Download pdf - How to Construct an Astrolabe, Using Your PC · ments did not survive the ravages of time and human events. Your instrument will suffer the same fate, unless you plan to engrave or

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.

ASTRONOMYREPORT

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

21stCenturyScience&Technology Winter2011-2012 41

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

ASTRONOMYREPORT


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


Figure11CLIMATECIRCLEPROJECTION

Figure12CONSTRUCTINGTHECANCERCIRCLE

ASTRONOMYREPORT


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


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

ASTRONOMYREPORT


Figure16THECONSTRUCTEDHORIZONCIRCLE

Figure17THETRIGONOMETRYOFTHEHORIZONCIRCLE


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

ASTRONOMYREPORT


Figure20ALLALMUCANTARS

Figure19ALMUCANTARRELATIONSHIPS


Figure21AZIMUTHLINEOFCENTERS

Figure22AZIMUTHPRIMEVERTICAL

ASTRONOMYREPORT


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


Figure25AZIMUTHSVIEWEDINTHESMALL

Figure26AZIMUTHSWITHRINGFILL

ASTRONOMYREPORT


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


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