1976AJ 81.1162L the ASTRONOMICAL JOURNAL VOLUME 81, NUMBER 12 DECEMBER 1976 Far-Ultraviolet Albedo of the Moon R. L. Lucke, R. C

Home , Geometric albedo

1976AJ 81.1162L 2o THE ASTRONOMICALJOURNALVOLUME81,NUMBER12DECEMBER1976 the far-ultravioletreflectivityoflunarfines(dust)ob- viously reportedfar-ultravioletlunaralbedodetermi- deduced, bycomparingtheirresultwithexistingdirect tained duringtheApollo11,12,and14missions.They LUCKE, Henry,andFastie(1973)have nations hadgivenmuchtoolowavalue. measurements ofthelunarbrightness,thatmostpre- lunar far-ultravioletalbedoobtainedduringtheApollo vious conclusion:Ifanything,thelunarfar-ultraviolet are described.Bothtypesofnewdatasupportthepre- lunar samples,nowincludingsamplesfromApollo17, claimed. albedo issomewhathigherthanwehavepreviously Service ModuleoftheApollo17spacecraftonlunar 17 missionispresented,andmoreaccurateresultson of thisexperimentwasdetectionlunaratmospheric described indetailbyFastie(1973).Theprimeobjective in the118-168-nmrange,whichwasmounted using ascanningfar-ultravioletspectrometer,sensitive during theperiodinlunarorbit,instrumentspent species byobservingresonantreradiationofsunlight.No mission ofDecember1972.Theinstrumenthasbeen orbits overaspanoffivedays),observingthesunlit many hours(approximately1honeachof37different lunar atmospherewasdetected(Fastieetal.1973),but geometry. Theinstrumentallineofsightwasdirected hemisphere oftheMoonwithpreciselyknownviewing cepted, roughly,a30X30-km patch(aboutIXin the localvertical.The11.°65 squarefieldofviewinter- toward theMoon,andmadeanangleofabout30°with lunar latitudeandlongitude) onthelunarsurface. © American Astronomical Society • Provided by the NASA Astrophysics Data System In thepresentpaper,adirectmeasurementof The lunarobservationsdiscussedhereweremade The scatteringofvisiblelight fromapatchofthe l reportedinthesepageslaboratorymeasurementsof The albedoandphotometricfunctionoftheMoonhavebeenmeasuredbetween121.6168.0nmby comparing thebrightnessofMoon,observedwithanorbitingfar-ultravioletspectrometerduringApollo is confirmedbynewlaboratorystudyoflunarsamples.Abriefreviewalbedomeasurementsinthe of theMoonisfoundtoincreasetowardshorterwavelengths;“blue”infarultraviolet.This carefully crosscalibrated.Incontrasttowhatisfoundinthevisibleandnearultraviolet,brightness 17 mission,tothesolarbrightnessobservedsimultaneouslyfromasoundingrocket.Theinstrumentswere 120-600-nm rangeisgiven. I. LUNARORBITALOBSERVATIONS INTRODUCTION Department ofPhysics,JohnsHopkinsUniversity,Baltimore,Maryland21218 Far-ultraviolet albedooftheMoon R. L.Lucke,C.Henry,andW.G.Fastie (Received 28May1976;revised21September1976) 1162 did notcomeclosetograzingincidence(theobservation improved accuracyneargrazingincidence(Hapke metric functionsofHapke(1963),latermodifiedfor Moon’s surfaceisadequatelydescribedbythephoto- quate: Theamountoflight(e.g.,inphotons/sec)received angle wasalwayscloseto30°fromthevertical), source, 0°

NORMALIZED INTENSITY © American Astronomical Society • Provided by the NASA Astrophysics Data System -5 1164 visible. Theresult(Hapke1963)is J\(a) =loadüub-1+sin the partsofMoonthatarebothilluminatedand for visiblelightand tended bytheMoonasseenfromEarth(6X10sr), outgoing light,or,inthiscase,theanglebetween and ais,asbefore,theanglebetweenincoming for ultravioletlight,where¿/Qmisthesolidanglesub- to unityatfullMoon.Therapiddropinintensityaway phase anglemeasuredfromfullMoon. albedo Aiswhatoneusuallythinksofasanalbedo.It let. from fullMoonisstriking,especiallyintheultravio- Earth andSunasseenfromtheMoon.Thisislunar defined astheratioofbrightnessafullMoonto the otherhand,p,geometric,ornormal,albedois is definedtobetheratiooftotalamountlight Moon’s albedos,andofthephaseintegral.TheBond same distance.Finally,q,thephaseintegral,isbydefi- the brightnessofaperfectlydiffusingdisk(100%, Moon reflectstotheamountoflightincidentuponit.On Lambert’s lawreflector)ofthesamediameterat nition theratioofthesetwoalbedos:q=A/p.The shown (see,forexample,Lucke etal.1973)that notation herefollowsthatof Allen(1964).Itiseasily where /m(«)=^m(«)/^m(0) isnowthenormalized light curvefor theentireMoon[/m(o0is the quantity Equations (6)and(7)areplottedinFig.2,normalized It willbeusefultowritedownthedefinitionsof /(a) =/i(a)XS2:(7) X tan^In^tanj2](o;)2?(a,0.7)(6) 21 q =2\/m(«)sinada, (8) If .a LÜCKE, HENRY,ANDFASTIE visible light),orEq.(7)(forfar-ultravioletlight). plotted inFig.2]./m(«)herewouldbeeitherEq.(6)(for be givenintermsofEq.(1)forasinglespotontheMoon. of lighttheinstrumentreceivesfromMoonand where i=ebecausea0.Here/(/,e,0)istheintensity We write,usingquantitiesfromEq.(1), (Is/Tr)adœ istheintensityitwouldreceivefroma Moon. (e.g., Earth),asafunctionofthe phaseangleaawayfromfull An equivalentdefinitionforthegeometricalbedocan Fig. 2.Normalizedintensityofmoonlight seenatalargedistance p =7r/(/,€,0)/lsado)56/6,(9) o crater Neper,andthebumpatabout10° tion. Thedisplacementbetweenthe observations, thesmoothlineisobtained surface. Thejaggedlineshowstheactual experimental curveat85°Eisthelarge tween 50°Eand65°E.Thebumpinthe text. MareCrisiumwasobservedbe- peaks ofthetwocurvesisexplainedin from thetheoreticalphotometricfunc- from aIXpatchoftheMoon’s Rille formations. E occurredovertheSulpiciusGallus Fig. 1.Intensityoflightreflected 1976AJ 81.1162L Eq. (1)[using Eq. (5)for2(a)],canbemuch morere- Bond albedoA.Thisisbecause thedata,asexpressedby reliable estimateofthegeometric albedopthanofthe by LaneandIrvine’sresults. limit fallsonalinearextrapolation ofthecurvedefined limit ishigher.Itmaybeworth notingthatthisupper terpreted; thedatadonotruleoutpossibilitythat of thisincreaseisabout10%,whichwouldraise^to upper limitisreasonable,butshouldnotbestrictlyin- of a,andthiswillinturnincreaseq.Aroughestimate tion mostprobablyneedstoberaisedforlargervalues can beseeninFig.1,thetheoreticalphotometricfunc- ^ 0.5,andthisisshownbytheupperlimitinFig.3.This obtained, isknowntobemediocrebeyonda~70°.As above, thefitprovidedbyEq.(1),fromwhich(7)is periment didnotincludea>100°,andasdiscussed over 0°

00 1166 LÜCKE, HENRY, AND F ASTI E ^0 O uo r-

Fig. 4. The lunar spectrum obtained in this experiment is compared to the solar spectrum given by Rottman (1975), which has been multiplied by 0.038 to place it on the same scale. The ratio of these two spectra is the albedo of the Moon.

13 Dec 1972. Taking the solar and lunar spectra simul- errors between the two spectrometers (as can be seen in taneously eliminated any possible error caused by vari- Fig. 4, solar lines in the two spectra do not line up pre- ations in the solar far-ultraviolet flux, which can be as cisely), the Apollo spectrum was summed over wave- much as 20% per day or even more during a large flare length intervals beginning and ending in a reasonably flat (Vidal-Madjar a/. 1973). region of the spectrum (e.g., around 143 nm) where Taking the spectra from the peak of the Apollo light small wavelength errors do not matter, and was divided curve minimizes the error involved in correcting the by a similar sum of the synthetic spectrum. The resulting signal from that at the minimum value of a actually seen ratios are then multiplied by 1.27 to account for the (10° on orbit 38) to the signal that would result for a = Hapke function correction mentioned before, and by 0°. The correction factor, obtained from Eq. (l),is 1.27. 0.95 to account for the fact that the peak of the light The signal used was actually the average of ten spectra curve on orbit 38 occurred over the eastern part of Mare taken around the peak of the light curve along a line from Crisium, where the local albedo is about 5% above the 64.°5 E, 12.°2 N to 57.°0 E, 13.°5 N. These were all good lunar average. The results are shown in Fig. 5 (together spectra with no data dropouts or anomalies. with the value at La), where the wavelength range used Rottman’s solar data (supplied to us as a private is given in Table I and the vertical bars include both communication) gave a numerical value in photons cm-2 wavelength-dependent errors estimated from the re- sec-1 nm”1 for the solar flux at intervals of 0.1 nm over producibility of the instruments’ calibrations (about the spectral range of 123-158 nm, with a resolution ±5%), and wavelength-independent errors stemming about 0.1 nm. These data were folded through the Apollo from uncertainties in the Hapke function correction and instrument’s response (the Apollo spectrometer had the imperfectly known slit width of Rottman’s spec- 1.15-nm resolution) to generate a synthetic spectrum of trometer (about db 10%). The point at La is assigned a direct sunlight to compare with the spectrum of moon- light that was actually obtained. These two spectra are shown in Fig. 4, where the synthetic solar spectrum has been multiplied by 0.038 in order to show both spectra TABLE I. Observed lunar albedo. on the same scale. It will be noted that the La line at Wavelength A 121.6 nm is missing from the synthetic spectrum and is range (nm) p q = 0.45 q = 0.5 off-scale in the actual spectrum. This line is about 0.1 nm 160-167 0.046 0.021 0.023 wide, which makes it, as far as the Apollo instrument is 150-160 0.044 0.020 0.022 concerned, monochromatic, so that this point can be 145-150 0.044 0.020 0.022 138-145 0.052 0.023 0.026 treated individually, without having to go through the 128-135 0.063 0.028 0.032 folding process just mentioned. 121.6 0.063 0.028 0.032 In order to avoid difficulty with slight wavelength

FAR-ULTRAVIOLET ALBEDO OF THE MOON 1167

III. LUNAR DUST SAMPLES r- The values for the lunar far-ultraviolet albedo obtained from the Apollo 17 experiment were generally corroborated by laboratory measurements of the ultraviolet reflectance of lunar dust samples. These measurements were made with the equipment and methods described by Lucke et al. (1973), however, improved experimental techniques have resulted in substantially more accurate results than those originally reported. The Fig. 5. The geometric albedo of the Moon given by this experiment. problem of inferring the geometric albedo of the Moon The line drawn through these points shows the shape of the curve to (at any wavelength) from laboratory measurements of be expected from the theory developed by Henry et al. (1976), based the reflectance of a flat sample has been treated else- on the wavelength dependence of the complex index of refraction of 1 where (Lucke et al. 1973; Lucke 1975). In the present lunar material. Also shown is the Moon’s albedo inferred from labo case the inferred geometric albedo is obtained by ratory studies of the reflectance of lunar dust samples. multiplying the laboratory reflectance by 2.05. The result for one of the lunar samples (within the accuracy given here, all the samples had the same reflectance) is shown in Fig. 5 along with the actual lunar observations total uncertainty of ±20% because of the uncertain from Apollo 17. Agreement between the curves is only correction for instrumental dead time resulting from the fair, but there is no particular reason to expect that it high intensity of this line. The shape of the line labeled should be better. The laboratory samples used (sample “Moon” in Fig. 5 is based on the theory of Henry et aL numbers 10 084.9, 12 070.92, 14 259.195, 75 081.71, (1976), and is the same as in Fig. 6. and 78 481.26 from Apollo 11, 12, 14, 17, and 17, re- The geometric albedo of the Moon in the far ultravi- spectively) may not have ultraviolet reflectances that are olet, from Fig. 5, rises from 0.045 at about 165 nm to close to the average for the whole Moon (or the 3% of the 0.063 at 121.6 nm, with an average value of about 0.052. lunar surface covered in this experiment). Also, their For q = 0.45, the average Bond albedo is ^4 = 0.023, and reflection properties may be slightly altered [although for q = 0.5, it is ^4 = 0.026. For comparison, the values reflectance measurements in visible light indicate oth- in visible light (about 580 nm) are p = 0.12, ^4 = 0.07. erwise (Nash et al. 1970)] by the small amounts of Table I summarizes the values of p and A as functions oxygen and water vapor they absorb from the Earth’s of wavelength. atmosphere (Cadenhead a/. 1973).

300 400 WAVELENGTH (nm) Fig. 6. A compilation of lunar albedo measurements from the far-ultraviolet to visible wavelengths. With the possible exception of the dotted portion, the line should be a good approximation to the Moon’s geometric albedo throughout the wavelength range shown.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1976AJ 81.1162L 1168 LUCKE,HENRY,ANDFASTIE that theStairandJohnstonobservationsareinerror. observations ofsmallpatchestheMoon’ssurfaceby compromise amongthelunarobservationsofother long-wavelength partoftheline(A5;250nm)isa be agoodapproximationtothegeometricalbedoof not includedbecauseFig.6isalreadytoocrowded,and nm. Otherinvestigatorshavealsomadelaboratory tometric functiontocorrecttheir values(takenatsome revision camefromtakingintoaccountthelunarpho- short-wavelength (200-250nm)results(1967a)which since neitherthesubsequentobservationsofeitherHarris A conflictingground-basedobservation(notshownin laboratory measurementsinthefarultravioletaswell. lunar observationsalreadydiscussed,isconsideredtobe ground-based observationsreasonablywelldowntothe results withinexperimentalerror(AdamsandMcCord because thesemeasurementsgenerallymatchthepresent samples inthevisibleandnearultraviolet,buttheseare measurements ofthereflectancevariousMoondust normalizing tothevaluegivenbyHarris(1961)at560 around theApollo11,12,and14landingsites, eraging theirrelativereflectivitycurvesofsmallregions of viewwasabout500kmwide(andlookedatthelunar tomultiplier tube aswasthe200-250-nm range(Le- geometric albedo.AllofLebedinsky’s resultsweretaken nonzero observationandillumination angles)tothe are nowinreasonableaccordwiththestraightline.This a sharpdropinalbedoto~3%near340nm.However, a strongsupportingargumentforthevalidityofthese this, togetherwiththeagreementfar-ultraviolet limit (~300nm)atwhichthelattercanbemade,and in Fig.5. workers. Pointsontheshort-wavelengthpartofline Moon throughoutthewavelengthrangecovered.The farside), andthetwopointsattributedtoMcCordetal. the resultsofLebedinskyetal.(1967b,1968)whosefield inferred fromlaboratorymeasurements).Theseare McCord etal.(1972a)showsuchadrop,itseemsclear mostly observationsofthewholelunardisk,exceptfor all ofwhichrepresentactualobservationstheMoon a bewilderingvarietyofresultsfromotherinvestigators, the visibleregion.ThisisdoneinFig.6,whichincludes et al.1967b)wascoveredby filmratherthanbyapho- Fig. 6)isthatofStairandJohnston(1953)whoreported albedo throughoutthefarandnearultravioletinto a pictureofthewavelengthdependenceMoon’s the longer-wavelengthrange(280-360 nm)(Lebedinsky (1961) orLaneandIrvine(1973),noranyofthemany (A <170nm)arethelunaralbedomeasurementsgiven (1972b) whichdefinethestraightlineobtainedbyav- (our resultsforthelunaralbedolongwardof200nmare reported herewiththeresultsofotherworkerstoobtain from theZond3spacecraftas itpassedtheMoon,but 1971; Nashetal.1970).ThelinedrawninFig.6should The laboratorymeasurementsmentionedabovematch Lebedinsky etal.(1968)revisedupwardtheirearlier We cannowcombinethelunarfar-ultravioletalbedo © American Astronomical Society • Provided by the NASA Astrophysics Data System IV. WAVELENGTHDEPENDENCEOFALBEDO viding theirpublishedBondalbedosby0.59. the lunaralbedomeasurementwould,inourestimation, plotted inFig.6aregeometricalbedosobtainedbydi- should alsobementionedthattheCarveretal.results taken fromfreelyspinningandprecessingrockets.It those ofCarveretal.(1974)andHeddle(1962)were from anattitude-controlled,Moon-pointedrocket,while downward trendalmostperfectly.Itisperhapsworth these resultswerenormalizedtotheground-basedob- tage ofextendingintothevisibleregionandagreeing noting thattheresultsofBentleyetal.(1974)weretaken servations at330nmtheywouldcontinuethelinear fairly wellwithground-basedobservations.Infact,if covering therange260-330nm,whichhaveadvan- consistent withthevaluesgivenbyBentleyetal.(1974) consistent. Theyarealsoconsistentwiththesingleob- to obtaintheresults. servation ofHeddle(1962).Theyarenot,however, represent valuesobtainedfromfivedifferentrocket cause (exceptforasingleobservationat121.6nm)they these pointsisduetouncertaintiesinthesolarfluxesused results. Wedonotknowhowmuchoftheerrorbarson and ParkinsonReeves(1969),wouldresultin solar fluxmeasurementofRottman(1975)isroughly be moreaccuratelyplacedbetween170and180nm.The rapidly longwardof160nm,theeffectivewavelength length axis.However,sincethesolarfluxrisesvery an appropriateadjustmentofAhmadandDeutschman’s halfway betweentheolderresultsofWidingetal.(1970) length oftheirfilterstolocatethepointsonwave- from their1972paper,whichusedtheeffectivewave- flights, withallbuttwomeasurementsbeingmutually attributed toAhmadandDeutschmanaretakendirectly mately) 105-200and135-200nm.ThepointsinFig.6 broad-band filtersthatcoveredtherangesof(approxi- taken withatelevisionphotometerlookingthrough be consideredaprimarymeasurement. Johnston’s resultsatthesewavelengths.The280- given byaRussiangroupin1956(Barabashevand Chekirda 1956),whichisinagreementwithStairand curve wasnormalizedtothenear-ultravioletalbedovalue was thensenttothegroundviatelevision.Because a goodabsolutemeasurement,the280-360-nmalbedo almost inevitableinaccuraciesofsuchasystemprevented bedinsky etal.1967a,1968).Thedarkeningofthefilm 360-nm resultsofLebedinskyal.cannot,therefore, of thereflectivity oflunardustsamples (Fig. 5).An tween theseobservationsand laboratorymeasurements at 120nm(Fig.5).Thereis reasonable agreementbe- albedo risingfromabout0.045 at165nmtoabout0.063 measurements oftheMoon’s lightreflectingproperties in the120-165-nmrange,which showthegeometric The resultsofCarveretal.(1974)areapuzzlebe- The resultsofAhmadandDeutschman(1972)were We havepresentedtheresults ofthefirstextensive V. CONCLUSIONS 1976AJ 81.1162L Carver, J.H.,Horton,B.O’Brien,R.S.,andO’Conner,G. Cadenhead, D.A.,Jones,B.R.,Buergel,W.G.,andSetter,J.R. Donnelly, R.F.,andPope,J.H.(1973).NOAATRERL276-SEL Adams, J.B.,andMcCord,T.B.(1971).Science171,567. Ahmad, I.A.,andDeutschman,W.A.(1972).Astron.J.77,692. to theJohnsHopkinsUniversity. Fastie, W.G.,Feldman,P.D.,Henry,R.C.,Moos,H.W.,Barth,C. Fastie, W.G.(1973).Moon7,49. Fastie, W.G.,andKerr,D.E.(1975).Appl.Opt.14,2133. Bentley, A.N.,DeJonckheere,C.G.,andMiller,D.E.(1974).Astron. Barabashev, N.P.,andChekirda,A.T.(1956).Circ.Astron.Obs. NAS 9-11528,andbyNASAGrantNGR21-001-001 lunar materialhasbeengivenelsewhere(Henryetal. length dependenceofthecomplexindexrefraction nation fortheshapeofthiscurveintermswave- tion oftheMoon’salbedowithwavelength.Anexpla- lected inFig.6,whichgivesagoodpictureofthevaria- results ofourmeasurementsandothershavebeencol- which fitstheobservationsreasonablywell(Fig.1).The tometric functionhasbeengiven[Eqs.(1),(3),and(5)], analytic expressionfortheMoon’sfar-ultravioletpho- based onthetheoreticaltreatmentofHapke(1963), 1976). A., Thomas,G.E.,andDonahue,T.M.(1973).Science182, 710. J. 79,401. 25. (1973). ProceedingsoftheFourthLunarScienceConference (1974). Moon9,295. (Pergamon, NewYork),p.2391. Kharkov StateU.No.15. © American Astronomical Society • Provided by the NASA Astrophysics Data System This workwassupportedbyNASA/MSCContract ACKNOWLEDGMENTS REFERENCES FAR-ULTRAVIOLET ALBEDOOFTHEMOON Stair, R.,andJohnston,R.(1953).J.Res.Natl.Bur.Stánd.(U.S.) Widing, K.G.,Purcell,J.D.,andSandlin,G.D.(1970).Sol.Phys. Vidal-Madjar, W.,Blamont,J.E.,andPhissamay,B.(1973). Rougier, G.(1934).L’Astronomie48,220,281. Parkinson, W.H.,andReeves,E.M.(1969).Sol.Phys.10,342. Nash, D.B.,Conel,J.E.,andGreen,R.T.(1970).Science167, Rougier, G.(1937).L’Astronomie51,165. Rottman, G.J.(1975).Privatecommunication. McCord, T.B.,Charette,M.P.,Johnson,V.,Lebofsky,L.A.,and McCord, T.B.,Charette,M.P.,Johnson,V.,Lebofsky,L.A.,and Lucke, R.L.,Henry,C.,andFastie,W.G.(1973).Astron.J.78, Lucke, R.L.(1975).Thesis,JohnsHopkinsU.,p.107(availablefrom Lucke, R.L.,Henry,C,andFastie,W.G.(1974).LunarScience Lebedinsky, A.L,Krasnopolsky,V.A.,andAganina,M.U.(1968). Lebedinsky, A.L,Aleshin,G.M.,lozenus,V.A.,Krasnopolsky, Lebedinsky, A.L,Krasnopolsky,V.A.,andKrysko,(1967a). Lane, A.P.,andIrvine,W.M.(1973).Astron.J.78,267. Henry, R.C.,Fastie,W.G.,Lucke,L.,andHapke,B.(1976). Heddle, D.W.O.(1962).Nature(Lond.)193,861. Harris, D.L.(1961).PlanetsandSatellites,editedbyG.P.Kuiper Hapke, B.(1966).Astron.J.71,333. Hapke, B.(1963).J.Geophys.Res.68,4571. Geophys. Res.78,1115. 51,81. 721. 12, 52. Pieters, C.(1972b).Moon5,52. Pieters, C.(1972a).J.Geophys.Res.77,1349. 65. Planets, editedbyA.Dollfus(North-Holland,Amsterdam),p. A., Selivanov,A.S.,andZasetsky,V.(1967b).Moon dam), p.59. 263. sterdam), p.47. Moon andPlanetsII,editedbyA.Dollfus(North-Holland,Am- Moon andPlanets,editedbyA.Dollfus(North-Holland,Amster- University Microfilms,AnnArbor,Michigan). and G.M.Middlehurst(Univ.ChicagoP.,Chicago),Ch.8. Moon 15,51. V (LunarScienceInstitute,Houston),p.469. 1169