Recent developments in asteroid science

PHYSICSREPORTS(Review Sectionof PhysicsLetters) 132. No. 5 (1986)261—276. North-Holland,Amsterdam

RECENT DEVELOPMENTS IN ASTEROID SCIENCE

Nicholas EATON

.4 ctronomv Department.i,eiceslerUniversity, Leicester,LE I 7RH. (7 K

Receised2t~August 955

(ontenc;

I. Introduction 263 4. Composition and surfacestructure 2s5)

2. Sizesand masses 263 5. Distribution and origin 772

3. Rotationand shapes 265 References 275

.4hstract;Someof the major discoveriesin asteroidscienceof the past few yearsarc discussed.There isan increasinginterestin using spacetechnoIog~.

which has resultedin observationswith theIUE and IRAS satellites,andwill continuewith the SpaceTelescopeand possiblya fly~hv/rende~viiu~

mission.

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RECENT DEVELOPMENTS INASTEROID SCIENCE

Nicholas EATON

AstronomyDepartment,Leicester University, LE1 7RH, U.K.

INORTH-HOLLAND - AMSTERDAM

N. Eaton,Recentdevelopmentsin asteroidscience 263

1. Introduction

It is nowoverfive yearssincethepublicationof the excellent‘Asteroids’ book (Gehrels,1979)whichsummarisedthe major advancesin this field during the seventies.The impetusgiven by the book hasresultedin greaterawarenessandimprovedmethodsfor studyingthesebodies.In general,thesciencehasmovedaway from scoutingsurveysto moredetailedstudiesof individual objects,but this biaswill partlybe reversedwhen the catalogueof asteroidsobservedwith the IRAS satellite becomesavailable.Thisinfrared survey instrumenthasobservedan estimated20000 minor bodies, only 15% of which havewell-defined orbits allowing recovery at a later date. It is clear that evenif all theseobjects wererecoverableit would not beefficient or evenjustifiable to obtaindetailedinformationon everyobject.Ina sensethe philosophyof asteroidscienceis to do the minimum work necessaryto describethe largestcross-sectionof objects. If it can be establishedthat two bodies are similar in some respect,thenobservationof one should (partly) describethe other. This approachis important if an asteroidfly-by/rendezvousspacemissionis to beachieved,as only a handfulof objectswill be examinedclosely,and the resultswill haveto be extrapolatedvia Earth-basedobservationsto the entire population.

The asteroidsaremost likely aresultof the failure to form aplanetin theearlysolarsystemdueto thedisturbing influence of Jupiter(Chapman,1979). While there is controversyabout the origin of thecomets,the asteroidsprobablyrepresentthe only suredepositoryof solarnebulasolidswhich have,to alargeextent,beenunchangedby the geologicalactivity which occurredon largerbodies.This is borneoutby the fact that the composition of asteroidsis seen to changewith heliocentricdistance,which ispostulatedto be due to the solidification of different materialsat different temperaturesin the solarnebula (Gradie and Tedesco,1982). Subsequentcollisions and orbital perturbationshavenot beensufficientto hidethis effect.The propertiesof the asteroidswill revealmuchabouttheformationof theplanetsandthe compositionof the solarnebula,astheymark theboundarybetweenthe rockyterrestrialplanetsand the gas giants.

Observationaldata on asteroidsare usedto determinetheir physical andchemical properties.Thefollowing sectionsdescribesomeof theserecentresults.

2. Sizesand masses

As seenfrom Earth,all asteroidshavesizeswhich subtendan angleof lessthanonearcsecondon thesky; in comparison,Neptune’sdiscsubtendsover two arc secondsas seenfrom the Earth.Althoughtheoptics of ground-basedtelescopescan haveangularresolutionsof tenthsof an arc second,the observedresolutionis degradedto approximatelyonearc secondby atmosphericturbulence,andthus direct sizedeterminationis difficult evenfor thelargestasteroids.Indirectmethodsof size determinationhavebeenusedwhich give reasonableresults; the most commonis the radiometricmethod which balancesthereflectedvisible light againstthe thermally emitted infrared radiation, and from this the albedo(orreflectivity) as well as the size can be derived(Morrison and Lebofsky, 1979). If the albedo can beindependentlydetermined,thenthe sizecan be directly obtainedfrom the visible brightness.Doilfus andZellner(1979) showhowthealbedocanbe derivedfrom observationsof thepolarisationof light reflectedfrom asteroids.Of course, an irregular shapedobject will show different cross-sectionalareasas itrotates,andthis hasto be takeninto account.Theseindirect methodsdependon modelsof the thermalradiation andoptical polarisationpropertiesand thereforearelimited in their accuracy,beingat bestperhaps10% accurate.

264 V. Eaton. Recentdevelopmentsin asteroidscience

Two methodsof observationhave been developedwhich circumventthe problemof atmosphericseeingand obtain direct measurementsof an asteroid’ssize. The first is by occultationstudies: if anasteroidpassesin front of a star,as bright or brighterthanitself, thena measurabledecreasein light willbe observed.The shadowcaston the Earthwill be the samesize asthe asteroid,andif theshadowedgescan be determinedthenthe size(and shape)of the bodywill be seen.Observersareset up perpendicularto the predictedoccultationtrackto determinethe lateralextentof the shadow.Accuratetiming of thelength of occultation for one observergives a chord acrossthe asteroidface, and parallel chordsareobtainedfrom observersspacedperpendicularto the occultationtrack. Fitting an ellipse to the chordendsgives the size and shapeof the asteroidas seenat that time.

Occultationobservationshavebeenmadefor a numberof asteroids,but only a few havesufficientchordsto determinetheir size accurately.Sincethe shadowscan be up to 1000km wide, it is necessarytospaceobserversoverlong baselines,andproblemsof weatherandsuitableobservingequipmentbecomeimportant.The mostsuccessfulobservationshavebeenwhenthe shadowhaspassedacrossthe mainlandUnitedStates;see for example Millis et al. (1981).

Theproblemwith occultationstudiesis that suitableopportunitiesarerarelyobserved,astheeffort foressentiallyone measurementis substantial.The results can, however,be used to check the resultsobtainedby the morecommonindirect methodssuchas the radiometrictechnique.Brown et al. (1982)find that up-to-dateestimatesof the radiometricdiametersof asteroids2 Pallasand 3 Juno give goodagreementwith the occultation results.The TRIAD (Tucson revisedindex of asteroiddata. Zellner.1979)quotedradiometricresults(MorrisonandZellner, 1979)are, however,—5% too high andthus theTRIAD albedosare —-10% too low.

Some of the occultationobservationshavealso given rise to controversialresults. A few observershaveseen,outsideof the main eclipse,some secondaryeventswherethe star’s light also diminishes,whichhavebeenascribedto satellites,or cloudsof smallerbodiescircling the asteroid.It hasnot, as yet,beenfully establishedthat theseeventsare real.

Speckleinterferometry is the other direct methodof obtainingasteroidsizes (Worden, 1979). Thistechniquerealisesthe true diffraction limit of the telescopeoptics, overcomingthe problemsof imagedegradationdue to atmospheric turbulence and telescopeaberrations.Temperaturevariations inatmosphericconvection cells changethe refractive index of the gas, which altersthe speedof lightresultingin phasedifferencesfor different light paths.The characteristicsize for this turbulenceis about10cm, so that all telescopesproduceimageswith resolutionno better thanthat of a 10cm telescope,namelyonearc second.Shortexposurephotographs,of the orderof a hundredthof asecond,freezetheturbulencein the atmosphere.Thesepicturesstill do not realisethetrue resolutionastheconvectioncellshaveblurred the picture, but therewill be regionsof the picturewhich areat the samephase.If theseregionscan be identified thentheycan becombinedto give the improvedresolution.Unfortunately,forfaint astronomicalobjects,suchfastexposuresmay resultin the arrival of only afew photons.Generallythesespecklephotographsare analysedusingFourier transformtechniques.whereobservationsof anextendedsourceare comparedwith the speckleimageof a point source.

A few observationsof asteroidshavebeenmadeusingthis technique.BaierandWeigelt (1983)haveobtainedpicturesof 3 Junoand29 Amphitrite. The derivedsize andshapefor Junoare in reasonableagreementwith those obtainedby the occultationtechniqueby Millis et al. (1981).

A studyof thedistributionof asteroidsizescanrevealinformation on their history. A size distributionis establishedby plotting the cumulativenumberof asteroidssmallerthan the given size againstsize.Hughes(1982) fits the size distribution for asteroidslarger than 130km with two power laws, whichchangeslopeat a size of approximately250 km. He suggeststhat the transitionseparatesasteroidswhich

N. Eaton, Recentdevelopmentsin asteroidscience 265

90 2O~ \

0 30 60 90 120 150 180 210 240 270 300 330 360Longitude

Fig. 1. Thedistributionof asteroidrotationaxesplottedin eclipticcoordinates,for thenorthernhemispheresolutionsfrom bothmethodsdescribedinthe text. Eachmethod producestwo solutionsfor thepole axiswhich have approximatelythe samelatitude but with longitudesspacedby 1800.Multiple entriesindicatesolutionsby differentauthors.The distributionappearsto showno preferentialdirection,whichcouldbecausedby collisionalevolution randomlyorienting thepole positions.

arecollisionally evolvedfrom the largerasteroidswhichhavenotbeendisrupted.In otherwords, thesizedistributionfor asteroidssmallerthan250km reflectsthat which might be expectedfrom the continualfragmentationdueto collisions.Thoserelativelyfew asteroidslargerthan250km havenot experiencedacatastrophiccollision over the lifetime of the solarsystem(due to the rarity of encountersbetweensuchlargebodies).

However,Donnisonand Sugden(1984) have fitted the size distributionof all asteroidslargerthan130km with a singlesize distributionfunctionwith apowerindex of approximately3, correspondingto amass distribution with an index of 2. They suggestthat this distribution is a product of collisionalfragmentation,so that essentiallyall asteroidshaveundergonedisruptiveencounters;theythusquestionthe statisticalsignificanceof the changeof slopeseenby Hughes(1982).

From the Earth,asteroidmassesare perhapsthe most difficult physical parameterto derive. Themassesof thethreelargestasteroids,Ceres,PallasandVesta,havebeenestimatedfrom perturbationsofotherasteroidorbits duringclose approaches(SchubertandMatson,1979). The errors in the quotedmassesrange from 5% for Ceresto 20% for Pallas. Williams (1984) hasrecently pointed out thatperturbationson theorbit of Mars by the largestasteroidswill be measurabledueto the accuracyof theViking landerrangedata. The measureddistancesto theseprobesshould be accurateto 5 m andit isestimatedthat aboutthreedozenasteroidswill produceperturbationsby atleastthat amount.Thelargestthreeasteroids,thoughtheydo not approachMars closely, will produceeasilydetectableeffects. Thisshouldimprovethe accuracyof their massesby a factorof two within a few yearsaccumulationof data.

Asteroidmasseswill be mucheasierto estimatefrom fly-by or rendezvousprobes.Forafly-by missionit hasbeenproposedthat the satellite should releaseradar reflecting tracerswhose deviationsin thegravitationalfield will be monitoredandconvertedinto the centralattractingmass.A rendezvousprobewill give the mostaccuratemassdetermination,sincethe satellite’s orbital parameterswill be instantlyconvertibleinto the centralgravitatingmassfrom Newtonianmechanics.

3. Rotation and shapes

Periodicbrightnessvariationsseenin asteroidsare ascribedto changingalbedoor cross-sectionalareaasthe bodyrotates.In general,alightcurvecausedby changingcross-sectionalareawill producetwo light

266 N. Eaton. Recentderelopinentsin asteroidscience

maximaduring onerotation,whereasa body with two areasof differentalbedo.suchasSaturn’ssatelliteIapetus,will produceonly onemaximum per rotation.Assumingthat the rotationaxis is fixed in space,andnot freelyprecessing,then,as an irregularly shapedasteroidorbits the Sun,the lightcurveamplitudewill exhibit variations.The maximumamplitude is seenwhenthepoleaxisis perpendicularto the line ofsight, andthe minimum is seenwhenthepole is pointingclosestto the line of sight. A lightcurvevariationdueto varying albedois lesslikely to show a changeof amplitudewith heliocentriclongitude.Harris andYoung (1983) have compiled a cumulative list of lightcurve observationsof some 380 dillerentasteroids.

If the asteroid has a smooth convex shape, then the resultant lightcurve, although possiblyasymmetrical,will also be smooth.Most asteroidlightcurvesshow,on the otherhand,somedeviationsfrom a smooth curve, which are interpretedas large-scalesurface roughness,such as craters ormountains.Someasteroidshavevery complicatedlightcurves.and thesebodiesmust deviatestronglyfrom a convexshape.

The problemof deducingan asteroid’strue shapefrom a lighteurve.or seriesof lightcurves at allaspects,is unfortunately impossibleto solve. There are, however, some methodswhich allow thedeterminationof generalshapecharacteristics(e.g. theratio of theaxesof the body). Asteroidshapescanbe inferredby fitting triaxial ellipsoids to the lightcurve variationsand this method is discussedlater.Ostroand Connelly(1984) havederivedan inversiontechniquethat will give a meantwo-dimensionalrepresentationof an asteroid’s equatorial cross-sectionfrom its lightcurve. If the observationsareobtained when the solar phase angle is zero— that is no shadowsare seen on the face of theasteroid— thenthe derivedconvexshapefrom thistechniquerepresentstheoutline of the asteroidseenasif lookingdownfrom oneof the rotationpoles.Thismethodis restrictedby someseriousconstraints,suchas the assumptionsthatthe EarthandSun directionslie on the asteroid’sequator,andthat the scatteringof light from the surfaceis uniform and geometric.Despitethesedrawbacks,Ostroand Connellyhavedefinitely shown that a few asteroidshave non-elliptical sections.

Now that asteroidrotation rateshavebeenreliably obtainedfor over two hundred asteroids,it ispossibleto seehowrotationratesare relatedto asteroidsizeandtype. Farinellaet al. (1981)andDermottandMurray (1982) useddatapublishedin the Asteroidsbook (Tedesco,1979) to show that significantcorrelationsare present.Dermottet al. (1984) haveuseda largerdataset to investigatethe statisticalsignificanceof thesecorrelations. It is shown that for all asteroidtypes thereis an increasein meanrotational frequencywith increasingdiameterfor sizes between120 and 270km. For larger sizes therotationrateflattensoff at ——3.5 rev/day.For sizesless than 120km theasteroidsin the dataset show anincreasein meanrotationalfrequencywith decreasingdiameter,but thisobservationmaybe affectedbyobservationalselectionand mustbe treatedwith caution. It is clear, however,that thereis a significantchangein mean rotation rate at about 120 km and this may representthe transition between theprimordial larger bodies and their collisional fragments.Rotation ratesof small asteroidsare under-sampledand it is as yet uncertainif this transitionat mid-sizedobjectsmarksan increasefrom a flat sizeversusrotationdistribution or is a true minimum.

If this minimumin therotationratesfor mid-sizedobjectsis real, thenan explanationmustbe sought.A promising proposalhas beenput forward by Dobrovolskisand Burns (1984) who calculatethat anintermediatesizedobject’s angularmomentumwill be lost due to ejectaescapingpreferentially in thedirectionof rotation,resultingfrom the impulsegiven by the rotationalvelocity. This effect resultsin anet braking of the asteroid,and it is estimatedthat the effect will be maximum in the size range of-—100km.This mechanismwill only operateon mid-sizedasteroids,since for the largestasteroidsverylittle ejectaescapein any direction dueto the higher gravity,whereason the smallestobjectsessentiallyall ejecta escapeno matter in which direction they are thrown.


Dermottetal. (1984)havealsoinvestigatedthe distributionof rotationrateswith taxonomicclassandfamily membership.(Taxonomicclassdistinguishesasteroidswith different surfacecompositions,andisdealtwith morefully in a latersection;asteroidfamilies arecomprisedof objectshavingsimilar orbits,andarepostulatedto beformedfrom the break-upof largerbodies). In general,it is seenthat M typeasteroidsrotatefasterthanS typeasteroidswhich in turnrotatefasterthanC types.This is understoodtobedue to differencesin their meanbulk densities.The changeof slopein the size versusrotationratediagram,which possiblymarks thetransitionbetweencollisional fragmentsandprimordial objects,alsoappearsto betype-dependent.This transitionoccursat smallersizeswhengoing from C to S to M types,whichcan alsobe understoodin termsof increasingdensityor increasingmaterialstrengthof the bodies.Thereis alsosomeevidencein thedataset thatfor all typesof all sizes,family membersrotatefasterthannon-family members.

Althoughthe dataset showsthatfor smallasteroidsrotation rateincreaseswith decreasingsize,thereseemsto be an excessof small, very slow rotators, above that which would be expectedfrom aMaxwellian distribution of spins,derivedfrom acollisional evolution. It is a problemto explaintheverylongperiodsseenin afew asteroids,but tidal despinningby asatellitecompanionhasbeenputforward asan explanation(Farinellaet al., 1981).

As well as giving information on asteroidrotationrate and shape,the lightcurvescan be used todeterminethe directionof therotationaxis in space.Two independentmethodsareusedfor the solutionof the pole position. Both give the best resultswhen the asteroidis viewed from as many aspectsaspossible,which meansobservingthe Iightcurveat differentplacesin the asteroidorbit, or equivalentlyatdifferentecliptic longitudes.For instance,if the asteroidis observedwith onepolepointingtowardstheEarth then the other pole will be hidden; however, the situation is reversedwhen the asteroidhascompletedhalf an orbit with the previouslyhiddenpolenow pointing towardthe Earth.

The first methodis thatof photometricastrometry,describedby Taylor(1979)whichusestiming of themeridiancrossingof asteroidlightcurve featuresto derive thesiderealperiod,senseof rotation andpoleorientation.Themajor difficulty with this methodis that thetiming of eventsmustbe accuratelyknown,havingan uncertaintyno worsethan2% of the rotationperiod.Thereshouldpreferablybe at leastsixobservationswithin oneopposition, spacedover as wide an ecliptic longitudespanas possible,with aminimumof oneobservationfrom eachof atleastfour otheroppositions.It is evidentthat the lightcurvefeatureusedfor the timing mustbe seenin everyobservation,andmustbe assumedto befixed in phase(althoughit is knownthat featuressuchas lightcurveminima can changewith differentviewing angles).Anotherproblem which can ariseis “switching” — wherea primary maximum becomesa secondarymaximumata differentecliptic longitude.Thiseffectcanbecheckedby lookingfor smaller-scalefeaturesin thelightcurve,suchasthe shapeof theminimumprecedingthechosenmaximum.Theasteroid44 Nysawas used by Taylor and Tedesco(1983) to demonstratethis methodof astrometryand to discussitslimitations.

The secondmethodusesthe observedvariation of lightcurve amplitudesandabsolutemagnitudes,with ecliptic longitude,to estimatetheshapeof the asteroid,assumingthattheobjectis atriaxialellipsoidrotatingaboutits minor axis. Thepoleorientationisalsofoundfrom thismethodasdescribedby Zappala(1981).Basicallyaguessismadeatthe triaxial shapeandpolepositionof the asteroid,andwith thesetheamplitudeandmagnitudedependencewith longitudecanbe calculated.Thisdependenceis comparedtothe observedbehaviourand the estimateschangeduntil a reasonablefit betweenthe observedandcalculatedamplitudes/magnitudesis achieved.The assumptionthat theasteroidshapeis representedby atriaxial ellipsoid is very restrictive,andthemethodcanonly beconsideredsuitablefor asteroidsshowingregular lightcurves with well-defined maxima and minima. This methodalso assumesa geometricalscatteringsurfaceof theasteroid;that is, the brightnessis proportionalto theprojectedilluminated area.

268 N. Eaton. Recentdevelopmentsin asteroid science

Barucci and Fulchignoni (1983) have shownfrom the scatteringpropertiesof model asteroidsthat thescatteringby realistic surfaceswill give larger amplitudesthan the geometricprojectedarea mightsuggest.This phenomenonis dueto limb darkening,wherethe intensityof the scatteredlight dropsofftowardthe edgeof the body, in contrastto geometricalscatteringwherethe intensityremainsconstantright to the edge.The consequenceof an elongatedbody is that the limb darkeningoccupiesa largerproportion of the projectedareaat minimum than at maximum,andso increasesthe amplitude of thelight variation. This correspondsto an overestimationof the axial ratios using simple models of thescatteringproperties.

Baruccietal. (1983)haveconductedexperimentson fragmentsof a concretetriaxial targetwhich hasbeenshatteredby ahighvelocity impactwhile in free fall. The distributionof the massesin thefragmentswas found to be similar to smallC-typeasteroids,whicharealso postulatedto becollisionally evolved.Afew fragmentswerealso investigatedfor their lightcurveproperties.Theseshowedmanysimilaritiestoobservedasteroidlightcurves.Onefragmentshowedthat anirregularbodywith two lightcurvemaximaatone aspectcan haveone maximum only at a different aspect.

6~4

39 S192 2

- ~________________________ ~ SRI. S19___________ 30 589230 563 2

I __

I I I.4 •3 •2 •1 0

Fig. 2. Taxonomicdendrogramof 61) asteroidsfrom theTRIAD file (Zellner.1979) havingU—B, B—V. R/B, BEND, DEPTH.albedoandminimumpolarisationmeasurements.The asteroidtypesarealso from the TRIAD file. The axis indicatestaxonomicdistanceordecreasingsimilarity. Theseparationinto the two major C and S groupsis readily apparent.


If an asteroidhas one or more patchesof lighter, or darker material than the averagesurfacereflectivity, thena lightcurvewill resultasthebodyrotates.This variationof light dueto changingalbedois consideredin most casesto be a minor or non-existentcontributor to asteroidlightcurves. If alightcurve is obtainedat only one wavelengthit is almost impossibleto determinewhether albedovariationsarepresent.If anyalbedopatcheshavedifferentcoloursthensimultaneousmeasurementsattwo wavelengthswill reveal colour variationsas the asteroidrotates.These colour variationswill beindependentof any lightcurvevariationsdueto changingshape.Schoberand Scroll (1982) havelistedmulti-colourvisible lightcurveobservationsof asteroidsandconcludethat tenobjectsshowevidenceforcolour variation; theseare 3 Juno,4 Vesta,6 Hebe, 25 Phocaea,39 Laetitia, 42 Isis, 71 Niobe, 201Penelope,349Dembowskaand944Hidalgo. The lightcurvesof Vestado notshow achangeof amplitudewith ecliptic longitude,which impliesthatthe lightcurveis probablynot dueto non-sphericalshape,andthus mustbe mainly dueto albedovariations.Colour variationsof Laetitiahaveonly beenseenat oneorientation,andthis implies that the albedospotwill be nearoneof the poles(McCheyneetal. 1984a).Using a wider wavelengthrange to investigatecolour variationscan give greatersensitivity for suchsearches.McCheyneet al. (1984b)haveuseda simultaneousopticalandinfraredphotometerto obtainlightcurvesof asteroids.Theyobservedcolourvariationsin threeasteroids,4 Vesta,31 Euphrosyneand115 Thyra. The optical and infrared coloursof Vestawere also comparedto meteoriticanaloguestoobtaininformationon the surfacecomposition;the resultsareconsistentwith a modelhaving aeucritesurfacewith a patch,or patches,of brighterdiogeniteto accountfor thealbedoandcolour changes.Thepropertiesof thesetypesof meteoritesuggestthat the surfaceof Vestahaslava flows ratherlike thoseseenon the Moon.

The adventof the SpaceTelescopeshouldresolvea lot of theseproblems.The FaintObjectCamerawill workat aresolutionof 0.022arcsec,whichcorrespondsto alinear dimensionof approximately25 kmin the middleof the asteroidbelt. Theoverallshapeandsurfacefeaturesof thelargestasteroidsshouldbereadily observable,and by following featuresarounda rotation,the pole orientationwill be directlydetermined.It is unlikely, however,thatthe SpaceTelescope,becauseof demand,will observefor thispurposemore thana handful of objects,andso againdetailedstudiesof a few objectswill haveto betransferredto the majority via standardtechniques.

4. Composition and surface structure

It haslong beenknown that the reflective propertiesof asteroidsare split into two major groups,identifiedasC andS types.Theprimarydifferencebetweenthesetwo groupsis their albedos.(An albedoof unity is totally reflecting,andan albedoof zerocorrespondsto no reflection of light). S typeshavevisible albedosp~,—‘ 0.15, C types havep,, -~ 0.04. Otherminor groupshavealsobeenidentified.At thetimeof writing of the ‘Asteroids’book,the otherrecognisedtypeswere the M,E,RandU groups.The Ctypeswere originally namedafter the Carbonaceousmeteorites,andthe S typesafter the Stoney-ironmeteorites.TheM typeswerenamedfor their metallicproperties,the Etypeshavehigh albedoandwerethoughtto resembleEnstatitechondriticmeteorites,the R typeswerenamedfor their Redspectra,andthe U typeswere thoseUnclassifiableunderthis scheme.This classificationschemewasdevelopedfromvisible reflectionandpolarisationproperties.Usingthesevisible observationaldata,Davieset al. (1982)examinedtheclassificationschemewith themethodof numericaltaxonomy.Taxonomyis the methodbywhich a classificationschemeis establishedfrom relationshipsbetweenobservedpropertiesof bodies.Numericaltaxonomy,developedfrom the biological sciences,usescomputationaltechniquesto achieve

271) N. Eaton. Recentdevelopmentsin asteroidscience

this end. For instance,plotting a graph can establisha relationshipbetweentwo parameters,but in acomputerany numberof parameterscan be “plotted” in n-dimensionalspace.wheren representsthenumberof free parameters,and so all distinguishingcharacteristicscan he examinedon one “graph”.With numericaltaxonomy,the distancebetweenobjects in this n-dimensionalspaceis usedto examinethe degreeof similarity of individual objectsandclumpsof objects.The resultsareconvenientlyplottedas a taxonomicfamily tree,or dendogram,wheresimilar objectsareconnectedby branchinghighup thetree,whilst dissimilarobjectsareonly connectedby branchingmuchlower in thetrunk. AlthoughDavieset al. (1982)demonstratedthemain dichotomyof asteroidproperties,theseparationof the minor groupswas not so apparent.Two conflicting interpretationsof this result can be considered.Oneis that theminor groupsestablishedby previousschemesare really not sufficiently different to warranta separateclassification.The otheris that the numericaltechniqueusedwas too crude,anddid not takesufficientaccountof the relativeweighingof the variousparameters.It is probablethatthe true answeris amixtureof the two; the warning is that careshould beusedin establishingthe significanceof differencesbetweenobjectswhen creatinga classification scheme.

In orderto bridgethegapbetweenUBV photometryof asteroids,which cangive conflictingresultsforsometypes,andmediumresolutionspectrophotometrywhichrequiresbright objectsor largetelescopes.Tedescoet al. (1982)haveestablishedan eightcolourphotometrysystemwith which to conductasurvey.The systemspansthe wavelengthrange0.35 to 1.04 p.m, and the eight filters were chosento obtaincompositionallydiagnosticinformation for solar system objects.The preliminary results of the eightcolour asteroidsurvey for nearly six hundredobjectsare given in Zellneret al. (1984b). As is usual inclassificationschemes,new datahavenecessitatedthe introduction of new types, andthe full list nowcontains11 classes.Thiseightcolour surveyis importantin that it examinespredominantlyfaint asteroidsandcoversalmost all the orbital zonesand major families.

Some important theoreticalwork has, in recentyears,beenput into the study of the scatteringofradiationby the particulatesurfacesencounteredon atmospherelessbodies. Problemsto overcomearethe effects of scatteringoff randomly oriented facets, multiple scatteringand shadowing. The mostimportantobservationalresultthat the theorieshaveto addressis the oppositioneffectseenin asteroids.As the phaseanglebetweenthe Sun,asteroidandEarthdecreases,moreof the illuminated face is seenfrom theEarth, so increasingthe apparentbrightness.Simpletheoriespredictthatthis increaseshouldbelinearwhen phaseangle is plottedagainstmagnitude.Observationsof asteroidshaveshown,however,that the brightnessincreasesabovethat of alineardependenceat smallphaseangles.This is postulatedtobedueto non-isotropicscatteringof light by aroughsurface(preferentiallyreflectinglight in the directionof incidence).LummeandBowell (1981)haveformulateda theory which describesthe oppositioneffectas causedby porosity, with the linear part due mainly to roughnessof the surface.Hapke(1984) has,however,questionedLummeand Bowell’s treatmentandhashimself put forward a theory which usesscatteringfrom a smoothparticulatesurface(Hapke, 1981)correctedto includemacroscopicroughness(that is the effect of cratersandmountains).

The questfor spectralfeatureswhichwill discriminatebetweenasteroidtypesandgivecompositionalinformation has led researchersto examinewavelengthrangesoutsidethe visible region.

Usingobservationsfrom theIUE satelliteButterworthandMeadows(1984)haveinvestigatedspectraof 29 asteroidsin theultraviolet region 0.21 to 0.32p~m.This wavelengthrangehasbeenlittle studiedforasteroidsor for mineralogicalanalogues,andso the resultsare largely exploratory.Spectralfeaturesareseenfor thedifferent typesandthesehavebeententativelyidentifiedwith iron andtitanium. As expectedthe asteroidsreflect ultraviolet radiation lesswell than visible radiation, an effectwhich is alsoseenforthe lunar spectrum.

Most of the investigationof asteroidpropertiesoutsidethe visible region hasbeenconcentratedon the


infraredwavelengths.Shortwardof about5 p~mthe spectrumis still that of reflectedsunlight. Beyond5 p~mthe reflectancespectrumis submergedunder the thermal re-radiationof the absorbedsunlight.

Near-infraredJHK photometryhasbeenusedto providesurveyobservationsof thiswavelengthrange(Veederet al., 1982andVeederet al., 1983).The J,HandK wavebandsare broadwindowscentredon1.25 1.65 and2.2 p~m,respectively.At thesewavelengths,opticaldetectionsystemsdo not operate,andspeciallycooledsolid-statedetectorshaveto beused.Ontheirown, JHK coloursarenot very informativeof asteroidtype,but whencombinedwith visible colourstheywill separateout all typesincluding theC,M andEtypeswhichareotherwisehardto distinguishwithoutalbedoinformation(Veederet al., 1978).

Spectrophotometryin the1 to 2.5 p~mregion,whencombinedwith visible spectra,is a veryusefultoolfor establishingcompositionalinformationof the surfaceminerals.Pyroxenehasabsorptionbandsat 0.9and 1.9tim, olivine hasan absorptionat 1.1 l.tm, andboth of thesespectralfeaturesareseenin S-typeasteroids(Feierberget al., 1982).The C-typeasteroidshaveessentiallyflat featurelessspectrafrom 0.5to2.5 ~m.

An importantdiscoveryhasbeenmadein the 3 to 4 ~mregion.Lebofsky(1980)showedthat anumberof C- and U-type asteroidshavean absorptionin their reflectancespectrain thiswavelengthrange.Thetwo largestasteroids1 Ceresand2 Pallasboth show a well-definedabsorption.This absorptionfeaturehasbeen identified with similar featuresin hydratedclays and salts and is due to both structuralOHgroupsandabsorbedH2O molecules(Lebofskyet al., 1981). The spectraof CeresandPallasindicatecompositionsgeneticallyrelatedto known meteoriticcarbonaceouschondriteswhich haveundergonesubstantialaqueousalteration(Larsonet al., 1983). Observationsof thereflectancespectrumin the3 to4 p~mregion are complicatedby the presenceof the thermalemissionin main belt asteroids.In thiswavelengthregion, the increasingflux from the thermalemission crossesthe decreasingflux fromreflectedsunlight,andthe observedspectrumis amixtureof thesecomponents.This thermalcomponentmust thereforebeaccuratelyremovedto obtainthe reflectancespectrum.Variationsin thedepthof theabsorptionfeatureon Ceres are probably due to incorrect removalof this component(Eatonet al.,1983).

It is generallyacceptedthatthermalemissionfrom asteroidswill showsmoothgrey-bodyspectra,fromsurfaceelementsheatedby the solar radiation.A simple “standard” thermalmodel (Lebofskyet al.,1978)hasbeendevelopedandseemsto beapplicableto mostasteroids.In thismodel,asphericalbody isobservedat zero phaseangle,so that all the illuminated face is seen.Eachsurfaceelementreflects aconstantproportionof the incident light (given by the albedo),and the absorbedradiation raisesthesurfacetemperature,until thereis equilibrium betweenthe emittedandabsorbedradiation.The modelalsoassumesthatthereis no heattransferfrom thesurfaceelementsidewardsto aneighbouringelement,or inwardsto the bodyof the asteroid.This lastassumptionrequiresthe asteroidsurfaceto haveafineparticulatesurfacewith alow thermalconductivity.Thisdustycovering,or regolith,isprobablytheresultof impactsin the asteroidbelt. Thermalemissionfeatures,suchas the 10 ~imsilicatefeaturesometimesseenin small cometarygrains, are hard to envisageon an asteroidwith a well-developedregolith.Feierberget al. (1984),however,haveobservednarrowemissionfeatureson two asteroids,19 Fortuna(C type) and21 Lutetia(M type). To accountfor thesefeaturestheseasteroidsmusthavesignificant areaswhereoptically thin layersof micron-sizedparticlesoverlaycooler andlargergrains.The wavelengthoftheemissionmaximaareknownto be diagnosticof rocktype,andso identificationof suchfeatureson C-andM-type asteroidscan beusefulwherelack of featuresatshorterwavelengthsgiveambiguousresults.Greenet al. (1985a) observed12 other asteroidscovering a similar spectralrangeas FeierbergCt al.(1984), but saw no significant emission features, implying that their presenceis probably a rareoccurrence.

Johnsonet al. (1983)havesucceededin measuringthe polarisationof thethermallyemittedradiation

272 N. Eaton. Recentdevelopmentsin asteroid science

of Ceresat 10 p.m. Thelinearpolarisationof emittedradiationoccurswhena surfaceelementis observedat angles away from the normal. Thus, if an asteroidis observedat large phaseangles, the hottestsub-solarregion which accountsfor the majority of the emittedflux will be seencloserto the asteroidslimb, and will give rise to significant polarisation.The polarisationis sensitive to the temperaturedistributionoverits surfacewhichcan bedirectly relatedto thepoleorientationandthermalinertiaof thebody.Ceresis knownto be almostsphericalandshowsvery little variation in its lightcurve,thustheusualmethodof poledeterminationcannotbeapplied.The modellingof theinfraredpolarisationdemonstrateshow pole positionscan be derivedfor nearsphericalbodies.

Very few measurementsof asteroidsbeyond20 p.m havebeenpublished,althoughthe resultsof theIRAS asteroidsurvey will increase the number into the thousands.Le Van and Price (1984) haveobtainedmeasurementsof four asteroidsat 20, 27 and85 p.m from asoundingrocket. Their resultsareconsistentwith previousmeasurementsat 20 and27 p.m, but drop below the expectedvalue from the~standard’thermalmodelat 85 p.m. This deviationis suggestedto be dueto adropin the emissivity at thelonger wavelength,which is seenfor lunar typeregoliths. If this effect is generalto most asteroidsthenthe ‘standard’ thermal model maybecomeredundantin the flood of IRAS observations.The IRASsatellitehasobservedmost of the known asteroidsandmanyunknownonesat wavelengthsof 12,25,60and 100p.m. The IRAS asteroidcataloguewill constitutethe standarddatabaseof thermalmeasure-mentsof asteroids.

5. Distribution and origin

As mentionedpreviously the averagecompositionof asteroidsis seento changewith heliocentricdistance,andthisseparationis believedto haveoccurredat formation. It hasbeenknownfor sometimethat theproportionof the darkerC-typeasteroidsincreaseswith increasingdistance.GradieandTedesco(1982)haveplottedout thefractionaldistributionof asteroidtypewith heliocenticdistancecorrectedforobservationalbias. They find that the asteroidbelt appearsto be composedof at least six majorcompositionallydistinctregions.The brighterE andS typesmainlyoccupythe inneredgeof the asteroidbelt, andthe darkerC andD typesbecomedominantin the outerbelt andtheTrojan regions.This trendof decreasingalbedowith increasingheliocentricdistancecanbeunderstoodif the moredistantasteroidsformedwith a largerproportionof low-temperature(organic?)condensateswhich darkentheconstituentminerals.

As well as the distributionof compositionaltypes,thedistributionof orbitalparameters(a,e,i) can berevealing.ZeilnerandThirunagari(1984a)havesuggestedthat theasteroidscould haveinitially accretedin nearlycircularco-planarorbits,distributedratheruniformly out to Jupiter.The asteroidsthenevolvedinwardsexchangingsemi-majoraxis for eccentricityand inclination. If this hypothesisis true, then thedistribution of eccentricity and inclination should show compositionalstructurewith darker asteroidshaving the morepeculiar orbits.

One of the most important problems of planetary dynamics is to explain the formation of theKirkwood gaps,whereasteroidsaredepleteddueto resonanceswith Jupiter.DermottandMurray(1982)haveindicatedthat thegapswere formedafterthe asteroidshaddispersedfrom the near-coplanardisk inwhich they accreted.Wisdom (1982, 1983) has shownthat an asteroidplacedin a resonantorbit willexperienceoccasionalincreasesin its orbital eccentricitydueto Jovianperturbations.(A resonantorbit isonein whichthe orbital period is a rationalfractionof Jupiter’sorbital period). If thisincreasein orbitaleccentricityis largeenough,the asteroidwill enterthe innersolarsystemwherethereis a chancethat a


closeplanetaryencounterwill removethe asteroidfrom its orbit. The advantageof Wisdom’s methodoverothertechniquesis thatit greatlyspeedsup the calculationof Jupiter’sinfluenceoverlongperiodsoftime. Previousnumericalsimulationsof perturbationsrequiresmall time stepsbetweenthe calculationsbecausethefull equationsof motionarenotintegrable.Wisdomhastakentheequationsof motion for anunperturbedsystem,which are integrable,and has introduced high frequencyterms to simulate theperturbations,in suchaway that the equationsremainintegrable.The calculationsthenonly haveto beperformedonceperorbit, comparedwith manytimesperorbit for the numericalcalculations.This workindicatesthat asteroidscan beremovedfrom resonantorbits,by changesin orbitaleccentricityleadingtocloseplanetaryencounters,which explainsthe presenceof theKirkwood gaps.Thismechanismmayalsohelpto explain the delivery of meteoritesand, possibly,Earth-crossingasteroidsfrom the main belt.

The origin of the Earth-crossingasteroidpopulationis still in question.It appearsthat theplanetarycratering rate hasremainedreasonablyconstantover a significant proportion of the age of the solarsystem,and this implies that the population of planetarycrossing asteroidsmust be in equilibrium

Eos

Flora

~eJ KoronisI Themis

>

~ Ill I~~T ~~ ~ ~‘I I ~

~4..77

~ eQ1~1

5210

Fig. 3. Thedistributionof asteroidorbitsplotted assemi-majoraxisversusinclination. Thesemi-majoraxisrangesfrom 0.7 to 6.0 AU in 0.1 AU steps,theinclinationrangesfrom0°to 44°in 1°steps.Thenumberof asteroidsin eachelementis plottedin theverticaldirection.Someof themajorfamilies,wheremanyasteroidssharesimilar orbits, arenamed.Thepositionof someof the importantresonanceswith Jupiteraremarkedon thesemi-majoraxisscale.The 2: 1 3: 1 4: 1 and5: 1 resonancesare depletedof asteroids(the Kirkwood gaps),whereasthe 3:2 and 4:3 resonanceshave aconcentrationof objects.

274 N. Eaton. Recentdevelopmentsin asteroidscience

Fable IPropertiesof a few representativeasteroids

IRIAI)No. Asteroidname Orbit a(AU) e Diam (km) Aihedo type Mass (M~Y

1)) Hygeia Main belt 3.14 II. 2 4 431) 0.05 ( 2 2., (129 Amphitrite Main belt 2.55 ((((7 6 2(1(1 0. IS S 2 .~ Ill911 Agamemnon Trojan 5.19 ((((7 22 155 ((.04 1 1))

1566 Icarus Earth-crosser 1.1)8 0.53 23 1.4 0.17 1 I x 1))

estimated

betweencollisions andreplenishment(Shoemakeret al.. 1979). It is estimatedthat thereareof the orderof 2000 Earth-crossingasteroidswith diametersapproximately1 km or larger(Helm and Shoemaker,1979).Although Wisdom’swork on chaoticbehaviourin the asteroidbelt hasindicatedamechanismfortransferof objectsinto Earth-crossingorbits,thereis still controversyas to whetherthe majority of thesebodiesare of asteroidalor cometaryorigin. Kresak (1979) has shownthat, in general,Earth-crossingasteroidsand short period comets,orbit in differentdomainsunderJupiter’s influence. hut there areexceptions.Asteroid 2212 Hephaistosappearsto he relatedto cometP/Encke.and this comet is itselfundergoing a switch from the cometary to the asteroidalorbital domain, probably due to non-gravitationalforces. These non-gravitationalforces are due to outgassingfrom the cometwhich canaccelerate,or decelerate,the object andso changeits orbit. The orbit of the Apollo asteroid1983 TB.discoveredby the IRAS satellite (Davies et al.. 1984), is very similar to the Geminidmeteorstream.Sinceit is believedthat meteorstreamsarederivedfrom comets,andthat no comethasbeenseenin anappropriateorbit, it is supposedthat 1983 TB is the deadparentcomet,in which all the volatiles havebeenevaporated,or aredeeplyburied undera rocky mantle.CochranandBarker(1984)foundthat 1983TB showedno cometaryemissionsandits spectrumresembledthat of the S-type asteroids.The mostrecentwork on 1983TB tends to indicate that it is a rocky asteroid,incompatiblewith a deadcometremnant,and that somemeteorstreamsmay thus be of asteroidorigin (Greenet al.. 1985).

It is reasonableto assumethatsomeEarth-crossingasteroidswill be extinctcometsandsomewill havebeenperturbedfrom the asteroidbelt, but it is unclearasyet whichis thedominantfactor. A clue to theirorigin maycomefrom the compositionalpropertiesof thesebodies.McFaddenet al. (1984)haveshownthat the spectraof near-Earthasteroidsare dueto mineralscommonlyseenon asteroidsurfaces,but thefractionof objectsof asteroidtypeandalbedosdiffer from the main belt. Oneobject,22OlOljato, hasaspectrumunlike any otherasteroid,andmayhe of cometaryorigin. The spectraldifferencesbetweennear-Earthandmain-beltasteroidsmay be explainedas beingdueto the collisionalorigin of the former:The surfaceof a collisionalproductwill haveexperiencedmuch lessweatheringby the solar wind andcosmic raysdue to being buried within a parentbody and thus its albedowill probably he higher.

Manyquestionswhichremainaboutthepropertiesandoriginsof the asteroidsmaybe answeredwithinthe nextdecadewith the adventof the SpaceTelescopeandthe possibilitiesof missionsto the minorplanets.It hasevenbeensuggestedthat a sample-returnmissionto an Earth-crossingasteroidis withinpresentcapabilities.

Acknowledgements

I would like to thank JackMeadowsfor overseeingthe script. I would also like to thank RobertMcCheyneandSimon Greenfor sometextualanddiagrammaticideas.At the time of writing I was inreceiptof an SERCresearchfellowship.


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Recent developments in asteroid science