DavorKrajnovićThecontrivanceofNeptune

1

ThecontrivanceofNeptuneDavorKrajnović

Celebrating170thanniversaryofthediscoveryofNeptune,Ireviewthestoryofthediscoverythatstartledtheworld.Thestoryisaninterplayofscientifictriumphandhumanweaknessandanexampleofhowscienceworksinasocio-politicalcontext."Le planète, dont vous avez signalé la position, réellement existe". This is theopening sentenceof an extraordinary letter sentby JohanGottfriedGalle fromtheBerlinObservatorytoJeanJosephUrabinLeVerrieronSeptember25,1846:"The planetwhose position youpredicted really exists". One can only imaginetheemotionsofGallewhilewritingit,orthoseofLeVerrierreadingitthreedayslater inParis.This sentenceannounced themost remarkableconfirmationofatheoretical prediction in the history of science. It heralded a triumph ofNewtonian theory of gravity, astonishing mathematical work, and masterfullyexecutedobservations.NeitherGalle,norLeVerriercouldhaveimaginedwhatastormitwouldraise.ThediscoveryThe showdown started on the morning of September 23 when Galle, theassistant astronomer to the director Johan Encke, received a letter from LeVerrier.ToreceivealetterfromtheeminentFrenchastronomerwassurprising,but not fully unexpected for Galle; it was just about a year and a half late. InMarch 1845, Galle defended a thesis presenting a new reduction of theobservationsbyOleRømerin1706,comprising88starsandknownplanets.AsLeVerrierwasthentryingtocalculatetheorbitofMercury,Gallesenthimthedissertationknowingthevalueofsuchearlyobservations.Therewasno"thankyou"orevenanacknowledgementfromLeVerrier,perhapsbecausebythattimeLe Verrier's focus had shifted to another mystery in the Solar System, theunpredictablemotionofUranus.LeVerrier'sletterstartedwithadelayedthankyou,acongratulationonthegoodwork,andapromisetowriteinmoredetailabouttheMercuryissue,butquicklychangingthetopictosomethingelse:asuggestiontoan"indefatigableobserver"to look at a very particular place on sky, where a planet could be found. Heexplained that the location is the resultofhisworkon the irregularmotionofUranus,andprovidedaveryclearlocationonthesky,aswellasalikelysizeoftheplanet,whichshouldberesolvablebyagoodtelescope.This letter was exceptional in many ways. It transmitted a bold, but clearpredictionof the locationofanewplanet,basedonNewton’s theoryofgravityandacomplexandnoveltheoryofplanetaryperturbations,presentedsome20daysearlieratameetingof theAcadémiedesSciences inParis. Itwasadirectsolicitation to search for the predicted planet, but it was addressed to anassistantatanobservatorysome900kmawayinadifferentcountry.Ontopofthis,itarrivedonthedayofthedirector's55thbirthday!

DavorKrajnovićThecontrivanceofNeptune

2

Today this seems as an amazing opportunity, an insider information, anunmissable tip-off that can secure fame for the recipient and the institution.Astronomy in mid-19th century was, however, very different. Stateobservatorieswere not research institutes in the present sense, but primarilyfactoriesofusefuldata, fromtimekeepingtochartingtheskies.Theuseof theobservatorytelescopeswereunderdiscretionofthedirectorand,asanassistant,Gallehadtoaskforapermissiontoobserveforhisownprivateresearch.ThedirectoroftheBerlinObservatory,EnckewasawareofLeVerrier'stheorythat a more distant planet perturbs the motion of Uranus, and did not thinkmuch of it. But when Galle approached him with the letter, he agreed that itpresented a "moral commitment" toGalle to look for the planet. The standardstory(e.g.Turner1911,Grosser1962,Standage2000)isthatEnckereluctantlygavepermissions toGalle toobserve thatnight,butGalle'sownaccount (Galle1877)isdifferent:whileEnckewasnotmuchinfavouroflookingfortheplanetbefore,oncetheletterarrivedhedidnotobject.Hehimselfdidn'twanttodoit,maybebecauseitwashisbirthday,buthegaveGallepermissionimmediately.Their planning was overheard by another, younger assistant (a student inmodern terms), Heinrich Louis d'Arrest, who immediately asked Galle forpermission if he could join the observations. And so itwas,while the directorwascelebratingwithhisfamily,thatGalleandd'ArreststartedthesearchforLeVerrier's planet. AsGalle later explained (Galle 1877), the nightwas clear andthey firstattemptedto look foranobjectwithacleardiscofabout3",but thiswasnotsuccessful.Itseemedthattheywouldneedtoidentifyallthestarsinthearea. d'Arrest then suggested to look among the new charts, prepared by CarlBremiker for the Royal Academy of Sciences in Berlin, to see if one of themcovered the area. Galle led theway toEncke's office,where they searched thechartsandrecognisedthatabottomleftcornerofachartforthehourXXIcoverstheregionindicatedbyLeVerrier(seeBox1,"Thechart").Back in the dome, Gallewas observing and reading out the positions of stars,whiled'Arrestwascheckingagainst thechart,untilan8thmagnitudestarwasfoundthatwasabsentfromthechart!Onecanimaginethesilencethatfollowedon that fresh early autumn night, just after midnight, the rechecking of thecoordinates,d'Arrest eager to see forhimself,Galledouble and triple checkingthe map, the last look in the eyes between the two astronomers, the first toactually see the new planet, just under one minute of arc away from thepredictedposition.Then theyrushed to informEnckeandwereallback in thedometocontinueobservinguntil theobjectset.Enckeagreedthisobjecthadaresolveddisc,althoughsomewhatsmallerthanpredicted.Theshorttimeleftforobserving,however,wasnotenoughtodetectitsmotion.Therewasnothingforitbuttowaituntilthenextnight.Ifitwereaplanet,anditssizewasagoodindicationthatitreallyis,itwillnotbeatthesamespotinthesky,and,especially, itwouldnotbeaforgotten-andaverybright!-entryinabrandnewmapfromarespectablechartmaker.24SeptembermusthavebeenaverylongdayforthesemembersoftheBerlinObservatory,nervouslyeyeingtheclouds. The night was clear; Galle, d'Arrest and Encke gathered in the dome.

DavorKrajnovićThecontrivanceofNeptune

3

Fromthestartofobservationsitwasevidentthattheobjecthadmoved,thattheplanetwhosepositionwassignalledbyLeVerrier,reallyexisted.BringingUranusundercontrolTheplanetUranuswasdiscoveredbyWilliamHerschelin1781,buthewasnotthefirsttoseeit.Therewere17earlierobservationsinwhichitwasconsideredastar, by J. Flamsteed, T. Mayer, P.C. Lemonnier, and J.J. Lalandel; Lemonnierobservedit11timesover21years!Theseobservationswereimportantastheyallowedtracingoftheplanet'smotionoverasignificantpartofitsorbit.Bythestart of the 19th century it was clear that there was something a miss withUranus. Its observed position on the sky was regularly not the same as thepredicted one: its behaviourwas very peculiar. For example, if onewould useonlythe"modern"observationsmadeafterthediscoverytodeterminetheorbitoftheplanet,onecouldnotaccommodatethe"ancient"observationsfrombeforethe discovery and vice versa. Furthermore, the discrepancy between thepredictedandobservedpositionwasincreasingtowardstheturnofthecentury,justtostabiliseandthenstartdecreasinginthe1820s,almostdisappeararound1830andthentosuddenlybecomelargerthaneverbeforeby1840s(seeFigure1).This was a major problem for the usually very precise science of celestialmechanics. Leading astronomers weremeasuring the deviations and debatingtheir origins. The Astronomer Royal, George Biddle Airy, lead an importantobservationalcampaignofUranus'motionattheRoyalGreenwichObservatory(RGO),whichlaterprovidedcrucialdataforestimatingthepositionofNeptune.Airy even determined that the distance of Uranus from the Sun (the so-called"radius-vector",which ismuchmoredifficult tomeasure in comparison to thelongitudinal displacement), was also changing (Airy 1838). Alexis Bouvardassembled tables of Uranus motion and struggled to bring forward anyresolution, even after the influence of Jupiter and Saturn were taken intoaccount.Such an interesting problem generated several possible solutions. Bouvardhimself was of the opinion that something must be wrong with the "ancient"observations, that they are not as precise as themodern ones. This ideawas,however,quicklyrejectedaseven themodernobservationsbecamediscrepantfromthepredictionssoonafterthepublicationofthetables.Asimilarfatebefella more physical conjecture, that a comet hit Uranus around the time of thediscovery,changingitsorbit;thecontinuingchangestotheorbitruledthatout,too.Otherphysical theories involvedtheexistenceofamediumthroughwhichUranusmovesandslowsitsmotion,orthesuggestionthatUranushadamassivemoon. Neither was compatible with the data spanning more than a century.Thereweretwofinalpossibilities,eitherthelawofgravitywasnotthesameatthose huge distances from the Sun, or there might be another, unseen planetdisturbingtheorbitofUranus.Alternativetheoriesofgravitywerenotanoveltythen,astheyarenotnow,butNewtoniantheoryofgravitydidwithstandallteststhrownatit.LeVerrierwas

DavorKrajnovićThecontrivanceofNeptune

4

never indoubt thatNewtoniangravity is correct, and that there couldonlybeonecausefortheanomalousmotionofUranus:anewplanet.Thefirstpaperdealingwiththe"TheoryofUranus"waspresentedbyLeVerrieron November 5, 1845 (Le Verrier 1845). It dealt with existing data on theanomalousmotion of Uranus, rejecting the claims of Bouvard that the ancientdatawerewrong,anddemonstratingthatwhentheinfluenceofbothSaturnandJupiter is removed, there are significant residuals between the observed andpredictedmotion(Figure1). Inhissecondpaper,presentedonJune1,1846tothe Académie des Sciences (Le Verrier 1846a), Le Verrier rejected all othertheories invoked to explain the motion of Uranus and showed that the newplanetcouldnotbeinteriortotheorbitofUranus.Hischoicewasthentoputtheplanet in theplaneof theecliptic (whereallotherplanetsare), at thedistancepredicted by the Titius-Bode rule of 38 AU (see Box 2, "Titius-Bode rule").Finally,hepresentedasolutiontoaninverseproblemofdeterminingtheorbitofthe trans-Uranian planet, by minimizing the residuals of the predicted andobserved locations of Uranus. Le Verrier's solution was elegant andauthoritative,inwordsofAiry(1846)1:"Itisimpossible,Ithink,toreadthisletterwithout being struck with its clearness of explanation, with the writer'sextraordinarycommand,notonlyofthephysicaltheoriesofperturbationbutalsoofthegeometricaltheoriesofthedeductionoforbitsfromobservations,andwithhisperception thathis theoryought toexplainall thephenomenaof theplanet'splace"Le Verrier concluded his paperwith a prediction of the location of the trans-Uranian planet at 01 January 1847 (325o of heliocentric longitude) andestimated an error of about 10o. This was a rather large error, but the paperdeliveringsuchasensationalclaimwasmetwithapprovalandapplause.Whileeverybody was impressed, nobody wanted to put it to test and look for theplanet-orsoitwasthought.ControversyandtheftWhilereadingLeVerrier'sJunepaper,Airyknewsomethingnobodyelsedid:LeVerrier's prediction was remarkably similar to a prediction of another youngmathematician:JohnCouchAdams.Thestory,asitisusuallytold(e.g.Standage2000),before thenewevidenceresurfaced in1999(Kollerstrom2003), is thatAdamsstartedworkingontheUranusmotionsoonaftergraduationin1843andbySeptember1845hadasolutionforanorbitofatrans-Uranianplanet,whichhetoldto JamesChallis, thePlumianprofessorofastronomyinCambridgeandtheDirectoroftheCambridgeObservatory.ChallisputAdamsincontacttoAiryand,asthestorygoes,Adamsmade2unsuccessfulvisitstoGreenwich,eachtimemissingAiry,butatlestleavinganotewithapossiblepositionoftheplanet.

1ThequotationactuallyreferrerstoaletterfromLeVerriertoAiryon28.06.1846,whichanswersAiry'squestion(inaletterfrom26.06.)onthesolutionoftheradiusvector,butIbelieveitcanbeappliedtogeneralimpressionbyAiryonLeVerrier'swork.

DavorKrajnovićThecontrivanceofNeptune

5

How precise was the prediction of the position of a new planet on the noteAdamsleft,andhowitwouldfare inacomparisonwiththeoneofLeVerrier'sJune 1 paper, is difficult to demonstrate. The reasons for this are discussedextensively by Rawlins (1992), Sheehan et al. (2003; 2007) and Kollerstrom(2006a; 2006b; 2009)2. These authors point out that the note claimed to beAdams'predictionofSeptember1845mightactuallybeofamuchlaterdate.ThedateonthenotesupposedlyleftbyAdamsatGreenwichisvague(October1845)andwritteninadifferenthandwritingtotherestofthemessage;itisimpreciseinexplainingwhatkindof calculationshadactuallybeendoneand itgives themean heliocentric longitude as 325o 2' degrees, which, when converted to thetrueheliocentriclongitudeatthedayofdiscovery,is328o41'.ThisvalueshouldbecomparedtotheactuallocationofNeptuneonthatday,326o57'.LeVerrier'sfirstprediction(June1)was324o35',whileinthefinalpaperon31August,theoneusedbyGalleandd'Arrest,hebothimprovedthepredictionto325o58'anddeclaredthattheplanetshouldberecognisableasadisc(LeVerrier1846b).Incontrast, all other predictions by Adams were significantly worse than(supposedly)hisfirstone(Rawlins1992;Kollerstrom2006).EventhoughAdams'predictionturnedoutnottobeasaccurateasLeVerrier's,itwas an amazing achievement. Thatwas not lost on Airy (amaster of celestialmechanicsandaformerPlumianProfessor),buthewasscepticalandwantedtosee if Adams can also explain his 1838 discovery of the change in the radialmotionofUranus.Adams,however,didnotanswerAiry's inquiryinNovember1845;thiswasthesamequestionAiryaskedLeVerrierinJune1846andgotanimmediate answer that impressed him so much. Adams himself also neverpublished anything of his (pre-discovery) calculations until November 1846(Adams1846b), even thoughhewasamemberof theRASandhadpreviouslypublishedanotablepaperonthetrajectoryofacomet(Adams1846a).Finally,theworkscitedabovestressthatthewholeBritishclaimofAdams'prediction,supposedlypredatingLeVerrier'sworkbysomeninemonths,wasactuallyputforwardafterthediscoveryofNeptune.Thepost-discoveryclaimmightbeeventakenasafullblownconspiracytheory,especiallyasalldocumentsoftheRoyalGreenwichObservatorypertainingtothediscoveryofNeptunedisappeared formore than30years (Kollerstrom2003).When scholars started asking for some of the files (Chapmann 1988; Rawlins1992)theyweretoldthattheywerenotintheRGOlibrary,butgonemissing.In 1999 they resurfaced in Chile, among the possessions of recently deceasedastronomer Olin Eggen (together with another large quantity of 17th centurymanuscriptsand60rarebooks).ItseemsEggen"borrowed"theNeptunefiles,asthey are usually called, in order towrite essays on Airy and Challis, probablywhile he wasworking at the RGO as an assistant to the Astronomer Royal in1964.Heneverreturnedhisloanstothelibrary,movingthemfirsttoAustraliathentoChile,straightforwardlydenyingofhavingthesefilesaslateasin19963.

2Seealso:http://www.dioi.org/kn/neptune/index.htm.3See:http://www.dioi.org/kn/neptune/takes.htm

DavorKrajnovićThecontrivanceofNeptune

6

AsecretivesearchandaninternationalscandalAfterreadingLeVerrier'sJunepaper,andhavingreceivedtheexplanationtotheradial motion of Uranus in a letter directly from Le Verrer, Airy was soimpressed that he thought the time had come to stir Challis into action. Airydevised away to search for the planet centred on the location of Le Verrier'sprediction. This is an interesting point: a director of the most prestigiousobservatory in the world was not actually starting a search for the planethimself, the largest prize in astronomy of the day, but outsourced the search,even offering a reliable assistant for help. As put forward by Chapman (1988)andSmith(1989),itislikelythatAirycouldnotimagineinterruptingRGO'sverypublic duties, butwasmore than happy to set up the discovery of the age forCambridgeanditsobservatory.ChallisindeedstartedarathersecretivesearchonJuly29.Thereisevidencethatthe search was kept secret from even his British fellow astronomers (seeRawlins1992,forexample).Unfortunately,eventhoughtheplanetwasobservedthreetimes,itwasnotrecognisedassuch(seeBox3,"Thefailedattempt").Afterthe news of the discovery was circulated in Britain by Joseph Hind, Sir JohnHerschelwas first to announce the (co-)prediction of Adams (Herschel 1846),whileonOctober17,ChallisandAdams(Challis1846b),usingalloftheavailableobservationsofthenewplanet,determineditsdistanceandproposedanameforit:'Oceanus'(seeBox4,"Namingoftheplanet").The reaction inParis caneasilybeguessed.Twoweeksbefore,LeVerrierwastheonepersonwho"discoveredtheplanetwiththepointofhispen";notevenGalleconsideredhimselfaco-discover,butjustapersonwhofoundit.Suddenlyand totally unexpected, there was another claim, with no actual proof, thatsupposedlypredatedLeVerrier'swork,andassumedenoughcredittotakethehonourofnamingthenewplanet.TransportingthescenetoaJaneAustennoveland one can easily imagine Paris Observatory director François Arago fumingand pacing in the shrubbery exclaiming: "Is it to be endured?But itmust not,shallnotbe."Thisiswhathedid,butnot,however,in"aprettyishkindoflittlewilderness"ononesideofthelawn,butinthehalloftheAcadémiedesSciences.His audience was the cream of the Parisian scientific establishment andjournalists, and Arago proclaimed he would forever call the new planet "LeVerrier". The press was more than happy to take it from there and made aninternationalscandaloutofit.LouisPasteur isaccreditedwithsaying that scienceknowsnonationality,onlyscientists do. The case of the discovery of Neptune adds another layer to it:scientific results have a tendency to be wrapped in the national (university,institute, or funding body) flag. Early historians have either struggled tounderstandor ignoredAiry'swritings (e.g. see Smart1946a,b), supporting theBritishclaim for co-prediction.A reanalysisof thehistoricaleventsbyRawlins(1992)andtheevidencecomingfromthefilesresurfacedin1999,aspresentedbyKollerstrom(2006),showedclearlythatAirywasbuildingacaseforBritish(and Cambridge) role in the discovery of Neptune. Once therewas a rigorouspredictionwheretolook(andaconfirmationofalessrigorousbutneverthelessindicativeestimate),hepushedforthesearch,whichunfortunatelydidnotresult

DavorKrajnovićThecontrivanceofNeptune

7

ina foremostdiscovery.Airy'splanmisfiredandinthepost-discoverynationalfervouritwasAiry(togetherwithChallis)whowasblamedforthefailureinaneventthatovershadowedtherestofhisillustriouscareer.Twoco-discoverersIn a private letter to Le Verrier on 14 October 1846, Airy wrote: "You arerecognised beyond doubt as the real predictor of the planet's place", and in hisNovember13addresstotheRAS(Airy1846),hecomparedLeVerrier'sworkasnothingas"sobold...inastronomicalprediction"sinceCopernicus,concluding"itisherethatweseethephilosopher"(ratherthanjustamathematician).ButAiryalso called thediscovery: "themovement of theage; ... it has beenurgedby thefeeling of the scientific world in general, and has been nearly perfected by thecollateral,butindependentlabours,ofvariouspersonspossessingtalentsorpowersbestsuitedtothedifferentpartsoftheresearches."In both cases Airy is right. Le Verrier in three rigorous papers solved theproblemofthemotionofUranus,andopenlyputhisnamebehindatheory,forgood or worse. It was he who urged the observers to test his prediction, anopportunitythatmostpeoplerejected,orattemptedinlukewarmfashion(e.g.attheParisObservatory).Thecreditforthepredictionhastogotohim.Airy isalsocorrect inhisassessment that thiswas the "movementof theage".This is especially true inmodern science,wheremanypeopleworkon similartopicsandsimultaneousornearlysimultaneoussolutionsordiscoverieshappenoften. The problem of Uranus was certainly one of the top problems inastronomyofthefirsthalfof19thcentury.LeVerrierwastoldbyAragothatheshouldhavealookatit.AdamsgotinspiredreadingabouttheproblemofUranusinareportbyAiryandabouttheperturbationtheoryinthe6theditionofMarrySomerville's "On Connexion of the Physical Sciences" (Chapman 2016). Theuncertainty of Adams' predictions (spanning more than 20o), which had anunfortunate effect ofmisdirecting the secret search, cannot be used to simplydismissAdams.HedidworkonthetheoryofUranus,hemightevenhavehadacomparablesolution,butheneverwentpublicwithhisprediction,haddifficultysettlingonthe finalpositionand,essentially,didnot influencethediscovery intheleast.Ontheotherhand,therewasaco-discoverwhocertainlydidplayamajorpart,but whose credit was slow in coming. d'Arrest was present during theobservations,itwashisideatolookforthenewcharts,andhewascheckingthestarsonthemap.Itishewhoexclaimed:"Thatstarisnotonthemap!"(Dreyer1882).When Encke, as the director of Berlin Observatory, sent a letter to theAstronomischeNachrichtenannouncinganddescribing thediscovery,he failedtomentiond'Arrestatall.Almostnothingwasknownabouthisroleuntilsome30 years later. In themean time d'Arrest became a famous astronomer in hisownright (seeBox5, "Thediscoverers).Whend'Arrestwasawarded theGoldMedal of the RAS in 1875, in the address delivered by none other than RASPresident John Couch Adams there was no mention of d'Arrest's role in thediscovery of Neptune; the Gold Medal was awarded for his work on nebulae

DavorKrajnovićThecontrivanceofNeptune

8

(Adams 1875). The obituary published in the Monthly Notices also makes noconnectionbetweend'ArrestandNeptune.Still,therewerepeoplewhoknewd'Arrestbetter.InaGermanobituarybyJ.E.L.Dreyer(Dreyer1876)thereisasentencedeclaringd'Arrestparticipationinthediscovery. Motivated perhaps by these oversights, Galle himself wrote twodescriptions of the discovery (Galle, 1877, 1882) in which he gave credit tod'Arrest.AnotherinfluentialrevelationwasthepublicationofDreyer(1882),inwhichhedescribedobservingwithd'Arrest's in1874,whend'Arrestretoldhismemoriesofthenightofthefamousdiscovery.Whywasd'Arrestinitiallyneglected?Oneshouldprobablytakeintoaccountthespiritoftheage,whendiscoveryannouncementswereshortletterstotheeditorof a journal and the directors of observatories reported what their namelessassistants discovered. Galle, already an established astronomer, featuredprominentlyinEncke'sreport(Encke1846),butthemerestudentd'Arrestwasnotmentionedatall.WolfgangDickshowedthatEnckewaslateractuallysorrynotto included'Arrest inthereportandexpressedhismisgivings ina lettertoOttoStruve,thedirectorofthePulkovoObservatory(Dick1985,1986).d'Arrest's role in the discovery of Neptune is now securely known, butrecognitioncamelate.Thenamingof theringsofNeptune(Guinanetal.1982)serves as a reminder how perceptions change; they were named after theprinciple participants in this scientific drama. In order of distance from theplanet themain rings are called: Galle, Le Verrier andAdams; fainter featuresalso carry the names ofWilliamLassel (discoverer ofNeptune'smoonTriton)andArago.Itseemsthatevenatthistime,d'Arrest'srolewasnotwidelyknownorappreciated.Ahappyaccident?ThepredictionofthepositionofNeptunebyLeVerrierwasanastonishingandinspirationalapplicationofatheory,demonstratingthepowerofscience.Itisawonderfulstorymadeveryhumanwiththecontroversyofwho-did-it-first, thenamingscandal,thepresswar,thetheftofcrucialdocumentsandtherecentre-evaluation of the British contribution. Yet there is even more in this drama.Having two (unrecognized) pre-discovery and one (unrecognized) post-discoveryobservationsbyChallis,spanningsomesixweeks,Adamswasabletocalculate the new orbit of Neptune (Challis 1846a). In the new orbit, NeptuneturnedouttobemuchcloserthanpredictedbyTitius-Boderule,at30AU,andcloser thanhisandLeVerrier's solutionsrequired.Thedatastilldidnotallowforamorerobustestimateoftheeccentricityoftheorbit;alargertimespanwasneededforthis.AmericanastronomerSearsCookWalker,workingattheUSNavalObservatory,readLeVerrier'spublicationofJune1846andsuggestedtohissuperiorofficerthat theyshouldstartasearch for theplanet.Thiswasrejectedbecauseof thebusy observatory schedule.When the news of the discovery steamed into theBoston harbour onboard SS Caledonia on 20 October 1846, the search for the

DavorKrajnovićThecontrivanceofNeptune

9

planet was no longer necessary, but Walker recognised the importance ofexamining if there were, as in the case of Uranus, previous observations ofNeptune (Table 1). Indeed, Walker discovered that J.J. Lalande's well known"Historie céleste française" contained an observation of a star that wasconsistent with the known orbit of Neptune, but was not in subsequentcatalogues,andcrucially,itwasnotvisibleanymoreonthesky(Hubbell&Smith1992).FurtherinvestigationshowedtheobservationsconsistedoftwosightingsonMay8and10,1795,remarkedasdoubtful,asitseemedthatthe"star"moved.Thisgaveabaselineofmorethan50years,asufficientperiodforcalculatingtheorbitofNeptune.Walker'sresultwastostuntheastronomicalworld.ThemainorbitalparametersofNeptuneareitsdistance,periodandeccentricity.WalkerscalculationconfirmedAdams'estimateof30AUforthemeandistance,derivedtheeccentricityof0.0088andtheperiodof166years.BothvalueswereradicallydifferentfromtheLeVerrier's(andAdams')prediction(seeTable2forcomparisonoforbitalelements).Theorbitwasmuchmorecircular,andasitwascloser,theperiodwasalsoshorter.ThiswasfurthertakenbyBenjaminPeirce,aPerkinsProfessorofastronomyandmathematicsattheHarvardUniversity,whoconfirmedWalker's result and publicly proclaimed that "the planet Neptune isnottheplanettowhichgeometricalanalysishaddirectedthetelescope;...;andthatitsdiscoverybyGallemustberegardedasahappyaccident".Furthermore,Peircenoticed that the orbital periods of Uranus and Neptune are close to 1:2 ratio,implying that the two planets could be in near resonant orbits. What madePeirce'sstatementworld famous is thathedisputedtheLeVerrier'sorbitwiththecalculatedperiodof217years.ThisperiodputUranusandNeptuneclosetothe2:5resonance;thiswouldbelikelytohaveverypeculiareffectsontheorbitofUranus,whichLeVerrrierhadnot taken intoaccount.Pierce'spositionwasthatNeptunewasnotresponsible for theperturbationsofUranus.AfterPiercecalculated the mass of Neptune based on the observations of the orbit of itsmoonTriton,hechangedhisopinionandproclaimedthatNeptunecanaccountfor the perturbation of the Uranus' orbit, including the earliest recordedobservation of Uranus from 1690 by Flamsteed,which always had the largesterror in both Le Verrier's and Adams' calculations (for a detail discussion seeHubbel&Smith1992).Butwasitachancediscoveryornot?LeVerrier'spredictionputNeptune'sorbitmuchfurtherfromtheSun,butonlyonaverage.Theorbitalsohadasignificanteccentricityofabout0.1.Moreover,atthetimeofdiscoverythepredictedplanetwas essentially closest to the location of the actual planet, at about 33 AU(Rawlins1992;Kollerstorm2006).AsDanjon(1946)showed(Figure2),bothLeVerrierandAdamshadtoconstructorbitssuchthattheyapproachedNeptune'sorbit in order tominimise the terms of the discrepant Uranus'smotion. Theircalculations, while globally incorrect, did approach the actual position ofNeptuneonthesky.ModerninsightsAmodernapproachtothesolutionoftheperturbationsofUranuswasdiscussedin details by Lai et al. (1990), providing an insightful analysis of Neptune's

DavorKrajnovićThecontrivanceofNeptune

10

influenceontheorbitofUranus.Theysolvedboththeforwardandtheinverseproblem,respectivelypredictingtheperturbationsofUranusgiventhemodernorbitalelementsofUranusandNeptuneanddeterminingtheorbitalelementsofNeptune using the residuals between observed and predicted positions forUranus.Laietal.showedthattheresidualsoftheUranusmotionsdependontwodominantterms(Box6,"ExplainingUranus'motion"):theforceNeptuneexertson Uranus which is dependant on Neptune’s mass and radius, MN/R2N (theinhomogeneous solution); and the difference between two Keplerian orbits,expressedastheorbitofUranuswithperturbedsemi-majoraxisandeccentricity(thehomogenoussolution).Neptune has a large pull and, if other contributions are removed, it wouldaccountforalmost550arcsecondsinthedeviationoftheUranusposition.Atthetime of the discovery the observed deviations were of the order of 50 - 100arcseconds,aboutafactorof5-10less(Figure1).Thisarisesbecausetheotherterm, that describing the shift in eccentricity ofUranus, has also an amplitudethatwouldproduceabout500arcsecondsofdeviationifconsideredalone.Hereis the crucial insight first indicatedbyPierce:NeptuneandUranusare innear1:2 resonance (less than 2% deviation), so the orbital periods introduce animportant beat effect. As demonstrated by Lai et al., the phases of the twodominant termsaresuchthat theynearlycancelledeachotherout in theearly1800s. Today or at the time of Galileo, the perturbation are constructive andresultinmuchlargerdeviations.ThediscoveryofNeptunewasnotjustlucky:asthepredictionsweresolid.Theinverse problem that Le Verrier and Adams attempted to solve has sevenunknown elements: Neptune's orbital period, time of conjunction, Neptune'smass, and four constants of the homogeneous solution describing the true(perturbation free) orbit of Uranus. As Lai et al. show, a perturbed orbit ofUranus can also be described as a unperturbed orbit with a modifiedeccentricity.Thus,understandingtheperturbationNeptuneexertsonUranusbyitsmass and radius ismadedifficult by thedegeneracybetween theunknowntrueorbitofUranus(ifUranuswerealoneintheSolarsystem)andaperturbedoneofslightlydifferentorbitalparameters.OneyearonNeptuneThe discovery of Neptune took place 170 years ago, just a little more than ittakesNeptune tomakeone revolutionaround theSun.ThisoneNeptuneyearhasbroughtmajorchangesinbothhumansocietyandscience.Thedistributionof information is now essentially instantaneous, something that Otto Struvewouldhavevaluedtremendously.HealsoreceivedaletterfromLeVerrier,senton the same day as the one to Galle, but it arrived 6 days later to PulkovoObservatorynearSt.Petersburg,bywhichtimethediscoveryhadalreadybeenannounced(Dick1986).Nowadaysit isunthinkabletosubmitanobservationalproposalnotsupportedbysomekindoftheoreticalpredictions,whileLeVerrierstruggled to persuade observes to look. The distribution of orbits of trans-Neptunian bodies shows tantalising evidence for a ninth planet (Trujillo &

DavorKrajnovićThecontrivanceofNeptune

11

Sheppard2014;Batygin&Brown2016), and theSolarSystemnow looksverydifferentfromthatknowntoLeVerrier,Galle,d'ArrestandAdams.Somethings,however,donotchange.Adiscoveryrequiresdeepknowledge,boldthinking and some luck. The luck was absent in Cambridge, but Le Verrier'sdauntless audacity, as well as Galle's and d'Arrest's willingness to take thechallenge, should be celebrated. The discovery of Neptune is a quintessentialstoryaboutprogress inourunderstandingof theuniverse,andalsoabouthowscienceworksinasocio-politicalcontext.Itisastoryworthrememberingandagoodwaytoengagethegeneralpublicinadialogueaboutscience.Acknowledgements. Iwould like to thank librarians Regina vonBerlepsch,Marcel Thies(AIP)andSianProsser(RAS) forprovidingmanyusefularticles,andMatthiasSteinmetzfor stimulatingmy curiosity to develop thiswork. I amgrateful toRobertMatthews forspottingamistakeinTable1regardingthedateofGalileo'sobservations.BOX1.Thechart

ApartialscanofthechartHoraXXIusedbyGalleandd'ArrestintheirsearchforNeptune. It was produced by Carl Bremiker at the Berlin Observatory for theRoyalAcademyofSciencesinBerlin.Bremikerproduced4othercharts(HoraVI,IX,XIIIandXVIII),morethananyotherastronomer in thatseries. In the lowerleft corner there is a square and a circle, showing the predicted ("Neptunberechnet") and observed ("Neptun beobachted") positions of Neptune,respectively.(LibraryoftheLeibniz-InstitutfürAstrophysikPotsdam.)

DavorKrajnovićThecontrivanceofNeptune

12

Figure 1. Uranus out of control. Discrepancy in predicted and observedheliocentric longitude of Uranus (points) and the fit to the model. The upperpanel shows themeasurements from the period used for the prediction by LeVerrier and Adams, while the lower panel shows the predicted residual on alongertimescaleassumingthesamemodelthatfitsthehistoricdata.Theboxedregioninthelowerplotcorrespondstotheupperplot.

BOX2.Titius-BoderuleTitius-Boderule(or law)describesa factthatthedistanceofaplanetfromtheSun follows a sequence, expressed as a formula a =0.4+0.3×2n, where a is thedistanceinAU,andnincreasesby1foreachplanet,startingwith-∞forMercuryand0 forVenus. Itwas introducedby JohanDanielTitius in thepreface tohistranslationof"ContemplationsdelaNature”byCharlesBoinnet,andJohanElertBode, thepredecessor ofEncke as thedirector of theBerlinObservatory,whowasalmostevangelicalinadvertisingit.WhenitwasdiscoveredthatUranusalsofitstotherule(withn=6),andthatmultipleminorplanetscircleatthevalueforn=3 (betweenMars and Jupiter), Titius-Bode rulemoved frombeing a curiousfact to amain streamastronomy tool. Crucially, itwasusedbyLeVerrier andAdamsasastartingestimateforthedistanceoftheperturbingplanet,breakingadegeneracy between mass and distance (~M/R2). The discovery of Neptuneeventuallyshowedthenon-universalityofthisrule.

DavorKrajnovićThecontrivanceofNeptune

13

BOX3:ThefailedattemptTheonlyobservatorytotakeLeVerrier'sinitialpredictionseriouslyandmountasystematicsearchtofindthenewplanetwastheCambridgeObservatoryunderdirectorship of James Challis (1803 -1882). The spiritus movens of the searchwas, however, Geroge Biddel Airy (1801 - 1892), Astronomer Royal, who gotconvincedthatthereindeedcouldbeaplanethavingseenbothLeVerrier'sandAdams'predictions.HepushedChallistodothesearch,proposedamethodandtheareaofthesearcharoundLeVerrier'sprediction,andsenthelpinformofanassistant observer from the Royal Greenwich Observatory. The role of JohnCouch Adams (1819 - 1892) for the search was crucial. Not only did he firstpredict the existence of a perturbing planet in 1845, but during the search heprovidedseveralotherpossiblelocationsoftheplanet.Unfortunately,theyweremostlyinconsistentwitheachother,swingingsome20degreesandsendingthesearch inwrongdirections (Rawlins1992).Challis' search isalso infamous forhavingobservedNeptunethreetimes,butnotrecognisingitasaplanet.Whenhewas checking the validity of the search method, comparing observationsbetween the nights of 4 and 12 August, he stopped at star number 39, beingsatisfied that the method was working. If he had continued but a bit longer,Challis would have no doubt noticed that the entry number 49 of the 12thchangeditspositionsincethe4th.TheCambridgesearchwasessentiallyatotalfailure,andinthepost-discoveryassessmenttwolegendswereborn.ThefirstonerelatestothefactthatChallislackedBremiker'sHoraXXIchartthatGalleandd'ArrestusedattheBerlinObservatory.Thisis,ofcourse,true,butitisremarkable thatChallishadHoraXXII chart,adjacentandpartiallyoverlappingthemapinBerlin.AsKollerstorm(2006a)noticed,duringAugustNeptunewasonthemapChallishad.TheotherlegendisrelatedtothefactthatChallistoldanassistanttonotenexttoanentryinthelogbook:"Thelastoneseemedtohaveadisc".Thiswasindeed,asChallislaterfoundout,Neptuneandnotastar.Thefirstpart of the note "The last one" was crossed over, probably post-discovery,becauseChallisneverstoppedhistelescopetoverifytheclaim,eventhoughhewasbythenawarethatLeVerrieradvocatedlookingforadisc.The Neptune affair had profound implications on the careers of the mainparticipants. It completely overshadowedAiry's and Challis'work, but createdfrom Adams a star. The re-assessment of the British part in the discovery ofNeptune, however, paints quite a different picture, especially of Airy and hiscrucialroleinbothestablishingthesearchfortheplanetandbuildingtheBritishclaimforco-discovery(Kollerstrom2006a).Table1.Pre-discoverysightingsofNeptune*Dateofobservation Observer Discoverer28Dec1608&27Jan1609 G.Galilei KowalandDrake(1980)08and10May1795 M.Lalande S.C.Walker,A.C.Petersen,F.Mauvais(1847)25Oct1845 J.Lamont J.Hind(1850)04and12Aug1846 J.Challis J.Challis(1846)7and11Sept1846 J.Lamont J.Hind(1850)*DatatakenfromRawlins(1992)

DavorKrajnovićThecontrivanceofNeptune

14

Table2.OrbitalelementsofNeptune*orbit LeVerrier Adams Walker Neptunesemi-majoraxis[AU]

36.15 37.25 30.25 30.11

discoverydistance[AU]

33 32 - -

eccentricity 0.10761 0.12062 0.00884 0.009456orbitalperiod[yr]

217.4 227.3 166.4 164.8

mass[MSUN] 0.00011 0.00015 0.000067 0.0000515*Comparisonofpre-andpost-discoveryorbitalelements.ForLeVerrier,AdamsandWalkerelementsdataaretakenfromGrosser(1962),andthediscoverydistancesfromhttp://www.dioi.org/kn/neptune/witihin.htm.Table3.ComparisonofthefitsoftheLaietal.(1980)andinthiswork. γ β1 β2 β3 β4Laietal. 890" -18.1" -45.4" 841" 76.8"Thiswork 550.36" -8.48" -13.59" 504.63" 33.25"Figure 2. Orbits of Neptune.A schematic description of the orbits of Uranusand Neptune and the predictions by Le Verrier and Adams. Note differenteccentricitiesinthepredictedorbits,theirmutualsimilaritiesandtheapproachtothetrueorbitofNeptunearoundthetimeofdiscovery.(FromDanjon1946).

DavorKrajnovićThecontrivanceofNeptune

15

BOX4Namingtheplanet*FindingthenameforNeptunewasextremelyquick,butagreeingonusingit,asalmost anything in the story of its discovery, was a scandalous affair (e.g.Kollerstrom 2009). In the letter announcing the discovery of the predictedplanet,Galle,assumingthathecouldputforwardanameasapersonwhofoundit, suggested the name "Janus", the Roman god of beginnings and passage. LeVerrier, who in his announcement of the discovery in the French newspapersalready suggested "Neptune", immediately rejected Galle's suggestion, sayingthatthenamewaschosenbytheBureaudesLongitudes,thelatteractuallynotbeingtrue.Inthevariousannouncementsthatfollowedacrossthecontinent,liketheoneinBritainbyJosephHindinTheTimes,theplanetwasoftencalled"LeVerrier'splanet".TherealstormwasstartedbyawrittensuggestionbyChallisand Adams in the Athenaeum the planet should be called "Oceanus". J. Hindconsideredthisanunfortunatechoicewriting"itisnomorelikelytosucceedwiththe French (who have the only right to name it) than if it had been dubbed'Wellington'".Indeed,thechoiceupsettheFrench,andAragoproclaimedthathewillalwayscallit"LeVerrier"(andUranus"Herschel").LeVerrierfoundhimselfin an awkward situation of suggesting one name, but using the one Aragoproclaimed. Sir John Herschel proposed a few other mythological names:"Demogorgon", "Minerva" and "Hyperion". "Neptune", however, stuck in theminds ofmost continental astronomers and Airy adopted it in early 1847. Hemight have been following the reasoning of the president of the RAS, CaptainW.H.Smyth,whoforgettingthataGermandiddiscoverbothUranusandNeptunewrote:"Idon'tquitelikethisproposedchangeinthenomenclatureofthePlanets,for mythology is neutral ground. Herschel is a good name enough. Le VerriersomehoworothersuggeststheideaofaFabriquant&isthereforenotsogood.Butjust thinkhowawkward itwouldbe if thenextplanet shouldbediscoveredbyaGerman:byaBugge,aFunk,oryourhirsuite friendBoguslawski!".Thechoiceofthemythologicalnamehadoneimportantconsequence, it finallyconvincedtheeditors of the Nautical Almanac to adopt the name Uranus, instead of "TheGeorgian".*Quotesaretakenfromhttp://www.dioi.org/kn/neptune/corr.htm

BOX5:Thediscoverers

Le Verrier found Neptune "with the point of his pen", but it was Galle andd'Arrestwhoidentifieditinatelescope.JeanJosephUrbainLeVerrier(1811-1877)wasborninSaint-Lô,Normandy,andstartedasachemist,butgotapositionofassistantprofessorofastronomyatthe École Polytechnique, switching his interests to celestial mechanics. Heworkedon thestabilityof theSolarSystemandorbitofMercurybeforeArago

DavorKrajnovićThecontrivanceofNeptune

16

sawinhimtherightpersontotacklethemotionofUranus.AfterthediscoveryofNeptune, he returned to the Mercury problem, and, not willing to give up onNewtoniangravity,predictedtheexistenceofanotherplanetclosetotheSun,orat least a belt of smaller bodies, within Mercury's orbit. In 1859 an amateurastronomerE.Lescarbaultannouncedasightingofsuchaplanet;itwasquicklycalledVulcanbythepress,butwasneverseenagain.ForMercury,itwasthelawof gravity that needed adjustments, as Albert Einstein showed in 1915. LeVerrierservedasadirectoroftheParisObservatory,untilhewasfiredforrashtreatmentofhisassistants,butwasreinstatedafterthefollowingdirectordied.Le Verrier died on 31. anniversary of the discovery of Neptune at the ParisObservatory.Johann Gottfried Galle (1812 - 1910) was born in Pabsthaus, about 100kmsouth of Berlin. He went to a gymnasium in Wittenberg and attended theuniversity in Berlin. Hewas a gymnasium teacher, before getting hired as thefirst employee (assistant to the director) of the new Berlin Observatory. HediscoveredtheCringofSaturn,butbecamefamouswiththediscoveryofthreecometsinconsecutivemonthsin1839-1840(Wattenberg1963).Forawhilehewas considered as a suitable successor of Friedrich Bessel at the KöningsbergObservatory,buteventuallymovedtoBreslau(Wroclaw)as thedirectorof theobservatoryandprofessorofmathematics.In1872heproposedanewmethodof measuring the solar parallax using asteroids and organised a world wideobservations of Flora's transit. Galle died in Potsdam, a month past his 98birthday.Heinrich Louis d'Arrest (1822 - 1875)was born in Berlin where he studiedmathematics and eventually joined theBerlinObservatory, sleeping in an atticroom.In1848hemovedtotheLeipzigObservatory,wherehe laterbecameanadjunctprofessorattheuniversity,atitlehereceivedinreturnfornottakingapostinWashington.In1852d'ArrestmovedtoCopenhagenastheprofessorofAstronomyandheadoftheobservatory.d'Arrestdiscoveredseveralcometsandanasteroid(76)Freia. InCopenhagenhestartedworkingonnebulae includingthe external galaxies (especially in the Coma Cluster). d'Arrest died inCopenhagen.Box6:ExplainingUranus'motion.Wheninfluencesofallknownplanetsweretaken out, Uranus showed a notable discrepancy between the predicted andobserved position, Δϕ. Figure 1 shows the heliocentric longitude data pointssimilartothoseusedbyLeVerrierandAdamsintheircalculations(aspresentedinLaietal.1990).Thelineisthesolutionoftheforwardmodel,whichtakesintoaccounttheknownorbitalelementsofNeptuneandUranus,andisgivenbythefollowingequation(eq.19ofLaietal.):

€

Δφ = −γ sin 2 ΩU −ΩN( )τ[ ] + β1 ΩU −ΩN( )τ + β2 + β3 sin ΩUτ( ) + β4 cos ΩUτ( ) whereΩUandΩNareangularvelocitiesofUranusandNeptune,respectively,andτ=t-t0isthetimewithrespecttotheyearofconjunction(t0=1822).Thefirsttermdescribes theperturbation onUranusdue toNeptune'smass and radius,whilethelastfourtermsdescribethedifferencebetweentwonearbyKeplerianorbitsofUranusandNeptune.Figure1alsoshowsanewfitof theequationtothe data, with somewhat different results to Lai et al. (see Table 3), but thetrendsarethesame.

DavorKrajnovićThecontrivanceofNeptune

17

REFFERENCESAdams,J.C,1846a,MNRAS,6,20Adams,J.C.,1846b,MNRAS,7,149Adams,J.C.,1875,MNRAS,35,265Airy,G.B.,1838,AN,15,217Airy,G.B.,1846,MNRAS,7,121Batygin,K.&Brown,M.E.,AJ,151,22Challis,J.,1846a,MNRAS,7,145Challis,J.,1846b,LettertoTheAthenaeum,no990,Oct17,p.1069.Herschel,J.,1846,LettertoTheAthenaeum,no.988,Oct3,p.1019Chapman,A.,1988,JHA,19,21Chapman,A.,2016,A&G,57b2.10Danjon,A.,1946,C&T,62,369Dick,W.R.,1985,TartuAstr.Obs.TeatedNr.,75,5Dick,W.R.,1986,Sterne62,5Dreyer,J.L.E.,1882,Copernicus,2,63Dreyer,J.,L.E.,1876,Vierteljahrsschr.Astron.Ges.11,1Encke,J.,1846,AN,25,49Galle,J.G.1878,AN,89,349Galle,J.G.1882,AN,101,219Grosser,M.1962,"ThediscoveryofNeptune",HarvardUniversityPress,CamGuinan,Harris&Maloney,1982,BAAS,14,658Herschel,J.,1846,LettertoAthenaeum988,1019Hind,J.R.,1850,MNRAS,11,11Hubbel,J.G&Smith,R.W.,1992,JHA,23,261Kollerstrom,N.2003,A&G,44,23Kollerstrom,N.2006a,HisSc,44,349Kollerstrom,N.2006b,JAHH,9,151Kollerstrom,N.2009,JAHH,12,66Kowal,C.T.&Drake,S.,1980,Natur287,311Lai,H.M.,Lam,C.C.&Young,K,1990,AmJPh,58,946LeVerrier,U.J.J.1845,Comptesrendus,21,1050LeVerrier,U.J.J.1846a,Comptesrendus,22,907LeVerrier,U.J.J.1846b,Comptesrendus,23,428Rawlins,D.,1992,Dio,2,3Sheehan,W.,Kollerstrom,N.,&Waff.B.,2004,SciAm,291(6),92Sheehan,W.,&Thurber,S.,2007,NotesRec.R.Soc.,61,285Smart,W.M.,1946a,Natur,158,648Smart,W.M.,1946b,Natur,158,830Standage,T.2000,"TheNeptuneFile",Walker&Comany,NewYorkSmith,R.W.,1989,ISIS,80,395Turner,H.H.1911,MNRAS,71,275Trujillo,C.A,&Sheppard,S.S.2014,Natur,507,471Wattenberg,D.1963,"JohannGottfridGalle",JohannAmbrosiusBarth,Leipzig