1971AJ 76. . 14IT THE ASTRONOMICALJOURNALVOLUME76.NUMBER2MARCH1971 future paperinthisseries. Vesta, (6)Hebe,and(110)Lydia.Theresultson ness-phase functionsnearopposition;theyare(4) Vesta areinPaperI(Gehrels1967)andonLydia THREE asteroidswereobservedattheMcDonald the 91-cmreflector:18Octoberthrough17November They weremadeattheMcDonaldObservatory;with 208-cm reflector:20Novemberthrough2December this paper,whilewearepreparingthoseonHebefora 1958 andon11December1958;withtheOttoStruve hI Table Iliststhecircumstancesofobservations. Obs. date Obs. dateR.A.Dec.VB—V comp,readings 58.10.18 58.11.17 58.11.04 59.01.25 58.12.11 58.12.02 58.11.29 58.11.25 58.11.20 58.11.09 58.10.18 426?l+21°02' 69.03.16 58.11.04 416.22111 58.12.02 349.421 19 58.11.25 356.021 08 58.11.20 401.821 22 58.11.17 404.62122 58.11.09 411.82129 69.03.16 958.2+21 18 58.12.11 341.820 53 58.11.29 352.321 08 59.01.25 330.221 19 © American Astronomical Society • Provided by theNASA Astrophysics Data System U.T. U.T. 1950(mag) (mag) Remarks Observatory in1958-59specificallyforthebright- hm The synodicperiodis105536®24±0?04(p.e.).absolutemagnitudeB(1,0)=8.80,andthecolorsat clearly evident.AstrikingsimilaritywasfoundamongtheoppositioneffectsofVesta,Massalia,andLydia. zero phaseangleareB—V—+0.71andZ7—B=+0.29.Theoppositioneffectreddeningwith Observatory. Thelightcurvehasthreemaximaandminima,itshowsthatLydiaanirregularshape. Lydia wasobservedin1958-59attheMcDonaldObservatoryand1969KittPeakNational ± 0.02 - 8.83 -14? 95 + 3.57 + 2.37 - 0.56 - 3.24 - 6.70 +10.27 +19.66 + 7.50 - 1.79 Minor PlanetsandRelatedObjects.VI.Asteroid(110)Lydia ±0.2 ±3 Phase angle I. OBSERVATIONS Lunar andPlanetaryLaboratory,TheUniversityofArizona,Tucson,Arizona from Sun ±0.0001 Distance (a.u.) 2.6687 2.6552 2.6798 2.6730 2.6915 2.6859 2.6823 2.6897 2.9445 2.7359 2.6990 R. C.Taylor,T.Gehrels,andA.B.Silvester Table II.Comparisonstarsandqualityofnights. ±0.006 ±0.005 from Earth 11.652 1.6870.008 11.802 0.9030.004 11.690 +0.777±0.005 12.504 0.7110.004 11.718 0.4080.010 11.972 0.9430.005 11.243 1.0300.008 13.492 +0.7820.009 ±0.0001 8.181 0.4670.007 Distance Table I.AspectdataforLydia. 9.486 1.5210.005 (Received 30November1970) (a.u.) 2.2275 2.0527 1.6986 1.6982 1.7147 1.7340 1.8419 1.7149 1.7073 1.6962 1.7565 141 Light time ±0.00001 made byGehrels.Anadditionalobservationwas by R.G.ThomaswiththeKittPeak41-cm“No.3” 0.01063 was madebySilvester,whileTaylorresponsible reflector on16March1969.Apartofthereductions and reductionsfollowedthemethodsdescribedin for thefinalreductionsandanalysis.Theobservations Paper I.O—Ccorrectionsin1958-59averaged+0+9 0.01186 in rightascensionand+6'declination. 1958 andon25January1959;theseobservationswere average deviationfromasmoothcurveofcomparison- Under “Scatterofcomp,readings”thetablegives star magnitudesversustime. Table IIgivesvariousdataforthecomparisonstars. 1001 1287 1014 981 990 981 980 990 986 Scatter of ±0.01 h 4 15.4 4 3.3 4 11.0 425+3 3 29.4 3 40.4 3 48.8 3 55.3 4 0.1 3 51.2 9 58.6 R.A. ±0.2 1950 One-hour lightcurveonly Cloudy andhazymostofnight Some cirrus Excellent skyuntilstoppedbyclouds Equipment trouble +21 7 +21 11 +21 12 +21 12 +20 54 +21 5 +21 9 +21° 1' +21 12 +21 16 +21 0 Dec. 1950 ±1 ±0.03 144.40 long. lat. 62.96 61.12 62.23 64.73 65.74 59.62 60.18 67?98 55.27 57.68 1950 Ecliptic ±0.03 +0.43 +0.94 +0.73 +0.54 +0.11 — 0?64 +8.30 +2.24 +1.28 +0.91 -0.07 1971AJ 76. . 14IT 142 TAYLOR,GEHRELS,ANDSILVESTER observations weremadeusing theVfilterofastandard UBV photometer;eachpoint inthefiguresis Figures 1-10showthelightcurves. TheMcDonald © American Astronomical Society • Provided by theNASA Astrophysics Data System II. LIGHTCURVESANDPHASE FUNCTIONS using aGG13filterwithaverages offourintegrations 40 sec.Theshortlightcurve of9November1958is not included.TheKittPeak observationsweremade straight averageoffourintegrations eachlasting30to 1971AJ 76. . 14IT o of 30sec.Opencirclesareusedwhentheprobable error isgreaterthanabout3timesthatofthenightly metry andtheyareindicatedbyhorizontalthinlines average. “MeanF”linesweredeterminedbyplani- vertical barsonthetopofeachfigure.Lydiaappears to haveanirregularshape.Thethirdmaximum(near near 8°whilethedashedanddottedlinesareforabout on thelightcurves. 7:00) isquitepronounced. 1-9 weresuperimposedasindicatedbythelettered findings ofsteeperlightcurvesawayfromoppositionresults.Foreachnumberarelativeweightisestimated," shape ofthelightcurveisseenalthoughpreviousTableIIIcontainsnightlyaveragesUBV 2° phase;overthissmallrange,littlevariationinthe Fig. 5.McDonaldobservationsat—Iphase. (Gehrels 1956,1967)appearsconfirmed. Figure 11isacalculatedlightcurveforwhichFigs. The solidlineinFig.11isforanaveragephaseangle Fig. S.lMcDonaldobserva- © American Astronomical Society • Provided by theNASA Astrophysics Data System tions at+8°phase. Fig. 7.McDonaldobservationsat+4°phase. ASTEROID (110)LYDIA usually aboutsixtransfermeasurementsweremade Fig. 6.McDonaldobservationsat+2°phase. 143 1971AJ 76. . 14IT 144 per night.NoUBVtransfersweremadeforthelight- were assumed(onlythedatafromnightswithphase curve of1969. The straightlinesofFig.12showtheserelations(the angles greaterthan8°wereusedfortheVfilter).The different ordinatescalesshouldbenoted). tions oftheorbitalphaseangle.Theoppositioneffect results are: (viz. Sec.IV)andreddeningwithphaseareclearlyseen. Obs. dateOTl,«)){B-V)(U-B) 58.11.04 8.383 58.10.18 8.585 58.12.11 8.322 58.12.02 8.127 58.11.29 8.025 58.11.25 7.868 58.11.20 8.011 58.11.17 8.120 58.11.09 8.300 59.01.25 8.738 In calculatingthephasefunctions,linearrelations Figure 12showsthemagnitudesandcolorsasfunc- U.T. (mag)wt. © American Astronomical Society • Provided by theNASA Astrophysics Data System Table III.UBVobservationsofLydia. F (l,o:)=8.09+0.0321aI, 5 -F=+0.706+0.00161o:I, £/-£ =+0.287+0.00251o!I. 3 0.722 2 +0.719 1 0.730 1 0.682 1 0.707 1 0.697 1 0.700 1 0.722 1 0.713 1 0.747 TAYLOR, GEHRELS,ANDSILVESTER 4 0.318 3 0.2984 3 +0.3172 3 0.2752 2 0.3053 2 0.342 1 0.3223 1 0.2632 1 0.334 1 0.2513 hm Obs. date Nov. 932516.8873 Nov. 4921511.8796 Nov. 25758532.8221 Nov. 20747527.8145 Nov. 17318524.6277 Oct. 1813549540345 Nov. 291019536.9200 Dec. 2353539.6519 Jan. 25814593.8302 Dec. 11625548.7573 1958-9 ObservedJ.D.(c)Number 58.10.18 58.11.17 58.11.09 58.11.04 U.T. 2436000+IntervalofcyclesPn 69.03.16 59.01.25 58.12.11 58.12.02 58.11.29 58.11.25 58.11.20 8y Date Table IV.Observedepochsandsynodicperiods. Table V.CalculatedamplitudesofLydia. Fig.9. McDonaldobservationsat+20°phase. dbl ±0.0006 mean V Above 0.082 0.087 0.080 0.109 0.084 0.079 0.079 0.076 0.078 0.079 ±0.0005 45.0729 99282 1648451 3704455272 5.0076 11236 3.1868 7257 5.0077 11245 9.1054 20270 2.7319 6317 4.0979 9322 7.7404 17318 mean V Below 0.102 0.088 0.085 0.078 0.075 0.095 0.108 0.099 0.094 0.112 Amplitude (mag) 0.19 0.11 0.18 0.16 0.16 0.20 0.19 0.18 0.17 0.16 0.16 1971AJ 76. . 14IT © American Astronomical Society • Provided by theNASA Astrophysics Data System ASTEROID (110)LYDIA hm and theEarth;middlecurve, B—Vcolors;bottomcurve,the opposition. angle indegrees.Ordinates,topcurve: theobservedmagnitudes U—B colors.Opencirclesare before andfilledcirclesafter 69.03.16 59.01.25 58.12.11 58.12.02 58.11.29 58.11.25 58.11.20 58.11.09 (F ontheUBVsystem)reduced to unitdistancesfromtheSun 58.11.17 58.11.04 58.10.18 was 0.18magontheaverage,andit0.11in and orientationofthepoleusingphotometricastrom- adjacent lightcurvefitting.Theamplitudein1958-59 period of105536?24db0?04(p.e.). according tothenumberofcycles,givesasynodic for lighttime).Aleast-squaresroutine,withweights of light. of thesubearthpoint,subsolarandapparentcenter curves weredeterminedbylinearinterpolationand the heightanddepthofeachlightcurvewithreference to themeanVline.Amplitudesofincompletelight- “A” withthecorrespondingJulianDateaftercorrection was foundwhichmayindicatethatthelightcurveis 1969, whichindicatesacloserpolaraspectin1969. caused mostlybyshape. (marked inFigs.1-9bytheverticallineslabeled Epoch Fig.. 12.PhasefunctionsofLydia. Abscissas,theorbitalphase Table VI.Eclipticlongitudeandlatitude,asseenfromLydia An attemptwasmadetodeterminethetrueperiod Table Vgivestheamplitudesobtainedbyplotting Table IVcontainstheepochsofmaximumlight No colorchange(U—V)overthesurfaceofLydia 324.40 235.27 237.68 239.62 240.18 241.12 242.23 242.96 244.73 245.74 247?98 long. lat. Subearth III. THEPERIODOPROTATION -0.94 -8.30 -2.24 -1.28 +0?64 -0.91 -0.74 -0.54 -0.43 +0.07 -0.11 342.67 245.56 222?13 273.94 250.37 239.25 244.09 241.92 237.57 233.63 230.90 long. lat. Subsolar -0.37 +0?28 -3.53 -1.22 -0.51 -0.21 +0.03 -0.35 -0.29 -0.17 -0.04 324.75 236.69 237.89 240.20 239.66 241.12 242.21 242.93 245.45 244.56 247?16 long. lat. Lightcenter -8.12 -2.18 -1.26 -0.90 -0.54 +0.07 -0.94 -0.74 -0.43 -0.11 +0?62 145 1971AJ 76. . 14IT m 146 etry (PaperIandrefinedinSec.VIIofPaperIV),but is needed.TableVIgivesthepresenteclipticcoordinates a widerrangeofobservationslightcentercoordinates were appliedtoadjustforthedifferencesinbrightness. Lydia, ofVmagnitudeversusphaseangle;corrections about 8°phaseto0°phase,wasfoundfor(20)Massalia on Lydiaforafuturedeterminationofthepole. effect. Figure13isaplotforMassalia,Vesta,and There isastrikingsimilarityoftheoppositioneffect phase, forVestaaswellLydia,andthesecurves The oppositioneffectthereforeappearstobeinde- superpose towithintheprecisionofmeasurements. o products, aswellforthebrighteronesthatmayhave and satellitesatsmallphaseangles.Thisshouldbe pendent ofwavelength. done forfaintasteroidsthatpresumablyarecollision of thesethreeasteroids. 0.6 (Gehrels 1956).Lydiashowsthatsameopposition 0.8 0.4 0.2 I .2 1.0 A pronouncednonlinearincreaseinbrightnessfrom We plottedthevaluesofBand£/asafunction It wouldbeofinteresttoobserveadditionalasteroids Fig. 13.Magnitude-phaserelationsofthreeasteroids. © American Astronomical Society • Provided by theNASA Astrophysics Data System 0° 5°10°15°20°PHASE “i i^m i IV. THEOPPOSITIONEFFECT .1 lIl... TAYLOR, GEHRELS,ANDSILVESTER ...I .1.11.i.1 ^ Lydia a Massalia o Vesta from photographicphotometry—thattheopposition originated byaccretion.InthePalomar-LeidenSurvey effect isthesameforfaintasbrightasteroids,while phase. WefoundthattheoppositioneffectofFig.13 the formerhaveasteeperphasefunctionbeyond8° is notthesameasthatofMoonorMars. and shadowingeffects,i.e.,theeffectisrelatedto that theoppositioneffectisduetointernalblocking has adetaileddiscussionoftheoppositioneffect.] ment bysmallparticles(andsolarwind).Iftheopposi- (Van Houtenetal.1970),anindicationwasfound— major axes,includingtheTrojans. The similarityofoppositioneffectsisthenexplained texture morethantocomposition.[Veverka(1970) different compositions,havehadthesamebombard- by thefactthatdifferentasteroids,whichmayhave bright andfaintasteroidsofvariousvaluesthesemi- from theSun,thiscouldbeanindicationofcometary opposition effectshould,therefore,beobservedfor rather thanasteroidaloriginofthesmallparticles.The tion effectcouldbeshowntoindependentofdistance National AeronauticsandSpaceAdministration. tory andKittPeakNationalObservatoryforthe .1967,Astron.J.72,929(PaperI). telescope assignments.Theworkwassupportedbythe Veverka, J.F.1970,Ph.D.dissertation,HarvardUniversity. Van Houten,C.J.,Houten-Groeneveld,I.,Herget,P.,and Gehrels, T.1956,Astrophys.J.123,331. Gehrels, T.,Roemer,E.,Taylor,R.C.,andZellner,B.H.1970, Laboratory studiesbyHapkeandothersindicate ibid. 75,186(PaperIV). Gehrels, T.1970,Astron.Astrophys.Suppl.2,339. We thanktheDirectorsofMcDonaldObserva- ACKNOWLEDGMENTS REFERENCES