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Total Solar Eclipse of 1998 February 26

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Total Solar Eclipse of 1998 February 26 NASA Reference Publication 1383 April1996 TotalSolarEclipse NASA of1998February26 FredEspenak andJayAnderson 1 2 E CLIPSE P REDICTIONS INTRODUCTION OnThursday,1998February26,atotaleclipseoftheSunwillbevisiblefromwithinanarrow corridorwhichtraversesthe WesternHemisphere.ThepathoftheMoon's umbral shadowbeginsinthe Pacific,continuesthroughnorthernSouthAmericaandtheCaribbeanSea(Figure3),andendsatsunsetoff the Atlantic coast of Africa. A partial eclipse willbeseenwithinthemuchbroaderpathoftheMoon's penumbralshadow,whichincludespartsoftheUnitedStatesandeasternCanada,Mexico,CentralAmerica andthenorthernhalfofSouthAmerica(Figures1and2). UMBRAL PATH AND VISIBILITY TheMoon'sumbralshadowfirsttouchesdownonEarthjustsouthoftheequatorinthePacific Ocean about 3000 kilometers southeast of the Hawaiian Islands (15:46:45 UT). Even at this extreme position, the total eclipse lasts nearly one and a half minutes. For the first one and a quarter hours, the umbrasweepsacross5500kilometersofopenwaterwhileencountering no majorbodiesofland.First landfallfinallyoccursshortlyaftercrossingnorthoftheequator(16:56UT)astheshadowrushesacross severalmembersoftheGalápagosIslands.MaximumeclipsetakesplaceshortlybeforenoonwiththeSun 69° above the horizon. Unfortunately, none of the islands are on the center line where the duration of totalityisonesecondunderfourminutes(Figure4).ThenorthernthirdofIslaIsabelalieswithinthepath andexperiencesadurationof3minutes21secondsalongitsnorthcoast.IslaPintaandIslaMarchenaare also situated in the path, but all three islands are uninhabited wildlife sanctuaries with access strictly controlledbytheEcuadoriangovernment. AfterleavingtheGalápagos,theumbralpathcontinuesonanortheasterncourse.Theinstantof greatesteclipse 1occursat17:28:23.2UTabout600kilometerswestofColombia'sPacificcoast.Atthat moment,thelengthoftotalityreachesitsmaximumdurationof4minutes8seconds,theSun'saltitudeis 76°, the path width is 151 kilometers and the umbra's velocity is 0.592 km/s. The axis of the Moon's shadowpassesclosesttothecenterofEarth(gamma2=0.239)atgreatesteclipse. Fifteenminuteslater(17:43UT),theumbralshadowentersSouthAmericaandfollowstheborder betweenPanamaandColombia(Figure5).StretchingacrosstheIsthmusofPanama,thepathcrossesinto northernColombiawherethecenterlinedurationdropsbelowfourminutes.Inspiteofa25secondpenalty foritsposition20kilometersnorthofthecenterline,theColombiancityofValleduparstillexperiencesa generous3minute29secondtotaleclipse.AfterclimbingtheAndes,thepathsweepsthroughnorthwestern Venezuela(Figure6).Thesemi-desertvegetationofthisregionisatestamenttoitsaridclimate.Although Maracaibolies50kilometerssouthofthecenterline,itmanagestoenjoynearlythreeminutesoftotality. TheeclipseoccurshereintheearlyafternoonwiththeSun65°abovethehorizon.– TheMoon'sshadowleavesVenezuelaviathePeninsula de Paraguaná and sweeps across the Caribbean where it encounters five major islands of the Lesser Antilles. The center line passes directly betweenArubaandCuraçao(Figures7,8and9),butbothislandsexperienceasmuchas3 1/2outofa possible 3 3/4 minutes of totality. Aruba's capital Oranjestad witnesses a 3 minute 6 second total phase whilethedurationinWillemstad,Curaçaois1minute58seconds.BothNetherlandsAntillesislandsmake goodlocationsfortheeclipsesincetheysharesimilarlypromisingweatherprospects.NearbyBonaireis justoutsidethe143kilometerwidepathalthoughitsnorthwesterncoastwillwitnessagrazingeclipsewith perhapsadozensecondsoftotality. The track continues across the Caribbean where it engulfs the Leeward Islands of Montserrat, AntiguaandGuadeloupe(Figures10through13).Here,theumbra'svelocityincreasestoover0.9km/sand thepathwidthdropsto136kilometers.Occurringinmidafternoon,theSun'saltitudeis49°atmaximum eclipse.AlthoughthecenterlinepassesbetweenGuadeloupeandtheothertwoislands,alllocalesenjoyas muchas3outofapossible3 1/4minutesoftotality.SincethesouthernextremesofGuadeloupeactually 1TheinstantofgreatesteclipseoccurswhenthedistancebetweentheMoon'sshadowaxisandEarth's geocenter reaches a minimum. Although greatest eclipse differs slightly from the instants of greatest magnitudeandgreatestduration(fortotaleclipses),thedifferencesareusuallynegligible. 2MinimumdistanceoftheMoon'sshadowaxisfromEarth'scenterinunitsofequatorialEarthradii. 3 lieoutsidetheumbralpath,mostobserverswillwanttopositionthemselvesonthenorthandwestcoastsin order to experience the maximum duration possible. Nevertheless, some may choose a site several kilometers inside the southern limit in order to witness the prolonged views of Baily's Beads and chromosphere afforded by such locations. While not as promising as Aruba and Curaçao, the weather prospectsofthisregionarestillquitefavorable. LeavingtheCaribbeanSea,theumbraracesacross the Atlantic towards Africa. About 1000 kilometerswestofMorocco,thepathendsalongthesunsetterminatorastheshadowfallsbackintospace (19:09:57UT).Overcourseof3hoursand23minutes,theMoon'sumbratravelsalonganapproximately 14000kilometerlongpathandcoversaregioncomprising0.3%ofEarth'ssurface. GENERAL MAPSOFTHE ECLIPSE PATH ORTHOGRAPHIC PROJECTION MAPOFTHE ECLIPSE PATH Figure1isanorthographicprojectionmapofEarth[adaptedfromEspenak,1987]showingthe pathofpenumbral(partial)andumbral(total)eclipse.Thedaylightterminatorisplottedfortheinstantof greatesteclipsewithnorthatthetop.Thesub-Earthpointiscenteredoverthepointofgreatesteclipseand isindicatedwithanasterisk-likesymbol.Thesub-solarpointatthatinstantisalsoshow. ThelimitsoftheMoon'spenumbralshadowdefinetheregionofvisibilityofthepartialeclipse. This saddle shaped region often covers more than half of Earth's daylight hemisphere and consists of severaldistinctzonesorlimits.Atthenorthernand/orsouthernboundariesliethelimitsofthepenumbra's path.Partialeclipseshaveonlyoneoftheselimits,asdocentraleclipseswhentheshadowaxisfallsno closerthanabout0.45radiifromEarth'scenter.Great loops at the western and eastern extremes of the penumbra'spathidentifytheareaswheretheeclipsebegins/endsatsunriseandsunset,respectively.Ifthe penumbrahasbothanorthernandsouthernlimit,therisingandsettingcurvesformtwoseparate,closed loops.Otherwise,thecurvesareconnectedinadistortedfigureeight.Bisectingthe'eclipsebegins/endsat sunrise and sunset' loops is the curve of maximum eclipse at sunrise (western loop) and sunset (eastern loop). The exterior tangency points P1 and P4 markthecoordinates wherethepenumbralshadow first contacts (partial eclipse begins) and last contacts (partial eclipse ends) Earth's surface. If the penumbral pathhasbothanorthernandsouthernlimit(asdoesthe1998Februaryeclipse),thentheinteriortangency points P2 and P3 arealsoplottedandcorrespondtothecoordinateswherethepenumbralconebecomes internallytangenttoEarth'sdisk.Likewise,thepoints U1 and U2 marktheexteriorandinteriorcoordinates wheretheumbralshadowinitiallycontactsEarth(pathoftotaleclipsebegins).Thepoints U3 and U4 mark theinteriorandexteriorpointsoffinalumbralcontactwithEarth'ssurface(pathoftotaleclipseends). Acurveofmaximumeclipseisthelocusofallpointswheretheeclipseisatmaximumatagiven time.TheyareplottedateachhalfhourUniversalTime(UT),andgenerallyrunfromnortherntosouthern penumbrallimits,orfromthemaximumeclipseatsunriseorsunsetcurvestooneofthelimits.Theoutline oftheumbralshadowisplottedeverytenminutesinUT.Curvesofconstanteclipsemagnitude 3delineate thelocusofallpointswherethemagnitudeatmaximumeclipseisconstant.Thesecurvesrunexclusively between the curves of maximum eclipse at sunrise and sunset. Furthermore, they are parallel to the northern/southernpenumbrallimitsandtheumbralpathsofcentraleclipses.Northernandsouthernlimits ofthepenumbramaybethoughtofascurvesofconstantmagnitudeof0%,whileadjacentcurvesarefor magnitudesof20%,40%,60%and80%.Thenorthernandsouthernlimitsofthepathoftotaleclipseare curvesofconstantmagnitudeof100%. AtthetopofFigure1,theUniversalTimeofgeocentricconjunctionbetweentheMoonandSunis givenfollowedbytheinstantofgreatesteclipse.Theeclipsemagnitudeisgivenforgreatesteclipse.For centraleclipses(bothtotalandannular),itisequivalenttothegeocentricratioofdiametersoftheMoon and Sun. Gamma is the minimum distance of the Moon's shadow axis from Earth's center in units of equatorialEarthradii.TheshadowaxispassessouthofEarth'sgeocenterfornegativevaluesofGamma. Finally,theSarosseriesnumberoftheeclipseisgivenalongwithitsrelativesequenceintheseries. 3EclipsemagnitudeisdefinedasthefractionoftheSun'sdiameteroccultedbytheMoon.Itisstrictlya ratioof diameters andshouldnotbeconfusedwitheclipseobscurationwhichisameasureoftheSun's surface area occultedbytheMoon.Eclipsemagnitudemaybeexpressedaseitherapercentageora decimalfraction(e.g.:50%or0.50). 4 STEREOGRAPHIC PROJECTION MAPOFTHE ECLIPSE PATH ThestereographicprojectionofEarthinFigure2depictsthepathofpenumbralandumbraleclipse in greater detail. The map is oriented north up with the point of greatest eclipse near the center. Internationalpoliticalbordersareshownandcirclesoflatitudeandlongitudeareplottedat20°increments. Theregionofpenumbralorpartialeclipseisidentifiedbyitsnorthernandsouthernlimits,curvesofeclipse begins or ends at sunrise and sunset, and curves of maximum eclipse at sunrise and sunset. Curves of constanteclipsemagnitudeareplottedfor20%,40%,60%and80%,asarethelimitsofthepathoftotal eclipse.AlsoincludedarecurvesofgreatesteclipseateveryhalfhourUniversalTime. Figures1and2maybeusedtoquicklydeterminethe approximate time and magnitude of maximumeclipseatanylocationwithintheeclipsepath. EQUIDISTANT CONIC PROJECTION MAPOFTHE ECLIPSE PATH
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