterofthat circle would be the line of circlecentersfortheazimuthcircleprojections(Figure21).ThatcirclesymmetricabouttheMeridianlineiscalledPrimeVertical(Figure22).
Tofindtheotherazimuthcircles,wemust find their center points along thelineofcenters.AlinedrawnfromeachcentertotheZenithorNadirprojectionpointwilldefinethatcirclesradius.Dou-blingthatradiuswillgiveusthediame-ters for thecirclesweneed.Tofindthecentersofthecircles,wemustmeasureanglesfromtheZenithtothelineofcen-tersequaltotheanglesoftheazimuthswewishtodraw.
Ifwewishtohaveazimuthcirclesforeach10degrees, then lineswith these
anglesmustintersectthelineofcentersonbothsidesoftheMeridianforeach10degrees. The intersections define theazimuth circle centers, and the linesdefinetheazimuthradii.PrimeVerticalisthespecialcaseofa0-degreeangle.Theotherspecialcaseisthe90-degreeangle,whichisaninfinitelylargecircleindistinguishable from the Meridian it-self.
Because theazimuthcirclesbecomeverylargealongthelineofcenters,wewillalignthatlineofcenterslefttorightontheslideuponacopyofthethreecli-matecirclescenteredontheslide.Don’tforgettoZoomliberally.Aswiththeal-mucantar circles, we start with a cen-teredcircleofdiameter4.Selectalinewith the qualities desired, copy andpaste thatlinetohaveaworkingcopy,andusethatlinetocreatetheanglesweneed.
Figure23givesthePrimeVerticalcir-cleand the two40-degreeazimuthcir-cles.Theslidehadtobereducedto75percent tofit the40-degreecircles into
Figure18ALMUCANTARPROJECTIONS
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Figure20ALLALMUCANTARS
Figure19ALMUCANTARRELATIONSHIPS
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Figure21AZIMUTHLINEOFCENTERS
Figure22AZIMUTHPRIMEVERTICAL
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thefigure.Figure24showsallthecircles in place, and Figure 25showsthemhighlyreducedtofitontheslide.
Theazimuthcirclesasseenonthe final astrolabe climate plateareonlyarcs,sincetheyareonlyexpressedabovetheHorizoncir-cleandarebounded,asaretheal-mucantarcircles,bytheTropicofCapricorn.Aswiththealmucantarcircles,aringobjectwillbelaterbeusedtoblockoutthosepartsofthe circles outside the desiredbounds.
AssemblingthePartsNow thatwehavecreated the
climate circles, the almucantars,andtheazimuthcircles,wehaveall themajorelementsnecessaryfortheclimateplate.Thenextstepis to assemble them together. Ifyoubuiltyouralmucantarsuponyourclimatecircleslide,theyarealreadyassembled.
Ifyouusedanewcircleofdi-ameter4inches,youmustaddtheTropic of Cancer and Tropic ofCapricorn circles to your almu-cantarslide,concentricwithyourEquatorcircle.Thesecircles,andtheirhorizontalandverticaldiam-eterlines,mustberight-clickedaf-terselecting,tobringupthemenu.ThenchooseArrange, andBringtoFrontforeachofthem.
Onceyouhaveyouralmucan-tars on your climate circles, youneedtogroupalloftheelements,thenrotate thegroup90degreescounter-clockwise. To finish offtheconstruction,youmustputanopaquewhiteringaroundtheHo-rizoncircletoremovetheazimuthlinesfromtheareabelowit,sincethey are needed only above thehorizon.
Select Donut from the objectsandsize itso the insidering justfitsaroundtheHorizoncircle.Theringfillshouldbeopaquewhitetomatchthebackground(Figure26).This group will now be copiedandpastedontoyourazimuthcir-cleslide,makingsurethatthe4-diametercirclescoincide.
Now,go to theObjectPaletteandselecttheDonutobject.Clickit onto your slide, format it to
Figure24ALLAZIMUTHS
Figure23AZIMUTH40-DEGREECIRCLES
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Figure25AZIMUTHSVIEWEDINTHESMALL
Figure26AZIMUTHSWITHRINGFILL
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white, no shadow, withlinestomatchyourotherlines,andsetthediame-ter to 12. Center it onyour circles. Next, clicktheyellowbox,anddragitsotheinneredgeofthering coincides with theTropic of Capricorn cir-cle. Small position ad-justments can be madeusing the keyboard ar-rowstonudgetheshape.
AlllinesoutsideoftheTropicofCapricorncirclehave now been coveredbyyourringfill.
Because the three cli-mate circles with theirvertical diameters doneed to be seen belowthe Horizon circle, theymust be selected andbrought to the front byright-clickingeachcircle,clicking Arrange, andthen clicking Bring toFront.Thehorizontaldi-ametermaybe includedor leftoff theplate.Onemore,atinyringwillbeusedtofillthespacebetweenthe80-de-gree almucantar circle and the Zenithpointat90degrees(Figure27).
Figure28showsthecroppedclimateplate,readytobelabeled.
LabelingtheClimatePlateHowyoulabelyourclimateplateisto
a large degree a matter of choice.Toomuch labelinggetscluttered,while toolittlecanleadtoextraworkwhileusingtheastrolabe.Thealmucantarcirclesarelabeled from 0 degrees at the Horizoncircle,to80degreesneartheZenith.Theplateusedasanexample,hasalmucan-tarsevery3degreesto60degrees,thenevery 5 degrees to 80 degrees. In thatcase,labelingevery12degreesto60de-grees, and every 10 degrees to 80 de-greeswouldwork.
The azimuths are labeled 0 degreeswestwheretheHorizoncirclemeetstheEquator circle on the right of your cli-mateplate.Ontheleft,itislabeled0de-grees east. Where the Horizon circlemeets the vertical line passing throughthecenteroftheplate,islabeled90de-greesnorth.
South,ofcourse, isoff thetopof the
Figure28CROPPEDCLIMATEPLATEBEFORELABELING
Figure27ANOTHERRINGFILLADDED
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plate,but the topof theplate is90de-grees in the south direction. Figure 29showstheclimateplatelabeled.SinceIhave seasonal hours on my plate, I la-beled themclockwise from I toXI (seebelow).Figure30showstheclimateplateplacedontothefrontofthematerIcre-atedinPowerPoint.
SeasonalHoursAncientclimateplateshadotherarcs
onthemaswell.Oftentheyhadseasonalhour arcs filling the mostly empty areaundertheHorizoncircle.Thesedividedthe day or night into 12 equal parts,whose hour-lengths depended on theseason.RatherthanhavemorehoursofdaylightintheSummer, therewerejust12longerhoursofdaylight.
Conversely,the12hoursofnightwouldeachbeshorterbyaproportionalamount.Theselinesareoftencalledunequalhourlines,butabetternamemightbepropor-tionalhours,sinceeachhouroccupiesaproportional12thofthedayornight.An-cientastrolabesalsooftenhadinscribedonthemarcsrepresentingthe12housesofheavenusefultoastrologers.
Figure29showsanastrolabeclimateplatewiththeseasonalhoursmarkedin.Ifyouweretotakeaseriesofcirclesrep-resentinglatitudesbetweentheTropicsofCancerandCapricorn,allcutoffbythesweepof thearcof theHorizoncircle,and divide each of those many circlesinto 12 equal parts below the Horizoncircle(theEquatorwouldbe180degreesdividedby12,whichis15degreeseach),asetofsmootharcsconnectingthedivi-sionsfromtheTropicofCapricorntotheTropicofCancerwouldrepresentthe12seasonalhours.
Inpractice,thiscanbeaccomplishedverycloselybyjustdividingthethreecli-mate circles of the astrolabe plate intotheir12equalsegments,thenfindingcir-clesthatcontaineachsetof3pointsonthe circumferences.Thatworks fine forcompass and straightedge (and a gooderaser),butforPowerPoint,itleavesasetof arcsabove theclimatecircle,whichcannotberemovedbytheringmaneuverusedearlier.
Onecan,however,usethecurvelinetotraceoverthearcsoftheseasonalhourcirclesfromthetropicofCapricorntotheTropicofCancer.YoudothisbyselectingthecurvelineandclickingitattheTropicofCapricorn.
Movealittlesmoothlyalongthehour
Figure29CLIMATEPLATELABELED
Figure30MATERANDCLIMATEPLATECOMBINED
ASTRONOMYREPORT
54 Winter2011-2012 21stCenturyScience&Technology
line and click. Repeat that action untilyoureachthetropicofCancer.Thendou-ble click to release the line.A smoothcurveshouldappear.Formatthecurvetoyourspecificationsandmoveon to thenextarc.Afteryouhavecreatedyoursea-sonalhours,youcansimplyerasethecir-clesyouusedastemplates.
You’veMadeYourClimatePlate.NowWhat?
Now that you have created your cli-mateplatefortheastrolabe,youwillnodoubtwishtouseit.That,ofcourse,re-quires creating the mater front limbscales,therete(withusefulstars),aswellasat leastasimplifiedmaterbackwithscales.Youwillalsoneedtomakearuleforthefrontandanalidadefortheback.
Thesethingscanallbecreatedonthecomputer,andalmostallcanbecreatedusingPowerPoint,usingtechniquessimi-lartothoseyouhavealreadyusedtode-signtheclimateplate.
You are also most likely itching to
know how to use this device to solvemedievalproblemsrelatedtotime,sea-son,theSun,andthefixedstars.Luckiswithyou.Thereareseveralgoodweb-sitesfocussingontheastrolabe,butthebestIhavefoundis“TheAstrolabe.”Thisis a very useful site, where there is awealthofresourcesrelatedtotheastro-labe.
Oneveryfunpartofthesitepresentsthe Electric Astrolabe (one running oncomputercodeoftheDOSvariety).ThisisaveryinstructionalprogramforpeoplerunningWindowsXPorbelow.Forotheroperating systems, a DOS emulator,calledDOSBoxmustbeused.WiththeElectricAstrolabe,youcaneasilyfindoutwheretheplanetswillbeatchosentimesinthepastorfuture,justbyenteringyourdateandlocation.Itisawonderfultoolfor learninghow the astrolabeworks. Ihighly recommendthatyou tryout thisprogram.
Thepersonwhocreatedthissite,James
E. Morrison (Janus), has recently pub-lishedabookabouttheastrolabe,whichiswellworththemoney.Thisbook,TheAstrolabe (Classical Science Press), isverycomplete,givingthehistory,theas-tronomy,thetrigonometry,howtouseit,andevenhowtoconstructone.
Another resource I have found veryvaluable is the book, The History &PracticeofAncientAstronomy,byJamesEvans (Oxford University Press). Al-thoughonlyasmallportionofthebookdealswiththeastrolabe,perse,youcanlearnalotabouttheancientastronomythat informed the development of theastrolabe.ThefirstastrolabeIbuiltwasfrom instructions and templates in hisbook.
Finally,ifyoureallywishtoknowhowtheastrolabewasusedinmedievaltimes,treatyourselftoreadingChaucer’sTrea-tise on the Astrolabe, written around1391tohissoneLowis,a10-year-old.
Figure31THEALMOST-COMPLETEDASTROLABE
Thephotosillustrateasimpleastrolabeinthefinishingstagesofconstruction.Thematerfrontwithclimateplate,andthematerback,wereprintedontocardstockandgluedtoasturdycardboardcircle.Therete(asyetwithoutstarsandconstellations),wasprintedontoacetate.Thefrontrule(asyetwithoutdeclinationhatches),andthebackalidadewerecutfromcontainerplastic;cardstockwasgluedontop.Holeswerecarefullymadeinallthepartstoreceivetheboltandnut.
Atthetopoftheinstrument,anotherholewasmadetoreceiveaboltfromwhichtohangalanyard.Athumbcanbeinsertedthereinsotheastrolabecanbeheldatarmslengthtosightstarsandplanets.Oncethefrontrulehasbeenmarkedwithdecli-nationhatches,itcanbeusedinconjunctionwiththeastrolabeandanephemeristomarkprominentstars/constellationsontotherete,ifdesired.
ASTRONOMYREPORT