Mon.Not.R.Astron.Soc.(2011) doi:10.1111/j.1365-2966.2011.18747.x A new astrometric reduction of photographic plates using the DAMIAN digitizer: improving the dynamics of the Jovian system (cid:2) V. Robert,1,2,3 J.-P. De Cuyper,4 J.-E. Arlot,1 G. de Decker,4 J. Guibert,5† V. Lainey,1 D. Pascu,6‡ L. Winter4 and N. Zacharias6 1InstitutdeMe´caniqueCe´lesteetdeCalculdesE´phe´meridesIMCCE-ObservatoiredeParis,UMR8028duCNRS,77avenueDenfert-Rochereau,75014 Paris,France 2Laboratoired’Astrome´trieApplique´eLASA,31rued’Yerres,91230Montgeron,France 3InstitutPolytechniquedesSciencesAvance´esIPSA,7-9rueMauriceGrandcoing,94200Ivry-sur-Seine,France 4RoyalObservatoryofBelgiumROB,avenueCirculaire3,B-1180Uccle,Belgique 5LaboratoireGalaxie-Etoile-Physique-Instrumentation-ObservatoiredeParis,UMR8111duCNRS,61avenuedel’Observatoire,75014Paris,France 6UnitedStatesNavalObservatoryUSNO,3458MassachusettsAveNW,Washington,DC20392,USA Accepted2011March17.Received2011March13;inoriginalform2011January8 ABSTRACT The astrometric monitoring of the natural planetary satellites is an important step to assess the formation and the evolution of these systems. However, in order to quantify relevant gravitational effects such as tidal forces, it is necessary to have very accurate observations over a long time interval. Unfortunately, the accuracy is decreasing as one considers older observations.Tosolvethisissue,digitizingofoldphotographicplatesisanattractivemethod, butahighaccuracyinthemeasurementandthereductionofthoseplatesisabsolutelynecessary. WehavedevelopedmethodsandalgorithmsadaptedtospecificplatesprovidedbyUSNO, using the DAMIAN digitizer of ROB. From a set of 35 plates taken in 1974, we have been abletoproducemeasurementswithanaccuracybetterthan0.08µmandafterreductionusing theUCAC2catalogue,rmsresidualsof35mas(1.7µm)forintersatellitepositions(whenthe original reduction provided 100 mas) and of 65 mas for equatorial RA and Dec. positions (whichwerenotpossibletogetwiththeoriginalreduction).Firstresultsonthedynamicsof thesatellitesandoftheplanetJupiterareprovided. Keywords: techniques:imageprocessing–astrometry–ephemerides–planetsandsatellites: general. ROBhadtheaimtopreservethehistoricandscientificinformation 1 INTRODUCTION containedinaerialandastrophotographicarchives,bothonfilmor Thestudyofthedynamicsofthenaturalplanetarysatellitesystems glassplatesandthentoprovidescientiststhecontentofthesepho- needsastrometricobservations,sampledoveranintervaloftimeas tographicimagesinadigitalformforfurtheranalysis(DeCuyper, longaspossible,inordertoquantifythelongperiodtermswhich Winter&Vanommeslaeghe2004;DeCuyper&Winter2005,2006; mayhelptoanalysetheevolutionofthemotion.Thesearchofold DeCuyperetal.2009).Forthatpurpose,theDAMIANmachine datamaybeusefulforthispurpose.However,theaccuracyofold (DigitalAccesstoMetricImagesArchivesNetwork)wasacquired observationsismostlypooranddoesnotprovideanyinformation bytheRoyalObservatoryofBelgium.Inautumn2007thedigitizer onsmalleffectsinthemotionofthesatellites. wasinstalledandhousedinatemperature-andhumidity-stabilized Anewreductionofgoodphotographicplatesmaybeasolution cleanroomwithadjacentarchiveroom.TheDAMIANmachinecan andaprojecthasbeeninitiatedforthatpurposebetweentheInstitut digitizephotographicimagesupto350-mmwideonglassplates, deMe´caniqueCe´lesteetdeCalculdesE´phemerides(IMCCE,Paris filmsheetsandfilmrolls.Themechanicalsubsystemincludesan Observatory,France),theRoyalObservatoryofBelgium(ROB)and automaticplateholderassembly,aplatetrayexchangerobotwith the US Naval Observatory (USNO, Washington DC, USA). The platetraymagazineandturntableforphotographicglassplatesand filmsheetsandanautomaticfilmrolltransportsystem.Thesecus- tommadedevicesallowarapidchangeandloadingintofocusof (cid:2)E-mail:[email protected] thephotographstobedigitizedwithoutmanualintervention. †GEPIretired. Inordertoevaluatethescientificabilityofthemachineforas- ‡USNOretired. trometricpurposes,aninternationalcollaborationhasbeensetup (cid:2)C 2011TheAuthors MonthlyNoticesoftheRoyalAstronomicalSociety(cid:2)C 2011RAS Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 3. DATES COVERED 2011 2. REPORT TYPE 00-00-2011 to 00-00-2011 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER A New Astrometric Reduction Of Photographic Plates Using The 5b. GRANT NUMBER DAMIAN Digitizer: Improving The Dynamics Of The Jovian System 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION United States Naval Observatory ,3458 Massachusetts Ave REPORT NUMBER NW,Washington,DC,20392 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES Monthly Notices Royal Astronomical Society,Online Early (MNRAS Homepage) (2011) 14. ABSTRACT The astrometric monitoring of the natural planetary satellites is an important step to assess the formation and the evolution of these systems. However, in order to quantify relevant gravitational effects such as tidal forces, it is necessary to have very accurate observations over a long time interval. Unfortunately, the accuracy is decreasing as one considers older observations. To solve this issue, digitizing of old photographic plates is an attractive method, but a high accuracy in the measurement and the reduction of those plates is absolutely necessary. We have developed methods and algorithms adapted to specific plates provided by USNO, using the DAMIAN digitizer of ROB. From a set of 35 plates taken in 1974, we have been able to produce measurements with an accuracy better than 0.08 μm and after reduction using the UCAC2 catalogue, rms residuals of 35 mas (1.7 μm) for intersatellite positions (when the original reduction provided 100 mas) and of 65 mas for equatorial RA and Dec. positions (which were not possible to get with the original reduction). First results on the dynamics of the satellites and of the planet Jupiter are provided. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF ABSTRACT OF PAGES RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE Same as 9 unclassified unclassified unclassified Report (SAR) Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 2 V.Robertetal. betweenthethreepartners:ROB,USNOandtheParisObservatory (IMCCE/LASA).TheROBprovidesthedigitizationsanditscon- siderableexpertisewiththedigitizersystems,calibrationofcamera andmeasuresystemforthemostprecisedigitization.TheUSNO provides astrophotographic plates of high quality for the science programme(Pascu1977,1979,1994)anditsastrometricexpertise with star catalogues and reduction methods. The IMCCE/LASA analysesthedataandprovidesitsexpertizeinimageanalysis,re- ductionmethodsanditsknowledgeofastrometry,ephemeridesand Figure2. DAMIANmeandark(left)andmeanflat(right). dynamicsofnaturalsatellites.Thispaperpresentstheworkwhich hasbeendonetosolvemanyproblemsbeforegettingtheneeded accuracyfromthemachine,andtheresultsobtainedwiththesetof areevenbetterthanpreviouslyobtainedfromtheStarScanmachine 35platesoftheGalileansatellitesmadein1974. atUSNO(Zachariasetal.2008). Inordertoreachandmaintainahighgeometricandradiometric accuracy,thedigitizerisplacedinanair-conditionedcleanroom,ata temperatureof20◦C±0.05◦Candarelativehumidityof50percent 2 DAMIAN FEATURES RH±1percentRH. 2.1 Hardware Fig.1shows the DAMIAN digitizer as on2009 March. Thema- 2.2 Digitizingprocess chineconsistsofagranitebasedAerotechABL3600openframe Most of the DAMIAN functions are computer controlled. At the air-bearing XY positioning table, with an automatic plate holder beginningofeachplatedigitization,thephotographicplateisput assembly suited for mounting glass plates and film sheets up to automaticallyintofocusbypressingitupagainstthecounterpres- 350-mmwide.Thegranitebasemeasures1.5m×1.2m×0.2m. sure plate. The illumination is set to just below saturation on the Extendedwithanautomaticfilmrolltransportsystemandanauto- plate’sskybackgroundbyadjustingtheDCpowersupplyunitto maticplatetrayhandlingandstorageassemblywithplaterotator, theLED.Theplateisdigitizedautomaticallyinstepandstaremode theDAMIANdigitizerisabletoprocessautomaticallyalmostall withstepscorrespondingtoexactly704pixelsintheXandYdirec- knowntransparentphotographicmaterial. tionsinazigzagpattern.Aftertheplateiscompletelydigitized,the TheopticalunitconsistsofaBCi4,12bitCMOSCamerafrom plateholderisunclampedandtheplateautomaticallyremoved.The C-Cam Vector International, mounted on a Schneider Xenoplan timeneededtodigitizeasingleplateof12cm×17cmis9min. telecentric1:1objective.ThissystemisattachedtotheZ-axisabove Fig.2showsmeandarkandmeanflatimages,obtainedbyaverag- theXYtable.The2DCMOSCameraprovidesimageswith1280× inga1000individualimagestakenatthesameintegrationtimeof 1024pixelsof7µm×7µm.Thephotographicimagesareillumi- 15ms,thatareusedtocorrecttheindividualrawplateimages.An nated from below with very bright Light Emitting Diode’s (LED overallmosaicFITSimageofthewholephotographicplateisalso lifetimemin.50000h),controlledbyahighprecisionDCpower generatedfromtheinnernonoverlapping(704×704pixels)part supply. oftheindividualimages.Thesteppingof704pixelswaschosenin ThepositionoftheXYtableisreadbyHeidenhainencoders.The ordertorestraintheopticaldistortioneffectsinthenon-overlapping linearity and orthogonality of the (X, Y) axes were calibrated by partsofthesub-images. Aerotechusingalaserinterferometer.ThelocalXYtablepositioning repeatability(howcloselythetablecanreturntoaninitialposition following movement over the entire X–Y) was measured with a 2.3 Geometriccorrectionofthecameraopticaldistortion capacitance by the manufacturer at 0.008 µm. The fitted object positions in different digitizations (7 µm × 7 µm pixels) of the Inordertocorrectfortheopticaldistortionoftheobjective/detector sametestplatewerefoundtorepeatwithin0.07µm.Theseresults unit,seven-parameterthirdorderpolynomials(equation1,Winter 2008)areusedtocalculatecorrectedxandyplatecoordinatesasa functionofthemeasuredplatecoordinatesx andy withrespectto 0 0 thecentreoftheindividualsubimage: (cid:2) (cid:3) x =ρxx0+(cid:2)νxy0−(cid:3)d(cid:5)x 3x02+y02 −d(cid:5)y(2x0y0) +dx x2+y2 , 0 0 0 (cid:2) (cid:3) y =ρyy0+(cid:2)νyx0−(cid:3)d(cid:5)x(2x0y0)−d(cid:5)y x02+3y02 +dy x2+y2 , (1) 0 0 0 where ρ and ρ are scales on the XY plate axes; ν and ν are x y x y rotation terms mixed with non-orthogonality and corresponding platescales;d(cid:5) andd(cid:5) aredistortionoffsets;disthethirdorder x y distortionterm.Inthesametemperatureandhumidityconditions, these parameters were found to be stable to within 1σ of their individualformalerrors. AsthepositioningrepeatabilityoftheXY tableistwoordersof magnitudebetterthantheresolutionofthedigitalcamera,theseop- Figure1. TheDAMIANdigitizeratROB,Brussels. ticaldistortionparametersareevaluatedbysteppingawellexposed (cid:2)C 2011TheAuthors MonthlyNoticesoftheRoyalAstronomicalSociety(cid:2)C 2011RAS Astrometricreductionofphotographicplates 3 Figure4. CentreoftheUSNOGalileanplaten◦0318. precision,toimprovethesatelliteorbitalmotions,andtoinferthe accuracyofJupiter’sephemeris.Moreover,thisnewreductionisa usefultestofthedigitizerwhichwilltellsusiftheremainingpart oftheUSNOplatearchiveshouldbedigitizedandanalysed. Figure3. Thecorrectionoftheopticaldistortionoftheobjective/camera unit,intheinner704×704pixelsfieldofviewofthecamera,shownas 3.2 Dataextraction vectorsenlarged100times(thelargestvectorisabout1.5-µmlong). EachUSNOplatecontainsthreetosevenexposuresshiftedinthe starinthefieldofviewofthedigitalcamera.UsingtheStarScan- Dec.direction.Fig.4showsthecentreoftheUSNOGalileanplate Viewsoftware(Winter2005)theaimedstarpositionisfittedanda n◦0318digitizedwiththeDAMIANmachine. tableisgeneratedcontainingthefitted(x,y)starpositionasfunc- Inordertoobtainaquickresult,the(x,y)oftheGalileansatellites i i tion of the corresponding (X, Y) table position. A least-squares andthestarswereextractedfromthemosaicFITSimagesbymeans i i fittingprocedureisusedtocalculatethesevenparametersofequa- ofaspecificprocess.FirsttheSourceExtractorsoftware(Bertin& tion(1).Fig.3showsthecorrectionsoftheopticaldistortionofthe Arnouts1996)wasusedtocreatealistofobjectsdetectedonthe objective/cameraunitinthecentral704×704pixels(correspond- plates; thousands of possible sources were generally detected on ing to 5 × 5 mm) field of view of the camera as vectors scaled eachplate,evenafteraselectionforcircularobjectsandamagnitude by a factor of 100, thus the largest vector is about 1.5-µm long. constraint. Hence, the objects assumed to be present in the field The magnitude of the optical correction, at the edges of a 704 × neededtobeidentifiedfromexistingcataloguesinordertoselect 704pixelssub-image,is1.26µmontheX-axisand0.78µmonthe only the real physical objects on the plates. The plate positions Y-axis.Thedifferencebetweenthetwoisduetothenon-zeroother obtainedwerecorrectedfortheopticaldistortionintroducedbythe termsinequation(1)causingaslightanisotropybetweenthexand objective/camera unit during the digitization and transformed to ycoordinates. celestialcoordinatesusingaplatescaleof20.84arcsecmm−1,after taking into account various corrections such as the aberration of light(Kaplanetal.1989)andtheatmosphericrefraction. 3 ASTROMETRIC TEST PROGRAMME Equatorial (RA, Dec.) and intersatellite astrometric positions were determined in an ICRF geocentric reference frame in order 3.1 Thedigitizedplates tobeeasilycomparedwithcurrentephemerides.Accordingtothe OneofthecurrentDAMIANdigitizerprogrammesdealswiththe highqualityoftheUSNOplates,andtotheaccurateplanetaryand digitizingandtheanalysisofphotographicplatesofplanetarysatel- Galileanephemeridesused,the(RA,Dec.)(O−C)differencesbe- lites.OurintentionistodigitizeasubsetoftheUSNOplatesarchive; tweenobservedandcomputed(theoretical)positionswereexpected 35platesfrom1974,consistingof100exposureswithalimitingV tobebetterthan50mas(Fienga1998).Notethat1mas(cid:4)3kmat magnitudeof10to12.TheseexposuresweretakenwiththeUSNO theJupiterGalileansystem.Thisaccuracywasalreadyachievedbut 26-inch refractor on Kodak 103aG glass plates by Pascu (1977, onlywithintersatelliteresults(systematiceffectsduetotheplanet 1979,1994).ASchottGG14filterwasusedincombinationwith positionareeliminatedwiththiskindofreduction). a neutral density filter to reduce the brightness of the planet and GalileanstothatofninthVmagnitudestars.Thissubsetwascho- 3.3 RepeatabilityoftheDAMIANdigitizerpositioning senbecausetheseplateswerealreadypreviouslymeasuredtwice; manually, using a MANN two-screw measuring machine (Arlot Inordertoobtainanestimateofthepositioningrepeatabilityofthe 1982)andthetrail-scalereductionmethod(Pascu1977)and,auto- DAMIAN digitizer, the USNO Galilean plate n◦2114, containing maticallyusingaPDSdigitizer(Arlot1980).Additionallybecause five exposures of 20 s each, was digitized several times in direct theephemeridesoftheGalileansatellitesareknownaccuratelyand andreversemodes(D–R)withtheDAMIANmachine.Thereverse studiedextensivelyatIMCCE,anewreductionoftheseplates,lead- modeisscanningaplateat180◦ totheusual(direct)orientation. ingtorightascension(RA)anddeclination(Dec.)ofthesatellites, Thisisanimportantmethodfordetectingandeliminatingmachine- andusingnewstarcataloguespermitustoimprovetheastrometric caused systematic effects, and in particular those that depend on (cid:2)C 2011TheAuthors MonthlyNoticesoftheRoyalAstronomicalSociety(cid:2)C 2011RAS 4 V.Robertetal. Table1. Intersatelliteplateaverageseparationdispersionsobtainedfrom USNO Galilean plates with the (a) MANN manual and (b) DAMIAN methods. Platepairs σsseparationdispersioninmas Plate 0306 0307 0326 0327 0336 0337 JI–JII (a) 55 91 96 67 40 69 (b) 30 30 66 62 20 32 JI–JIII (a) 49 43 91 102 65 – (b) 22 13 59 57 48 – JI–JIV (a) 58 64 118 102 64 54 (b) 11 14 66 64 49 51 tothelimitednumberofdata,notethattheσ dispersionisnotfully s significant.Neverthelessitstillprovidesaninterestingindicatorof Figure 5. Examples of positioning repeatability measures for two D–R satellitemeasurementerrors. DAMIANdigitizations. Wesupposeherethattheephemeriserrorsremainconstantduring thesmallintervaloftimethatwasneededtotakethesesuccessive plateexposures.Hence,thedifferencesbetweentheσ dispersions magnitude.Thuswechosetoperformaplate-to-plateanalysisfrom s withinthesameplatepairshouldbeminimum.Also,iftheorbitshad successive scans; in fact, the objects on this plate do not need noerror,thedifferenceswouldbemainlyduetomeasuringerrors to be identified but they are fixed and supposed to be measured at the same relative positions. The test compares the dX and dY andatmosphericseeingvariationsfromexposuretoexposure.The results presented in Table 1 allow us to appreciate the quality of differencesbetweenthesamerelativepositionscalculatedfromthe the forthcoming astrometric results. We remark that the residuals successive direct and reverse digitizations. We used six UCAC2 oftheMANNmanualmeasurementsarelargerandevennotstable (Zachariasetal.2004)andBSS(Urban,Zacharias&Wycoff2004) withinonenight,indicatingthattheyarelessreliable.TheDAMIAN starsoneachexposuretoperformthetest. Fig. 5 shows examples of dX and dY results of position- digitizationsproducemorestableandcoherentresults. ing repeatability measures for UCAC2 stars with respect to star BSS_50047604,asafunctionofmagnitudefortwoDAMIANdig- 3.5 Astrometricreductions itizationsindirectandreversemodes.Theseresultsarerepresenta- tiveoftheD–Rdigitizationsweanalysed.Wecalculatedasimple 3.5.1 Cataloguereduction matrixtransformationonthecoordinatesfromthereversescanso We calibrated the field of the USNO observations by tying the that the two sets of coordinates could be compared. This method measured(x,y)starplatecoordinatestoareferencestarcatalogue. letusknowwhethermachine-basedterms(magnitudeeffectduring Weuseatraditionalmethodofplateconstantsthatwecall‘starlink scanprocess)shouldbeconsidered. method’. Applicationtopositionofstarsshowsthattherearenoobvious Theconventionalplatemodelconsistsofafullsecondorthird machine-based terms with the two D–R DAMIAN digitizations, orderpolynomialexpansiontocompensateforvariousinstrumental atourlevelofmeasurementaccuracy.Weestimatepositioningre- andphysicaleffects.Becausethismodelneedsalargenumberof peatabilitybetterthan0.08µm.Actuallytheseerrorscomemostly reference stars to fit the plate parameters and because this model fromfittinguncertaintiesassociatedtotheUSNOplate.Weestimate doesnotallowustoseparatethecontributionsofthevariouseffects, the fitting precision to a few hundredths of micrometers, indicat- here we used a functional plate model with a minimal number ing that the current analysis is limited because the fitting errors of plate parameters after correcting the (x, y) measurements for dominate. all known instrumental and spherical effects, including the total atmospheric refraction and the parallax and aberration effects. It isjustifiedwiththeUSNOplatesbecauseofthesmallnumberof 3.4 Stabilityofthedataextractedfromsuccessiveobservations referencestarsavailable,usuallylessthansevenstars.Weusedthe Inordertoevaluatethestabilityofthedataextraction,severalplates following firstorder reduction equations modelling scales ρ and x taken successively during the same night were digitized with the ρ ,orientationsθ andθ ,offsets(cid:5) and(cid:5) tocalculatetangential y x y x y DAMIAN machine and compared with the results obtained from (X,Y)coordinatesforeachreferencestarmeasuredontheplate: previous measurements. As the PDS microdensitometer raw data X=ρxcosθxx−ρysinθxy+(cid:5)x, werenotavailable,weonlycomparedtheMANNmanualmeasure- mentswiththedataextractedfromtheDAMIANdigitizations.For Y =ρxsinθyx+ρycosθyy+(cid:5)y. (2) thederivedintersatellitedistancesJI−JII,JI−JIIIandJI−JIV, Theoretical star positions obtained from reference catalogues (O−C) values and plate average dispersions σ were calculated wereconvertedtotangentialcoordinatesusingthegnomonicpro- s by using the theoretical intersatellite separations given by the L2 jection. Differences between measured and theoretical tangential Galileanephemeris(Laineyetal.2009).Table1showstheσ dis- positionswereminimizedusingweightedleast-squaressolutions. s persionsfortheUSNOGalileanplatesn◦0306andn◦0307,n◦0326 In order to perform the instrumental calibration, we evaluated andn◦0327,n◦0336andn◦0337,resultingineightobservationsfor withPraesepeandPleiadesclusterimages(50referencestarsavail- eachdispersionmeasurement.Eachplatepairwasobtainedonone ableforeachexposure)differenteffectssuchasthetelescopein- nightrespectivelyin1974September,OctoberandNovember.Due strumentaldistortion,theplatetiltsandthecoma-magnitudeeffects. (cid:2)C 2011TheAuthors MonthlyNoticesoftheRoyalAstronomicalSociety(cid:2)C 2011RAS Astrometricreductionofphotographicplates 5 We incorporated in these equations a third order distortion term, twoplatetilttermsandtwocoma-magnitudeC x(m−m )andC y x 0 y (m−m )termswheremisthestarmagnitudeandm themeanmag- 0 0 nitudeavailableontheplate,toestimateeacheffectcontribution.We founddistortionandtilttermstobeinsignificant.Wealsofoundtwo constantcoma-magnitudetermsCx = −0.67±0.06µm−1mag−1 andCy = −0.92±0.06µm−1mag−1 withdiaphragmed(16-inch aperture) observations and Cx = −1.55±0.03µm−1mag−1 and Cy = −0.67±0.06µm−1mag−1 withfullaperture(26inch)ob- servations. Oncewetakeintoaccountthementionedinstrumentalandspher- icalcorrectionsbeforeadjustment,weuseequation(2)withdeter- minedconstantstocalculatetangential(X,Y)coordinatesforeach satellite,thenwecorrectforthephaseeffect(Lindegren1977)and weobtaintheequatorial(RA,Dec.)astrometricpositionsbyusing the gnomonic inverse projection. (O−C) residuals are calculated fortheGalileanpositionsmeasuredaccordingtoaJ2000geocen- Figure6. ScalefactorsinXandYobtainedwithPraesepeobservationsand tric frame and using the L2 Galilean ephemerides (Lainey et al. withoutcorrections. 2009).Wewillalsouseequatorial(RA,Dec.)positionstocompute intersatellitepositionswithrespecttothecentreofthediscs. 3.5.2 Theρ andρ scalefactors x y ThescalefactorsonbothXandYaxesarethemainindicatorsthat characterizetheisotropyofthefieldandinconsequence,therobust- nessofthereductionmodelused.InthecaseofMANNmanualand PDSmicrodensitometermeasurementsandinordertousethetrail- scalemethod,thescalefactorswerecalculatedwithdiaphragmed Praesepe and undiaphragmed Pleiades plates taken in 1974 and 1994.Eachexposurecontainsabout50referencestars.Thescale factorswereassumedtobestableandequalforalltheplatestaken withthesametelescope:ρx = ρy = 20.843±0.002arcsecm−1. Thisisthescalevalueofthe26-inchdiaphragmedto16-inchaper- ture,andcorrectedfordifferentialrefraction(Jostiesetal.1974). Otherwise,ifthemeasurementsarecorrectedfortotalrefraction,a scalevalueofρ =ρ =20.839±0.002arcsecmm−1 shouldbe Figure7. ScalefactorsinXandYobtainedwithPraesepeobservationsand x y used. withcorrectionsapplied. In the case of the DAMIAN star link method, we determined the scale factors with the same Praesepe and Pleiades images by aphragmed to 16-inch aperture, and outside the atmosphere. To identifying the corresponding parameters from the least-squares apply this scale factor, the measurements must be corrected for solution of our first order reduction model. We assume that the total atmospheric refraction. This mean value is lower than the scalefactorsonbothXandYaxesarenotequalbutdependoneach previous 20.843 arcsecmm−1 scale factor determined to use the individual observation, and we assume that if they are equal (not trail-scalemethodinsidetheatmospherebecauseinthislastcase, necessarilytrue),itwouldindicateanisotropy. the atmosphere acts as an optical element in increasing the scale Without the corrections mentioned above, the scale factors in value.Neverthelessthemean20.8388arcsecmm−1 scalefactoris X and Y are quite different because the constants tend to correct very close to the previous 20.839 arcsecmm−1 value. In the fol- the effective anisotropy of the field. Fig. 6 shows the anisotropy lowingorderofmagnitude,thetotalatmosphericrefractionbrings throughthescalefactorsonbothXandY axes.Theerrorbarsare the ρ value to the ρ value but a slight difference remains. The y x 1σ,representativeofthesingle-exposuremeasurementandofthe coma-magnitude correction finally tightens the scale values, and plateandcatalogueerrors.Theerrorsarecomparabletothesizeof theaberrationoflightshiftstheρ andρ scalefactors. x y thedatapoints. We reproduced the same analysis with the undiaphragmed Oncewetakeintoaccounttheinstrumentalandsphericalcorrec- Pleiades images and we estimate the following mean values: tions,andinparticularthetotalatmosphericrefraction,thecoma- ρ¯x =ρ¯y =20.8514±0.0003arcsecmm−1.Thisisthescalevalue magnitudeeffectsandtheaberrationoflight,thescalefactorsbe- oftheundiaphragmed26inchandinsidetheatmosphere.Toapply come equivalent for each individual Praesepe observation. Fig. 7 thisscalefactor,themeasurementsmustbecorrectedfordifferential shows the isotropy through the scale factors once the corrections atmosphericrefraction. are applied. The error bars are 1σ, representative of the single- We demonstrate here that it is possible to reduce plates with exposuremeasurementandoftheplateandcatalogueerrors.The veryfewreferencestarsbymakingtheoreticalcorrectionsandus- errorsarecomparabletothesizeofthedatapoints. ingauniqueρ factorfortheisotropicscale.Wealsoverifiedthat Weestimatethefollowingmeanvalues:ρ¯x = ρ¯y = 20.8388± the θx and θy orientation terms were equivalent for each individ- 0.0003 arcsec mm−1. This is the scale value of the 26-inch di- ual observation; in consequence, we have two parameters less in (cid:2)C 2011TheAuthors MonthlyNoticesoftheRoyalAstronomicalSociety(cid:2)C 2011RAS 6 V.Robertetal. equation(2)andtheplatemodelreducestoonlyfourparameters Table2. Detailsoftheintersatellite(O−C)inmaswithDAMIANdigiti- (modellingmeanscaleρ,meanorientationθ,offsets(cid:5) and(cid:5) ), zations:USNOGalileanplatesof1974. x y strengtheningthesolution: X=ρcosθx−ρsinθy+(cid:5)x, Satellite (O−LC2)αcosδ σαcosδ (O−L2C)δ σδ Y =ρsinθx+ρcosθy+(cid:5)y. (3) JI 3 30 10 32 JII 3 32 −8 32 JIII 7 36 9 32 4 ASTROMETRIC RESULTS IN (RA, DEC.) JIV −13 48 −11 31 POSITIONS Average 0 37 0 32 OnekeypointintheDAMIANmeasurementsassociatedwiththe starlinkreductionmethodistoprovidethepositionsofthesatel- lites as RA and Dec. in J2000 ICRF reference frame. Of course, satellites,andthestabilityoftheDAMIANmeasuresthroughthe intersatellite measurements are sufficient for the study of the dy- valuesofthedispersions.Averagesarethesquarerootsofthemean namicsofthesatellitesandmaybededucedfromthese(RA,Dec.) squaredsigmas.Notethatthedispersionforalltheseriesissmaller values.However,the(RA,Dec.)positionsofthesatellitespermit thanwiththeMANNmeasurements(Arlot1982). thedeterminationof(RA,Dec.)positionsofJupiterindirectlyfrom Let us come now to equatorial (RA, Dec.) positions. In order thesatellites;thisisrequired becausedirectmeasurements ofthe tocalculatethe(O−C)valuesandthedispersion,weneedtouse planetfromthephotographicplatesinvolvelargesystematicerrors. an ephemeris of Jupiter. We know that the external error of L2 We present here the results obtained from 35 plates (100 indi- ephemerisisabout15masandoneshouldalsokeepinmindthatthe vidual exposures) made during the opposition of Jupiter in 1974. Jupiterephemeriserrorwillbesuperposedwiththeerrorsfromthe Wewerenotabletocomparewithmanualmeasurementssincethe reductionandthedigitization.WeusedfourJupiterephemerides: trailscalereductionmethod,withnolinktoreferencestars,wasnot DE421(Folkner,Williams&Boggs2008),INPOP06(Fiengaetal. abletoprovide(RA,Dec.)positions.Comparisonsareonlypossi- 2008),INPOP08(Fiengaetal.2009)andINPOP10(Fiengaetal. bleforintersatellitepositionsandgiveninFig.8andTable2which 2010). Residuals areprovided in Fig.9and Tables 3, 4,5and 6, showtheaccuracyofL2ephemeridesthroughtheaverageindivid- inmas. ual (O−C) values with respect to the barycentre of the observed Figure 8. Intersatellite (O−C) with DAMIAN digitizations: USNO Figure 9. (RA, Dec.) (O−C) according to the DE421 theory and with Galileanplatesof1974. DAMIANdigitizations:USNOGalileanplatesof1974. (cid:2)C 2011TheAuthors MonthlyNoticesoftheRoyalAstronomicalSociety(cid:2)C 2011RAS Astrometricreductionofphotographicplates 7 Table3. Detailsofthe(RA,Dec.)(O−C)inmasaccordingtotheDE421 andparticularlycolourdependantsystematicerrorsinthetelescope theoryandwithDAMIANdigitizations:USNOGalileanplatesof1974. optics are other possible causes of the offsets seen in Fig. 9 and furtherinvestigationsareplanned.Offsetsinthecentre-of-massof Satellite (O−C)αcosδ σαcosδ (O−C)δ σδ theJupitersystem(DE421theoryerrors)cannotberuledoutby DE421\L2 DE421\L2 the data shown either. It is advisable to use the intersatellite data JI −6 54 41 65 asshowninFig.8whichwillbefreeoftheseeffectsbecausethe JII −6 55 21 73 samesetofreferencestarsisusedintheastrometricsolutionand JIII 0 63 36 70 a zero-point offset in the absolute coordinates is canceled out in JIV −20 67 17 70 coordinatedifferencesdata. Theaverage(O−C)valuesforthe100observationsmadeduring Average −8 60 29 70 the 1974 opposition of Jupiter are very small in RA for DE421, INPOP06 and INPOP10, and larger in Dec. (slightly smaller for Table4. Detailsofthe(RA,Dec)(O−C)inmasaccordingtotheINPOP06 INPOP10). The external error of DE421 (and INPOP06 and IN- theorywithDAMIANdigitizations:USNOGalileanplatesof1974. POP10)issupposedtobearound10mas(Folkneretal.2008)but wemaydeducefromourresultsthatthisexternalerrorisrealistic Satellite (O−C)αcosδ σαcosδ (O−C)δ σδ inRAbutreaches28masinDec.INPOP08showsamuchlarger INPOP06\L2 INPOP06\L2 externalerror,neverthelessthisisinagreementwiththedifference JI −9 54 34 68 of240km(80mas)betweenINPOP06andINPOP08providedby JII −10 56 14 70 Fiengaetal.(2009).Itisinterestingtoseethattheseobservations JIII 1 63 39 72 areveryusefulfortheevaluationoftheaccuracyoftheephemerides JIV −20 64 10 70 ofJupitersincetheyhavenotbeenusedforthefitofthenumerical integrationsleadingtoDE421,INPOP06,INPOP08andINPOP10. Average −10 59 24 70 In addition, we can see that intersatellite σδ dispersion values aresmallerthanintersatelliteσαcosδ.Butequatorialσδ dispersion Table5. Detailsofthe(RA,Dec.)(O−C)inmasaccordingtotheINPOP08 values are larger than equatorial σαcosδ. Such a systematic error theorywithDAMIANdigitizations:USNOGalileanplatesof1974. in the declinations was found by Pascu & Schmidt (1990) when theauthorsreducedUSNOobservationsoftheSaturnsystem.No Satellite (O−C)αcosδ σαcosδ (O−C)δ σδ causeduetothephotographicobservationscouldbefoundnorto INPOP08\L2 INPOP08\L2 thereductionmethod. JI 65 52 91 67 JII 64 55 82 77 5 CONCLUSION JIII 61 73 91 69 JIV 40 76 81 71 Wehavedemonstratedthevalueofanewastrometricanalysisof oldphotographicplates,resultingfromtheiraccuratemeasurement Average 57 64 86 71 with the DAMIAN digitizer. We analysed a complete series of photographicplatesoftheGalileansatellitestakenatUSNOduring Table6. Detailsofthe(RA,Dec.)(O−C)inmasaccordingtotheINPOP10 the apparition of Jupiter in 1974 and extracted all the important theorywithDAMIANdigitizations:USNOGalileanplatesof1974. informationcontainedintheplatedata.Wewereabletocorrectfor instrumentalandsphericaleffectsduringthereduction,decreasing Satellite (O−C)αcosδ σαcosδ (O−C)δ σδ thenumberofunknownparametersbyusingthesamescalefactor INPOP10\L2 INPOP10\L2 andorientationinXandY. Thenewreduction,usingnewastrometriccatalogues,provided JI 1 54 31 69 JII −1 54 11 71 finalaccuratepositions.TheseastrometricpositionsoftheGalilean JIII 9 65 34 73 satelliteswerenotonlymoreaccuratethanthosepreviouslyderived JIV −15 69 9 71 frommanualmeasurements,butprovidednewinformationdueto thestarlinkreduction;weobtainedequatorialRAandDec.posi- Average −2 61 21 71 tions of the Galileans, allowing us to deduce positions of Jupiter indirectlythroughaccurateephemeridesoftheGalileansatellites. Fig.9showsthedifferenceof(RA,Dec.)coordinatesofindivid- Finally,wecomparedtheseastrometricpositionsofJupitertothe ual satellites and plates, thus observed positions (from DAMIAN bestcurrentephemeridesoftheplanet.Dependingontheephemeris, digitizations andreduced toUCAC2reference stars)versusposi- we obtained residuals between a few tens of mas, to better than tionscalculatedfromtheDE421ephemeris.Offsetsareparticularly 100mas. seenfortheDec.coordinateasafunctionofepoch.Localsystem- The USNO archive contains more plates taken in the interval aticerrorsofthereferencestarcataloguecouldexplainpartofthese 1967–98andthepresentworkhasdemonstratedthatanewanalysis offsets.Theepochdifferencebetweenthese1974–75platesandthe oftheseplateswillprovidevaluabledataforthedynamicsofthe central epoch of the reference stars (around 1990 to 1995) is up GalileansatellitesystemandofJupiteritself.Inaddition,platesof to about 20 yr. Expected systematic errors of the reference stars theSaturniansystemarealsoavailableandwillbeanalysedsoon. at a 1975 epoch are about 15–40 mas. The data shown in Fig. 9 span about 15◦ along the path of Jupiter, thus each epoch data is ACKNOWLEDGMENTS linked to a different set of reference stars. With only about 7–15 reference stars per field the astrometric solution can be affected WethanktheRoyalObservatoryofBelgiumanditsdirectorRonald byaccidentallargeerrorsofindividualreferencestars.Magnitude VanderLindenforallowingustousetheDAMIANdigitizerand (cid:2)C 2011TheAuthors MonthlyNoticesoftheRoyalAstronomicalSociety(cid:2)C 2011RAS 8 V.Robertetal. theUSNavalObservatoryforsendingtheirplatesfordigitization JostiesF.J.,DahnC.C.,KallarakalV.V.,MiranianM.,DouglassG.G., andmakingplateholders.WethankIMCCE,thescientificcouncil Christy J. W., Behall A. L., Harrington R. S., 1974, in Publ. United ofParisObservatoryandtheCNRSforsupportingthisproject. 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