1992AJ 104. . 405R 1 THE ASTRONOMICALJOURNAL Uranus enabledsubmillimeterphotometricobservationsof with unprecedentedaccuracy,usingtheJamesClerkMax- this asteroidtobemadeon1989September2and4UT well Telescope(JCMT)locatednearthesummitof most importantcalibrationsourcesatthesewavelengths, Mauna KeainHawaii.HavingUranus,oneofthetwo reliably becauseoftheirextremesensitivitytoatmospheric taken withthe0.6mmfilterusuallycannotbecalibrated can etah1990)usingthesixbroadbandfilterscenteredat is basedonthemodelatmospheresofOrton(1986).The calibration processsincetheuncertaintiesarisingfrom only afewdegreesawayintheskydramaticallyaided dence. Theapertureofthebolometerwaschosentomain- tion enabledeventhesedatatobecalibratedwithconfi- variations, buttheunusualcircumstancesofthisconjunc- flux densitiesofUranusarelistedinTable1. computed usingthefluxesprogramatJCMTwhich sities ofUranus,theprimecalibrator,andNeptunewere the reliabilityofasteroidalobservations.Thefluxden- were greatlyreduced.Moreover,Neptunewasalsonearby of theS.E.R.C.UnitedKingdom, theNetherlandsOrganisationfor at theshorterwavelengths,but werenecessarytoobtain are muchlargerthanthediffraction limitofthetelescope tain thebeamsizebetween16"and21".Thesesizes 2.0, 1.1,0.8,0.6,0.45,and0.35mmwavelengths.Data and wasobservedwiththesametechniqueasacheckon atmospheric opticaldepthandinstrumentalcalibrations 405 Astron.J. 104 (1),July1992 0004-6256/92/070405-07S00.90 ©1992Am.Astron. Soc.405 Scientific Research,andtheN.R.C.of Canada. ’The JamesClerkMaxwellTelescope is operatedbytheR.O.E.onbehalf The 1989conjunctionofthebrightasteroid4Vestawith © American Astronomical Society • Provided by the NASA Astrophysics Data System The dataweretakenwiththeUKT14bolometer(Dun- peaked overthe5.342hrrotationperiod,unlikeopticallightcurvewhichissinglepeaked.Thislight ence ofadusty,porousregolith.At1mmwavelengththerotationallightcurveVestaappearsdouble wavelengths. Althoughtheinterpretationofspectrumisambiguous,itseemstoindicatepres- Rayleigh-Jeans temperatureisasloworloweratsubmillimeterwavelengthsitcentimeter of thesubmillimeterthermalspectrumandlightcurveasteroid4Vesta.Thedisk-averaged Precise andwell-calibratedobservationsmadewiththeJamesClerkMaxwellTelescopearepresented curve isapparentlydominatedbythetriaxialshapeofVesta,andnotsignificantlydistorted optical albedospots. MILLIMETER ANDSUBMILLIMETEROBSERVATIONSOFTHEASTEROID4VESTA 1. OBSERVATIONS HI A,NRCofCanada,Ottawa,OntarioK1A0R6,Canada HI A,NRCofCanada,Ottawa,OntarioKlA0R6,Canada Russell O.RedmanandP.A.Feldman Received 30September1991;revised2March1992 Joint AstronomyCentre,Hilo,Hawaii96720 I. HallidayandF.Creutzberg VOLUME 104,NUMBER1 H. E.Matthews ABSTRACT correction forthefluxdensityofUranusneverexceeded photometric accuracy.Asafringebenefit,thebeam-size ations oftheatmosphericwatercontentalongline submillimeter photometricdataarisesintherapidfluctu- not justthetransmissionbutalsowidthandcentral water vaporcloudspassingthroughthebeamcanchange actual bandpassisoftendefinedbytheatmosphere,sothat sight. UsingbroadbandfilterssuchasthoseinUKT14,the ilar spectrainthiswavelengthrange,thechangesshape so smallthatthedetailedbehaviorofatmospherewas lengths. Thetwosourcesweresocloseandthecycletimes frequent observationsofastronomicalcalibrationsources, wavelength ofthebandpass.Theonlyrealcureforthisis of thebandpasswouldhavehadnegligibleeffectson rendered unimportant.SinceUranusand4Vestahavesim- roughly 10minat0.8mmand30shorterwave- cloudlets willnotbeplaneparalleloverthemountaintop. preferably verynearthetargetsinceitisobviousthat observing Uranustocalibratethedata.Eachcycletook cycle consistedofselectingafilter,observing4Vestaand cycling rapidlybetweenthetwosources.Eachobserving made itfeasibletocalibrateeachdatapointpromptlyby 1.5%. Theprimarydifficultytobefacedwhencalibrating The proximityofUranusto4Vesta,lessthan2°apart, A (mm)F(Jy) v Table 1.CalibrationmodelfluxdensitiesofUranus. 0.35 0.6 0.8 0.45 2.0 1.1 257 108 184 49.1 20.54 82.9 JULY 1992 1992AJ 104. . 405R roughly tentimeslargerthanat1.1mm,thecorrection was normallylessthan15%. points. Evenat0.35mm,wheretheopticaldepthis tion at1.1mmrarelyexceeded1%foranyofthedata both nights.BecauseNeptunewasoverfourtimesfarther measured asteroidalfluxes.Theentireatmosphericcorrec- 406 REDMANETAL.:VESTA from Uranusthan4Vesta,theatmosphericuncertainties was observedinthesamewayas4Vestawitheachfilteron produce theshapeofpredictedspectrumwithpossible nights, withthemodelspectrumcomputedbyfluxes in thecalibrationarecorrespondinglylarger.Figure1 Neptune, whichwasroughly9°fromUranusatthetime, shows themeasuredspectrumofNeptuneontwo here havebeenaveragedoverVesta’srotationalperiodto program shownasasolidline.Themeasuredspectrare- long integrationtimesneededtodetectasteroidsatcenti- are alsorotationallyaveragedtemperaturesbecauseofthe VLA observationsofJohnstonetal.(1989)at2and6cm give afluxrepresentativeofitswholevisiblesurface.The given inTable2.Thesubmillimeterdatawearereporting systematic errorsofupto10%. meter wavelengths.Similarly,ourexperiencewiththe11m NRAO telescopeinthelate1970’ssuggeststhatobser- required mostofarotationalperiod,althoughitisnot vation byConklinetal(1977)at3.3mmwouldalsohave explicitly statedintheirpaper. temperatures onVesta’ssurface.Italsodoesnotcontain raw dataandalsorelatedinasimplewaytothephysical sent thedatasinceitisbothlinearlyproportionalto versus frequency.Thequantityrwaschosentorepre- disk-averaged Rayleigh-Jeansbrightnesstemperaturer 100 RJ RJ 25 60 12 fim 0.35 mm 0.8 0.6 0.45 2.0 cm 2.0 3.3 mm 6.17 6.14 1.1 © American Astronomical Society • Provided by the NASA Astrophysics Data System As acheckonthereliabilityofobservingtechnique, The measuredthermalemissionspectrumof4Vestais Figure 2showstheradiomeasurementsplottedas Table 2.FluxdensitymeasurementsofVesta. 2.1 RotationallyAveragedSpectrum 384.8 40.42.5692.153 165.2 15.82.5692.153 139.3 38.72.5692.153 67.55 21.42.5692.153 0.111 0.0152.42.248 Conklin 0.318 0.0482.1941.619 0.004300 0.0000542.2411.486 Johnston 9.65 0.342.1941.619 0.000322 0.0000542.5671.68 0.000146 0.0000162.5582.682 3.19 0.082.1941.619 5.91 0.122.1941.619 1.141 0.0172.1941.619 1.878 0.0232.1941.619 (Jy) F v 2. RESULTS (Jy) (AU) Tedesco (1986) et al(1977) et al(1989) this paper Reference materials atthesewavelengths.Forcomparisonwithour observations inFig.2(butnotTable2)thelonger al. (1977)havebeenscaledby wavelength dataofJohnstonetal.(1989)andConklin any hiddenassumptionsabouttheemissivityofsurface body withthesamediameteranddistancefromSunas where dandDweretheassumeddiameterdistance with aconstantslope,since temperature andfrequencyrangeisnearlyastraightline Vesta. Itisinterestingthatablackbodyspectruminthis from anonrotatingandrapidlyrotatingsphericalblack- of VestafromtheSun,respectively.Weusedadiameter reported byDunham(1991). 520 kmforVestabasedontheoccultationmeasurements a constantPlancktemperatureofabout130Kmightfitthe lengths. Aswillbediscussedbelow,thephysicalinterpre- wavelengths beforedroppingagainatsubmillimeterwave- us toexpectthatthespectrumwouldpeakatmillimeter sible systematicerrors.Conklineta/.’shigherpointhadled data from6cmto0.35mmifallowanceismadeforpos- solve theissue. our measurementat2mmaresufficientlyaccuratetore- wavelengths. Unfortunately,neitherthe3mmdatumnor tation isverydifferentifthespectrumflatatallradio the characterofvisiblelightcurve isdeterminedbya though thetriaxialityof4Vesta contributessignificantly, two maximaandminima in eachrotationperiod.Al- 1977) thespectrumappearstoberemarkablyflat.Infact, 217 T taken on1989September2and4UT,respectively. ature. Thedottedanddashedlinesconnecttheobserveddatapoints solid lineshowsthepredicteddisk-averagedRayleigh-Jeanstemper- Fig. 1.SpectrumofNeptune,measuredrelativetoUranus.The Also showninFig.2aretheexpectedPlanckspectra With theexceptionof3.3mmpoint(Conklinetal. For atriaxialasteroidthelight curvenormallyshows (

'o CN co

PQ

en

-3-2-10 1 2 logic \ (cm)

Fig. 4. Measured thermal spectrum of Vesta from 12 jum to 6 cm. The plotted quantity is the ratio of a disk-averaged intensity to the intensity of a nonrotating blackbody with the same diameter and distance from the Sun. Our data are shown with solid circles. Data from the published literature are shown with open circles. The upper and lower dotted curves show the relative intensities expected from nonrotating (NR) and rapidly rotating (RR) blackbodies, respectively. The dashed curve shows the predicted spectrum without the effects of scattering (NOSC), using material properties similar to Johnston et al. ( 1989). The solid line through the data (SC) includes the effects of scattering by dust grains in the regolith.

exceed 4asteroid. Since the fundamental term, which can only be due to albedo spots, data in Fig. 4 were obtained over several years under a is a lesser (2cr) effect. This is to be expected, since the wide variety of viewing conditions, this ratio has been com- amplitude of the temperature variations due to albedo will puted for each data point using the temperature appropri- be roughly four times smaller than the albedo variations ate for the distances of Vesta from the Sun and the Earth themselves. We conclude that the lightcurve at a wave- at the time of the observation. length of 1 mm appears to be produced mainly by the There are two standard models which are commonly triaxiality of the asteroid, and not by its albedo spots. It invoked in discussing thermal emission from asteroids. The should be noted that the significance of the harmonic terms “refined standard” model discussed by Lebofsky et al. relative to the mean is independent of most of the system- atic calibration problems which make an absolute measure- (1986) treats the asteroid as a nonrotating sphere whose ment of the submillimeter spectrum difficult. temperature at each point is obtained by balancing the heat lost by infrared radiation with the absorbed solar energy. The disk-averaged temperature ^NR calculated from this model is the maximum expected from a real asteroid near 3. DISCUSSION opposition, since all plausible physical mechanisms will re- duce the flux emitted from the surface. The standard non- Figure 4 presents the entire observed spectrum of ther- rotating model works well to predict the thermal infrared mal emission from Vesta in a format which emphasizes the radiation from asteroids.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1992AJ 104. . 405R 2 4 42 409 REDMANETAL.:VESTA by therapidlyrotatingmodelisausefulfiducialtempera- is calculatedbybalancingtherateofinfraredheatloss plane ofthesky.Thetemperatureasafunctionlatitude stant onlatitudebandsandthattherotationalaxisisin sphere isrotatingsorapidlythatthetemperaturecon- from deepbelowthesurface. ture fortheinterpretationofemissionwhichoriginates against theaverageabsorbedinsolation(see,e.g.,Johnston ues smallerthanTatcentimeterwavelengthsupto dust, predictthatthemeantemperaturewillrisefromval- measured dielectricpropertiesoftypicallunarbasaltic et al.1989).Thedisk-averagedtemperatureTrrpredicted ior isexhibitedbyallofthesemodels,whichsuccessfully behavior ofVesta’sspectrumatsubmillimeterwave- fitted theavailabledataforseveraldifferentasteroidswith from Fig.4itisclearthatthesemodelsdonotdescribethe Webster &Johnston1989;etal.1989).However, a rangeofdifferentsurfacematerials(Websteretal.1988; lengths. Asuccessfulmodelforthethermalemissionmust likely tobeimportantare(a)reflectionsattheoutersur- ture atradiowavelengthsofVestabelowTrr.Thosemost range. explain whytheapparenttemperatureremainsbelow face oftheregolith,(b)areductioninactualtemper- ^nr atshortsubmillimeterwavelengths.Thissamebehav- temperature variationsatthesurface,and(c)scatteringby ature ofthedeeperlayersregolithduetodiurnal grains withintheregolithwhichcanreduceemissivity from anasteroidwillcombineallthreeeffectsindiffering in awavelengthdependentfashion.Theactualemission RR amounts ateachwavelength. radiation atasmoothboundarybetweentheasteroidalre- 7rr> andmuchbelowr,overtheentiresubmillimeter been similartoourobservationsat0.45and0.35mm. IRAS (Tedesco1986)at25¡imandbeyondshouldhave index ofrefraction«,reflectionsatthesurfacewillreduce golith andthesurroundingvacuum.Ifrockhasan for thelowemissivityatshortsubmillimeterwavelengths, servations atcentimeterwavelengths(Johnstonetal. sivity woulddropto0.89;thiscouldaccountfortheob- the emissivitybyroughly4n/(n+l)-Forexample,with since therelativefluxdensitiesinFig.4measuredwith the stronglynonlineardependenceofblackbodyradiation average temperatureofthedeeperlayersbelowTrrdueto inertia, thediurnaltemperaturevariationswilldepress n^2, correspondingtoafairlyporousregolith,theemis- the Cauchy-Schwartzinequality whichgivesT on temperature(eaF).Thisisasimpleconsequenceof al. (1989)requireboththesurface reflectionandthisad- ers, whichisprobedatlongwavelengths, isthetimeaver- ditional coolingofthedeeplayers toexplainthedifference age ofthesurfacetemperature. ThemodelsofJohnstonet 1989). However,reflectionsaloneprobablycannotaccount NR = (F).The temperature ofthedeeplay- RR © American Astronomical Society • Provided by the NASA Astrophysics Data System The “rapidlyrotating”modelassumesinsteadthatthe The dustmodelsofJohnstonetal.(1989),usingthe Several mechanismscanlowertheapparenttempera- The simplestmechanismisreflectionoftheemerging If thesurfacelayerofregolithhasalowthermal s between theirobservedtemperaturesatcentimeterwave- lengths andTrr-Acceptingthismodelatfacevalue,itcan lengths, providedthattheopacityofdustinre- from thesurface.Infarinfrared(20-50/im)this this mightbemineralogicallysignificant. to increasesharplybetween0.35and0.1mm(=100jum); the IRASdataaswell,opacityofdustwouldhave golith ismuchsmallerthantheyassumed.Toaccountfor also explainourobservationsatsubmillimeterwave- have beenobservedat85/¿mforseveralasteroidsbyLe- mechanism hasbeeninvokedtoexplainthelowapparent emissivity bymakingitmoredifficultforphotonstoescape Van &Price(1984).Theeffectivenessofthismechanism emissivity oftheMoon(Simpsonetal.1981)andmay depends uponthewavelengthandgrainsizedistribu- tion. AssumingthenumberofgrainsdNinsizerange if S=4(Kheim1984).IfS<4,aswouldbeexpected believed, onthebasisofopticalpolarizationmeasurements the emissivitywouldincreasetoshorterwavelengths.Al- debris fromasingle,recentimpactdominatedtheregolith, ternatively, if5>4theemissivitydecreasestoshorter wavelengths. Thesizedistributionofgrainson4Vestais JCMT, andpossiblyeventocentimeterwavelengthsde- throughout thewavelengthrangeobservablewith shorter thanIna,theemissivityshouldbereduced 5>4. Forcomparison,ontheMoonS=4.2appearsto emissivity of4Vestaatcentimeterwavelengthsisleast pending uponthevalueofS.FromFig.4itisclearthat 50 fim.Sincescatteringbecomeseffectiveatwavelengths as highitisinthesubmillimeterrange,whichconstrains {a,a+da) canberepresentedbyapowerlawdN characterize thesmallerparticles(<0.5cm)inApollo core tubesamplesofthelunarmaria(Mitchelletal.1972, particles around100/¿minsizetoexistVesta’sregolith, below Tat0.45mm. without affectingthepolarizationresultsoremissivity depressing theemissivityatsubmillimeterwavelengths of grains100/xmandsmaller.Thespectratheasteroids system doappeartohaveregolithswithlargepopulations at centimeterwavelengths.Othersolidsurfacesinthesolar (Le Bertre&Zellner1980;Dollfus1990)tocutoffbelow highly simplifiedmodelsforthethermalstructureandra- all slopesteeplyfromnearlyat1.1mmdowntoor satellites GanymedeandCallisto(Matthewsetal.1990) 2 Pallasand3Juno(Redmanetal.1990)theJovian Johnston etal.(1989);theycannotbefittedtothewhole diative transferinanopticallydeepregolith(Redman and thecoolingofdeeperlayers,asdidmodels oc a~datheemissivitywillbeindependentofwavelength spectrum usinganyfixedvalue forthelosstangent.The The modelspectrumprovides a goodfittoallofthedata index is^5,andwhichcutsoff abruptlyatabout100¿¿m. from particleswithapower-law sizedistributionwhose solid lineincludestheeffects of scatteringintheregolith 1973). Inprincipleitispossibleforalargepopulationof 1992). Thedashedlineincludesonlythesurfacereflection rr (except thedatapointbyConklin etal.1977)usinga y Scattering bygrainswithintheregolithreduces Also showninFig.4aretwomodelspectra,using 409 1992AJ 104. . 405R provide agoodfittothedata,especiallyifinfrareddata are allsimilartothoseassumedbyJohnstonetal.(1989) istence ofsuchdustonVesta.However,withoutreliable However, othersetsofparametersalsocanbefoundwhich and providingthattheporosityisfairlylarge,p^0.85. 410 REDMANETAL.:VESTA ternoon warmingasseenintheinfraredregardlessofits lating dustlayerwhichshouldnotshowaphaseeffect,and could conclusivelydistinguishbetweenatransparent,insu- to estimatehowlargethephaseeffectmightbe.Suchob- trum ofVestapeakedatmillimeterwavelengths,however, knowledge ofthewavelengthdependenceabsorption wavelengths maythusbeconstruedassupportingtheex- are notincluded.Ourobservedspectrumatsubmillimeter dielectric constant,losstangent,andathermaldepththat interferometric observationsofDrummond&Hege for Vestathanmostotherasteroidssincethespeckle emissivity. an opaquesurfacewhichshouldshowsomedegreeofaf- servations wouldbequitevaluable,however,sincethey There arenotasyetsufficientdataatanyradiowavelength the aspectofpole.Thisismosttroublesomewhen asteroid arethelargelyunknowneffectsofphaseangleand the evidencefordustwouldhavebeenunequivocal. coefficient, thequestioncannotberesolved.Hadspec- data atdifferentwavelengthsaretakentimes. which indicateawarmertemperature,weremadewhenthe nificant thattheobservationsofConklinetal.at3.3mm, wavelength-independent emissivityof0.9.Itispossiblysig- idly rotatingmodeltopredictthetemperature,witha is possibletofitallofoursubmillimeterdatafrom1989 can behopedthegeometryofrapidlyrotatingmodel.It roughly 70°tothelineofsight,matchingaboutaswell rotation isprograde.In1989Septemberthepolewastilted warmer thantheywereduringourobservations.Unfortu- pole of4VestawasorientedtowardtheSunandEarth. techniques betweenthetwo runs. Ifthesewavelength- ing 72±6Kasagainst118±2in1989.Thereaderis was atanangleof95°withrespecttothelinesight,i.e., important issue. nately, theshortageofdatawithsufficientsignaltonoiseat This wouldhaveallowedthedeeperlayerstobecome September withinthecalibrationaccuracyusingrap- and thatthereweremajordifferences inthecalibration cautioned thatthequotederrors areinternalerrorsonly, comparable tothe1989data.Althoughmeantemper- we werelookingattheequatorwithsouthpolebarely man etal.1990),madein1988Decemberwhenthepole different aspectsandphasespreventsusfromresolvingthis indeed reducedbyscatteringin theregolith.Ifso,ap- strong evidencethatatshortwavelengths theemissivityis dependent changescanbeconfirmed, theywouldprovide at 0.45and0.35mmseemedtobecoolerin1988,averag- ature at1.1mmisverysimilar,thetemperaturesmeasured visible. Inprincipletheseobservationsshouldhavebeen (311;+ 67)in(1950.0)eclipticcoordinatesandthatthe (1989) haveshownthatthepolepositionisapproximately © American Astronomical Society • Provided by the NASA Astrophysics Data System The aspectoftherotationalpoleiseasiertodealwith Complicating theinterpretationofspectrumany We haveoneprevioussetofobservationsVesta(Red- ber isprobablyillusory.Severalofthephysicaleffectsdis- lengths. cussed abovewouldhavetoconspirereducethe apparent temperaturestoaboutthesamevalueatallwave- parent simplicityofthespectrumobservedin1989Septem- indicate afairlyloose,fluffydustlayerwithporosity physical parameterssimilartopreviousstudiesseems timeter wavelengths.Itdoesnotappeartobepossible more often,sincefar-infrareddatacouldprovideveryim- possible tofittheradiodata,althoughnotIRAS p~0.85 dominatedbylargenumbersofparticlesnearthe seeing thesamecoollayers.Arepresentativemodelusing ity increasesharplyintheinfraredtopreventIRASfrom of theregolith.Thiswouldrequire,however,thatopac- layer istransparent,allowingustoseethecold,deeplayers ously. Itispossiblethatatallradiowavelengthsthedust vents usfrominterpretingthedustpropertiesunambigu- explain thiswithoutsomekindofdustlayeronVesta’s cold orcolderatsubmillimeterwavelengthsasitiscen- by remeasuringtheemissionofVestaat2mmwithmuch portant constraintsforthemodels. using averydenseregolithwithporosityaslowp unique sincethereareanumberofdifferentwaysto cutoff sizeof100/im.Thissolutionis,unfortunately,not surface, buttheveryflatnessofradiospectrumpre- achieve aflatspectrumatradiowavelengths.Itiseven material forasteroidregolithsatsubmillimeterwave- demonstrate thepresenceofdustandallowamoredirect higher accuracy.Ifthespectrumappearssignificantly lengths. Withoutsuchmeasurements,oneisforcedtopro- measurements ofthelosstangentreasonablecandidate estimate ofitsproperties.Evenbetterwouldbelaboratory warmer at2mmthan1mm,thiswouldconclusively with modelswhichinevitablycontainlargenumbersoffree ceed bycomparisonwithotherasteroids(Redmanetal. signal tonoiseofthe1mmlight curvesincealargepartof mal infraredobservations.Itwould beeasytoimprovethe in combinationwithquasi-simultaneous visibleandther- of thisresultmakesithighlydesirablethatbeconfirmed thermophysical modelwhichcorrectlydescribesthether- proach, thesuccessofsimplescatteringmodelinFig.4 parameters. Notwithstandingtherisksinherentinthisap- of thesystemisrelativelypoor. Quasi-simultaneousobser- the spectrumatshorterwavelengths wherethesensitivity the observingtimereportedhere wasdevotedtomeasuring tion fromtheopticalalbedospots.Thelowsignaltonoise triaxial shapeofVesta,withoutanysignificantcontribu- lengths. mal spectrumfrom12¿¿mthroughtolongradiowave- lenge laidoutbyLebofskyetal.in1985toprovidea suggests thatwearegettingclosetoansweringthechal- ^0.05. ItisregrettablethatIRASdidnotobserveVesta 1990) whosetruepropertiesareequallyunknown,and The disk-averagedRayleigh-Jeanstemperatureisas It shouldbepossibletoeliminatesomeoftheambiguity The lightcurveat1mmseemstobedominatedbythe 4. CONCLUSIONS 410 1992AJ 104. . 405R Johnston, K.J.,Lamphear,E.Webster,Jr.,W.Lowman,P.D., Drummond, J.D.,&Hege,E.K.1989,inAsteroidsII,editedbyR.P. Drummond, J.,Eckart,A.,&Hege,E.K.1988,Icarus,73,1 Dollfus, A.1990,inAsteroids,Comets,MeteorsIII,editedbyC.-LLa- help ofJ.Tatum,D.Balam,andB.Marsdenindetermin- Dunham, D.W.1991,OccultationNewslett,5,No.4,93 Duncan, W.D.,Robson,E.L,Ade,P.A.R.,Griffin,M.J.,&Sandell,G. Conklin, E.K.,Ulich,B.L.,Dickel,J.R.,&Ther,D.T.1977,inComets, a singledataset. difficulty ofinterpretingobservationsatdifferentaspectsin vations atotherwavelengthsaredesirablebecauseofthe 411 REDMANETAL.:VESTA Lebofsky, L.A.,Sykes,M.Tedesco,E.F.,Veeder,G.J.,Matson,D. 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AJ, 98,335 Seidelmann, P.K.,Kaplan,G.H.,Wade,C.M.,&Hobbs,R.W.1989, I. 1985,Icarus,63,192 1990, MNRAS,243,126 The authorswouldliketoacknowledgethegenerous © American Astronomical Society • Provided by the NASA Astrophysics Data System REFERENCES ing accurateephemeridesforVesta,ofG.Sandellin- valuable adviceoncalibrationsusingUKT14,ofE.Te- Redman, R.O.,Feldman,P.A.,Halliday,I.,&Matthews,H.E.1990,in ing achallengingobservationalprogramwork. operators attheJCMTfortheirskillandpatienceinmak- desco fordiscussions,andofthestafftelescope Tedesco E.F.1986,“MSDOSFormattedFloppyDiskSubsetofthe Redman, R.O.1992,inpreparation Orton, G.S.1986,Icarus,67,289 Webster, Jr.,W.J.,&Johnston,K.J.1989,inAsteroidsII,editedbyR. Simpson, J.P.,Cuzzi,N.,Erickson,E.F.,Strecker,D.W.,& Mitchell, J.K.,CarrierIII,W.D.,Houston,N.,Scott,R.F.,Brom- Mitchell, J.K.,CarrierIII,W.D.,Costes,N.C,Houston,N.,Scott, Matthews, H.E.,Redman,R.O.,Feldman,P.A.,&Halliday,I.1990,J. 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