UNIGLOBEARMILLARYSPHERE INSTRUCTIONMANUAL DanielLeeWenger CONTENTS Introduction.............................................................................................................................................................................................. 1 DescriptionoftheUniglobe.................................................................................................................................................................... 2 Glossary..................................................................................................................................................................................................... 3 MeasurementofAnglesinthePlane ...................................................................................................................................................... 4 PositionsonaSphere............................................................................................................................................................................... 6 PositionsontheEarthGlobe .................................................................................................................................................................. 7 PositionsontheCelestialGlobe ............................................................................................................................................................. 8 RelativeOrientationofEarthandCelestialGlobesandtheMeasurementofTime ......................................................................... 11 SiderealTime.......................................................................................................................................................................................... 11 ApparentSunTime ................................................................................................................................................................................ 12 MeanSunTime....................................................................................................................................................................................... 12 ZoneTime............................................................................................................................................................................................... 13 DaylightSavingsTime............................................................................................................................................................................ 13 OrientingtheUniglobefortheCurrentTimeandtheObserver'sPosition...................................................................................... 13 UseoftheSpannertoMeasureBearingandZenithDistance(DirectionCoordinates)ofCelestialObject .................................. 15 TransitTime............................................................................................................................................................................................ 15 RisingandSettingTimes........................................................................................................................................................................ 15 UniglobeasaSundial............................................................................................................................................................................. 16 CelestialNavigation................................................................................................................................................................................ 17 PrecessionoftheEquinoxes(andZodiacalSystems) ......................................................................................................................... 18 EffectsofPrecession............................................................................................................................................................................... 20 EarthSatellitesandtheMotionoftheMoon....................................................................................................................................... 21 DeterminingAstrologicalData.............................................................................................................................................................. 23 HistoricalNotes...................................................................................................................................................................................... 24 INTRODUCTION FromtheearliestplanetariaofArchimedesthroughthecomplexarmillaryspheresofthe17thCenturytothepresentcombinationcelestialand terrestialglobes,manhasproduceddevicestounderstandandteachrelationshipsbetweenheavenlybodies.InNovember1973thecomet Kahoutecwasbeingwidelydiscussed.Itspositioncoordinateswerepublished,butthisinformationdidnotsufficetodeterminewhereinthe skytolookforthecomet.Beingatheoreticalphysicist,Iwasabletodesignadevicethatwouldgivethedesiredinformation.Irealizedthatsuch adevicewouldbeofvalueineducationandhaveagreatpopularappeal.AprototypeoftheUniglobewascompleteinJuneof1974.Thisdevice representsthe20thCenturyversionofthearmillarysphere,ananalogcomputerofpracticalvalue. DanielL.Wenger,PhD PublishedandprintedintheUnitedStatesofAmerica,1975,byDanielL.Wenger,Soquel,California. Copyright©1975byDanielL.Wenger.Allrightsreserved.Nopartofthisbookmaybereproducedwithoutpermissionofthepublisher. UniglobeisatrademarkofDanielL.Wenger. 1 DESCRIPTIONOFTHEUNIGLOBE TheUniglobeisaWORLDGLOBEimmediatelysurroundedbyatransparentCELESTIALGLOBEuponwhicharemarkedthestarsandother pertinentcelestialdata.ThetwoglobesaresupportedbyaYOKEMOUNTwhichrestsinaslottedBASEfororientingtheAXIStowardany direction.Abrakingsystemallowsthecelestialglobetobeturnedindependentlyandthetwoglobestobeturnedsimultaneously.ATIMERING attheequatorofthecelestialglobeallowssettingoftheearthandcelestialglobesaccordingtothetimeofday.Thetimeringismovable allowinguseofanyofthesystemsoftimemeasurementinuse. Ameasuringdevice,theSPANNER,allowsdeterminationofzenithangleandbearingofacelestialobjectfromanypontontheearth.APOINTER indicatesthedirectionofacelestialobjectatagiventimeandconversely,whenthepointerisdirectedtowardsthesun,theUniglobebecomesa sundial.TheUniglobeissuppliedwithaSATELLITESPANNERforindicatingtheregionofvisibilityofasatelliteandaGREATCIRCLEBANDfor indicatingsatelliteorbits.Agraphicalandtabularephemerisissuppliedtoallowplottingofthepositionsofthesun,moonandplanets. 2 Altitude.Angulardistanceabovethehorizon:thearcofaverticalcircle Latitude.Theangulardistancenorthorsouthoftheequatoranda betweenthehorizonandapointonthecelestialsphere,measured pointonthesurfaceoftheearth,measurednorthwardorsouthward upwardfromthehorizon. fromtheequatorthrough90°,andlabeledNorStoindicatethe Angle.Theinclinationtoeachotheroftwointersectinglines, directionofmeasurement. measuredbythearcofacircleinterceptedbythetwolinesforming Longitude.Theanglebetweentheprimeorreferencemeridianand theangle,thecenterofthecirclebeingthepointofintersection. anothermeridianofinterest,measuredfromtheprimemeridianEor AngularDistance.Theanglebetweentwodirectionsasseenfroma Wthrough180°. givenpoint. Meansun.Afictitiouspointconceivedtomoveeastwardalongthe Apogee.Thatorbitalpointfarthestfromtheearthwhentheearthis celestialequatoratauniformrateequaltotheaveragerateofthe thecenterofattraction(asinthecaseofthemoon). apparentsunalongtheecliptic. Apparentsun.Theactualsunasitappearsinthesky. Meridian.Agreatcircleperpendiculartotheequator. Apparenttime.Timebasedupontherotationoftheearthrelativeto Parallax.Thedifferenceintheapparentdirectionorpositionofan theapparent(true)sun. objectwhenviewedfromdifferentpoints. Azimuth.Thehorizontalanglebetweenareferencedirectionand Perigee.Thatorbitalpointnearesttheearthwhentheearthisthe anotherdirectionofinterest.Itismeasuredfrom0°atthereference centerofattraction(asinthecaseofthemoon). directionclockwiseorcounterclockwisethrough360. Polardistance.Theangulardistancefromacelestialpole,usuallythe Bearing.Thehorizontalanglebetweenareferencedirectionand elevatedpole. anotherdirectionofinterest.Itisusuallymeasuredfrom0°attrue Precession.Thechangeinthedirectionoftheaxisofrotationofa northclockwisethrough360°. spinningbody,asagyroscope,whenacteduponbyatorque. Celestialbody.Anyaggregationofmatterinspaceconstitutingaunit, Primemeridian.Themeridianoflongitude0°usedastheoriginfor suchasthesun,aplanet,etc. themeasurementoflongitude. CelestialSphere.Asphereconcentricwiththeearth,onwhichall Siderealday.Thedurationofonerotationoftheearthonitsaxis, celestialbodiesexcepttheearthareimaginedtobeprojected. withrespecttothevernalequinox. Coordinate.Oneofasetofmagnitudesdefiningapointinspace. Sideralhourangle.Theangulardistancewestofthevernalequinox; Declination.Theangulardistancenorthorsouthofthecelestial thearcofthecelestialequator,ortheangleatthecelestialpole, equator:thearcofanhourcirclebetweenthecelestialequatoranda betweenthehourcircleofthevernalequinoxandthehourcircleof pointonthecelestialsphere,measurednorthwardorsouthwardfrom apointonthecelestialsphere,measuredwestwardfromthehour thecelestialequatorthrough90°,andlabeledNorStoindicatethe circleofthevernalequinoxthrough360° directionofmeasurement. Siderealtime.Timebasedupontherotationoftheearthrelativeto Ecliptic.Theapparentannualpathofthesunamongthestars. thevernalequinox. Equator.Theprimarygreatcircleoftheearth,orasimilarbody, Solarday.Thedurationofonerotationoftheearthonitsaxis,with perpendiculartothepolaraxis. respecttothesun. Equinox.Oneofthetwopointsofintersectionoftheeclipticandthe