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F.Bagenal&R.J.Wilson,LASP–UofColorado 1

JupiterCoordinateSystems

IntroductionPurpose: ThisdocumentpullstogethervariouscoordinatesystemsthatmightbeusefulfortheJunoteamtouseatJupiter.Differentteamshavetheirownpreferredsystems toworkwith.Thepurposehere isnot to suggest teamschangeanything.The goal is to help the larger Juno team become familiar with the full range ofcoordinatesystemstheymaycomeacross.Furthermore,theJPLNAIFteamprovidenavigation tools – specifically SPICE – for the Juno project and we have tried torelatethenamesusedbySPICEtothesesystems.SixJunoSystems.WedescribethesixmaincoordinatesystemsofpotentialusebytheJunomission.# CoordinateSystem JunoFrame

SPICEnameOrigin Notes

1 JupiterSystemIII S3RH->IAU_JUPITERS3LH->noSPICEframe Jupiter InJupiter’srotating

frame.2 JupiterMagnetic JUNO_JMAG_VIP4 Jupiter BasedontheVIP4

magneticfieldmodel.3 Jupiter-De-Spun-Sun JUNO_JSS Jupiter Similarto1exceptnot

rotating.4

Jupiter-Sun-Orbit JUNO_JSO JupiterBasedondirectiontotheSunandJupiter’sorbitalmotion.

5JupiterHeliospheric JUNO_JH Jupiter

Forsolarwindintervalsonly.BasedontheSun’s

spinvector.6 JunoSunEquator

RadialTangentialNormal

JUNO_SUN_EQU_RTN JunoForsolarwindintervalsonly.BasedontheSun’s

spinvector.Notes:

1. AllthesesystemsareJupiter-centeredexcept#6JUNO_SUN_EQN_RTNthatiscenteredonthespacecraft.

2. The#1traditionalSystemIIILongitudethathasthelongitudeofasemi-stationaryobserver(suchasatEarth)increasingwithtime,isaleft-handedsystem.TheRHsystemhaslongitudedecreasingwithtime.

3. SPICEonlydoesright-handedcoordinates;thereforecoordinatesusedwith

SPICEshouldberighthanded.

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F.Bagenal&R.J.Wilson,LASP–UofColorado 2

4. SPICEkernelpck00010.tpcmustbeusedforallJunoSPICEwork.ThishasJovianradiusas71492km,spinperiodat9h55m29.711sandalsodefinestheJupiterpole(basedontheIAU2009report).UseofthisspecifickernelisessentialforJupiterSystemIIIcalculations.

5. Forother,oldersystems,seetheendofthedocument.

6. Noapparentpositions(aberrationcorrected)areusedinanyoftheseco-

ordinatesystemdefinitions.Thismakesiteasiertotransformbetweensystems.(TheapparentpositionoftheSunandthegeometricpositiondifferbyunder0.002°atJupiter,orinlocaltimeisunder0.6seconds;howevertheSPICElocalsolartimecommandroundsseconds,hencenopracticaleffecttowithinuncertaintyoftheSPICEcommand:et2lst with type = ‘PLANETOCENTRIC’.)

JupiterRadius(RJ) First we need to clarify the fiducial value of the radius of Jupiter. Dessler(1983) declareduse of the valueRJ= 71,400 km in the appendix ofPhysicsof theJovian Magnetosphere. A full description of the planetary parameters andcoordinate systems is provided in Appendix 2 of Jupiter: Planet, Satellites,Magnetosphere (Bagenal, Dowling, McKinnon, (eds), 2004) where the equatorialradiusatthe1-barlevelisgivenasRJ=71,492±4km(Lindaletal.1981).TheJPLnavigationteamthatprovidesJunotrajectoryinformationusesRJ=71492km,thevalue we propose for all Juno activities throughout the mission. Note thatbecauseoftherapidrotationoftheplanet,thepolarradiusofJupiter ismuchless(66,854km).SpinPeriod Jupiter has a spin period of 9h 55m 29.711s = 9.92492 hours (or angularvelocityof1.76x10-4rad/s=870.536°/day).ThisisthecurrentIAUvalue.

Note thatHigginset al. (1996,1997)proposed,basedon35yearsof radioobservationsof Jupiter, thattherotationrateoftheplanet interiormaybe~25msshorter thantheSystemIII (1965)rotationrate(seealsodiscussion inrelation tomagneticfieldmodelsbyRusselletal.2001;Yu&Russell,2009;Hessetal.2011).A25 ms shorter spin period amounts to just 0.2°/yr which is negligible over theduration of the Juno mission but is significant for comparing Voyager and Junoepochs. Since this is a minimal change in the rotation rate the IAU and the Junoproject have decided not to change the official System III rotation rate to limitconfusionbetweensystemsandtoalloweasycomparisonofdatasetsfromdifferentepochs.

Please note that the rotation rate (9.92425 hr) stated in appendix of theBagenaletal.(2004)Jupiterbookisincorrect.

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F.Bagenal&R.J.Wilson,LASP–UofColorado 3

JupiterPole Thejovianpoleisdefinedfromthe2009IAUreport.KeyJupiterparametersareinSPICEkernel“pck00010.tpc”:BODY599_RADII = (71492 71492 66854 ) BODY599_PM = ( 284.95 870.5360000 0.) BODY599_POLE_RA = ( 268.056595 -0.006499 0.) BODY599_POLE_DEC = ( 64.495303 0.002413 0.)

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F.Bagenal&R.J.Wilson,LASP–UofColorado 4

(1)JupiterSystemIII(S3LH,S3RH)

Figure 1a - Jupiter System III (1965) coordinates (S3LH). The Z-axis is defined by the spin axis of Jupiter. The X-axis is defined by 0° latitude on the System III longitude λIII=0° (prime meridian). The Y-axis completes the orthogonal left-handed system. Latitude (θIII) is defined from the equator. X=0°latitude,PrimeMeridianY=XxZZ=Jupiterspinaxis

Figure 1b – Right-handed System III. This coordinate system has the same basis as the left-handed System III except that longitude is (λRH) decreases with time and co-latitude (θRH) is used. X=90°colatitude,PrimeMeridianY=ZxXZ=JupiterspinaxisλRH=360°-λIII

ThissystemrotateswiththeplanetatthesiderealSystemIII(1965)spinperiodof9h 55m 29.711s = 9.92492 hours (or angular velocity of 1.76 x 10-4 rad/s =870.536°/day). This spin period was originally based on ground-based radioobservationsandthelongitude(λIII)wasdefinedtoincreasewithtime,asobservedfrom Earth. The problem with this system is that it is a left-handed coordinatesystem (whichwe label S3LH). Sincemany prefer right-hand coordinate systems,wealsodefineaRHsystem(S3RH)where the longitude(λRH=360°-λIII)decreaseswith time as viewed from Earth. These two variations on jovian System III areshown above. The location of the Prime Meridian (the meridian plane in bothsystems and where both longitudes are zero) is defined in terms of the CentralMeridianLongitude(i.e.Earth-Jupitervector)onaspecificdatein1965.S3LHuseslatitude(θIII)whileS3RHusescolatitude(θRH).

Z"

X"

Y"

λIII"

θIII"

θIII"is"la,tude"S3LH"

S3RH"

X"

Y"

λRH"

θRH"

θRH"is"cola,tude"Z"

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(2)JupiterMagnetic(JUNO_JMAG_VIP4)

Figure 2 – Jupiter magnetic coordinates. This system rotates with Jupiter but has the Z-axis aligned with the magnetic dipole, M. The X-axis is aligned with the intersection of the magnetic and geographic equators at λIII=290.8° or λRH=69.2° X = 69.2° from Prime Meridian (where λIII=λRH=0) Y = Z x X Z = Jupiter dipole axis

This system (above) is the System III (RH) but is tilted by the 9.5° of the dipoleapproximation to the magnetic field of Jupiter, tilted towards λIII=200.8° orλRH=159.2°.

ThistiltisbasedontheVIP4model(Connerneyetal.1998).Themagneticlongitudeisdefinedwithrespecttothemeridianwherethemagneticandgeographicequatorscross (whereθIII =0° andθRH =θMAG=90°) atλIII=290.8° orλRH=69.2°. Sincemostmodels tend to work in right-handed coordinates, we propose a right-handedmagneticsystemforJuno.

Not to be confused with… Jupiter SolarMagnetospheric (JSM) coordinates usedduringtheGalileomission,whichusedadipoleatiltof9.6°andλIII=202°basedonthe O4 model of Connerney (1981). For further info on JSM, see theDATA_SET_DESCRIPTION of PDS data set GO-J-POS-6-SC-TRAJ-JUP-COORDS-V1.0 :https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=GO-J-POS-6-SC-TRAJ-JUP-COORDS-V1.0InournewnamingconventionwewouldcallthisJMAG_O4.ComparisonsofdipoleapproximationsfordifferentmagneticmodelsareshowninAppendix2oftheJupiterbook(Bagenaletal.2004)andinConnerneyetal.(1998).ThefullrangeofinternalmagneticfieldmodelsisreviewedbyConnerney(2007)aswellasevaluatedinthelightofpossiblesecularvariationbyRidley&Horne(2016).Note:AllEarthdipoleMAGSPICEframeshave+Yinthedirectionwherethemagneticandspinequatorsalign.Intheabovesystemwehave+Xinthisdirection.DipoleMAGframesforother(butnotall)planetsalsotendtouseEarthdipoledefinitionswith+Yinthedirectionoftheintersectionofmagneticandspinequators.

X"

Y"

Z"

λmag"

θmag"

9.5°"

M JMAG_VIP4" θmag"is"cola,tude"

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F.Bagenal&R.J.Wilson,LASP–UofColorado 6

(3)Jupiter-De-Spun-Sun(JUNO_JSS)

Figure3–ThissystemhastheZ-axisalignedwithJupiter’sspinaxisbutdoesnotspinwiththeplanet.RJS=unitvectorofJupitertoSunZ=JOmega=unitvectorofJupiterspinaxisY=ZxRJSX=YxZ

JSSexpressedinradialdistance,latitudeandlocaltime

Analternative toCartesian (x,y,z) coordinates, the JSSsystemcanbeexpressed insphericalcoordinatesinradialdistance,latitudeandlocaltime(R,Lat,LonorLT) Radialdistanceisthemagnitude:R=(x2+y2+z2)1/2 Latitudeisgivenbytrigonometry:Lat=arcsin(z/R)*180/π (withthe180/πfactortogofromradiansintodegrees.)LocaltimeasananglewithrespecttotheSun(orsolarlongitude,Lon)wouldbethefour quadrant inverse tangent of y and x (i.e., arctan(y,x) in code), which can beexpressedindegrees Lon=arctan(y,x)*180/π).Iftheangleisnegativethen360°isaddedsothat0≤longitude<360degrees.LocalTimehasunitsofhours (24hours to360degrees) and translates longitudesuchthatnoon(12hours)localtimewouldbe0degreeslongitude,dusk(18hours)localtimewouldbe90degreeslongitude,midnight(00hours)localtimewouldbe180 degrees longitude, and dawn (06 hours) local time would be 270 degreeslongitude.

LocalTime=LT=[(Lon+180degrees)*24/360]MOD24LocalTime=LT=[(arctan(y,x)+π)*12/π]MOD24

TheSPICEcommandet2lst (with type = ‘PLANETOCENTRIC’) canalsobeused tocalculate local time, however it does include an aberration correction on the Sunposition(abcorr = ‘LT+S’).Howeverthedifferenceis<0.6sLTatJupiterandthecodereturnswholesecondsonly,sopracticallyisequivalenttousingnocorrection.

JSS"

X"

Z"

Y"

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(4)Jupiter-Sun-Orbit(JUNO_JSO)

Figure4-alignstheX-axiswiththeJupiter-Sunvector.SPICEdescribeitasX=JupSunPos/Y=JupSunVelVplanet=unitvectorofJupiter’smotionVmotion=-Vplanet=Sun’smotionwheninJupiterframe.RJS=unitvectorofJupitertoSunX=RJSY=Vmotion=-VplanetZ=X×Y

ThisissimilartoEarth’sGeocentricSolarEcliptic(GSE)system,andthatsinceVplanetisnolongerintheXYplanethen+Zisnoteclipticnorth.Note:

1) Jupiter’sorbitistiltedby1.303°totheeclipticplaneandby6.09°totheSun’sequator.

2) Jupiter’sspinaxisistiltedby3.13°withrespecttoitsorbitalplane.

JSO"

X"

Z"

Y"

Vmo,on"

="KVplanet""//"to"Vmo,on"

Vplanet"

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(5)JupiterHeliospheric(JUNO_JH)SinceJunomeasuressolarwindconditionssurroundingJupiter’smagnetosphereweneed a coordinate system that is based on heliospheric properties. This is theheliocentricsystemcenteredonJupiter.ForotherheliosphericcoordinatesystemsseeHapgood(1992)andFranzandHarper(2002).

Figure5-ThissystemisJupiter-centeredandtheX-axisistheJupiter-Sunvector,theY-axisisthesolarequator,andtheZ-axiscompletesthesystem.RJS=unitvectorofJupitertoSunlineSOmega=unitvectoroftheSun’sspinaxis=Z’infigureX=RJSZ=SOmegaY=Z×X

Note:

1) Jupiter’sorbitistiltedby6.09°totheSun’sequator(whichisperpendiculartotheSun’sspinaxis,obviously).TheSun’sequatorialspinperiodis25days).

2) WithJupiter’sspinaxisbeingtiltedby3.13°withrespecttoitsorbitalplane,thenthespinaxesofJupiterandtheSuncanbeseparatedbyupto9.22°.

X"

Z"

Y"Z’"

JH"

Y’"X’"

XY"plane"is"the"Solar"equator"plane,"Z"parallel"to"Z’."

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F.Bagenal&R.J.Wilson,LASP–UofColorado 9

(6)JunoSunEquatorRTN(JUNO_SUN_EQU_RTN)(NotJRTNwhichcouldbeconfusedwithJupiter_RTN,thatwouldhaveJupiterattheoriginandtheRvectorswouldbethealongtheJupiter-Sunline.)

Figure6–ThissystemiscenteredwithJunoattheoriginandtherelativeobjectistheSun.RJuno2S=unitvectorofJunotoSunlineRS2Juno=-RJuno2S=unitvectorofSuntoJunolineSOmega=unitvectoroftheSun’sspinaxis=Z’infigureX=R=RS2Juno=-RJuno2SY=T=SOmega×R=SOmega×XZ=N=R×T=X×Y

Callingaco-ordinatesystemRTNisnotsufficient-moreinformationisrequiredtodefine it, predominantlywhere the origin is andwhat object your RTN system isrelatedto.FortheJunomission,JUNO_RTNiscenteredwithJunoattheoriginandtherelativeobjectistheSun–alsoknownasJUNO_SUN_EQU.

The following description of RTN for solar wind missions is quoted from theCOHOWebwebsite:http://omniweb.gsfc.nasa.gov/coho/html/cw_data.html

“COHOWebprovidesaccesstoheliosphericmagneticfield,plasmaandspacecraftpositiondataforeachofmanyspacecraftidentified.”

“TheRTNsystemiscenteredataspacecraftorplanetandorientedwithrespecttothelineconnectingtheSunandspacecraftorplanet.TheR(radial)axisisdirectedradiallyawayfromtheSunthroughthespacecraftorplanet.TheT(tangential)axisisthecrossproductoftheSun'sspinvector(Northdirected)andtheRaxis,i.e.theTaxis is parallel to the solar equatorial plane and is positive in the direction ofplanetaryrotationaroundtheSun.TheN(normal)axiscompletestherighthandedset. TheRTN system is preferable for analyzing solarwind and energetic particledata.”

X=R"Z=N"Y=T"

Z’"

JUNO_SUN_EQU_RTN"

KR"

Origin"at"Juno""

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Othersandoldersystems LocalTime Mission

usedbySubsetofJSS.

JupiterSolarMagnetospheric

JSM Galileo SimilartoJUNO_JMAG_VIP4buttiltandlIIIanglesare

slightlydifferent(tiltof9.6°andλIII=202°,theO4model

parameters).EquivalenttoJUNO_JMAG_O4.

JMAG_O4 JMAG_O4 Proposedname

ProposednameforadipoleMAGframebasedontheO4model.Frameequivalent

toJupiterSolarMagnetospheric.

JupiterSolarEquatorial JSE Galileo EquivalenttoJUNO_JSS.DifferenttootherJSE

(JovicentricSolarEcliptic). JovicentricSolarEcliptic

JSE GalileoEPDteam

members

SimilartoJUNO_JSO,butusesaberrationcorrected

positions.DifferenttootherJSE

(JupiterSolarEquatorial).

JupiterSolarEquatorial(JSE)–UsedbyGalileoMission

This JSS co-ordinate system is the sameas Jupiter SolarEquatorial (JSE) thatwasused forGalileo instruments (see theDATA_SET_DESCRIPTION fromPDSdata setGO-J-POS-6-SC-TRAJ-JUP-COORDS-V1.0): https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=GO-J-POS-6-SC-TRAJ-JUP-COORDS-V1.0

ThedescriptionusedfortheJupiterSolarEquatorial(JSE)systemintheabovePDSlinkforGalileo(editsencasedinsquarebrackets):“Local Time angle is the angle (HA) between the observer's ([spacecraft]) sub-Jupiter meridian and the anti-sunward meridian, measured in the[Planetocentric] jovian equatorial plane in the direction of planetary rotation.Localtimeistheconversionofthelocalhourangleintounitsoftimebyusingtheconversionfactorthatequatesonehourtofifteendegreesoflongitude.Magneticlocal time follows the same convention with the difference being that thereferencepole is thedipolemomentvector(M)rather thanthe jovianspinaxis([JOmega]).Localtimevaluesareprovidedhereinunitsofdecimalhours.”

Note:planetocentricequatorialplaneisexpressedinthefigureonthesamepage,soaddedtothistexttoavoidambiguity.

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Donot confuse this ‘Jupiter Solar Equatorial’ (JSE)with ‘Jovicentric Solar Ecliptic’coordinates(JSE)thatwasusedbysomeforGalileoEPDdata.TheJovicentricSolarEclipticcoordinatesareequivalenttoJupiter-Sun-Orbit(JSO)below.IfyouseeJSEitcouldbeJSSorJSO–becareful!

TheJSOco-ordinatesystemhaspreviouslybeenreferredtoJovicentricSolarEclipticcoordinates (JSE) for Galileo EPD (see http://galileo.ftecs.com/handbook/LGA-software/coord-systems.html,whilethetermJSEisusedinPDSEPDbrowseplots,wehavenot located a description of thiswithinPDS as yet).Note that the aboveGalileo EPD webpage confirms use of abcorr = ‘LT+S’ in their SPICEtransformation to Jovicentric Solar Ecliptic. Do not confuse the ‘Jovicentric SolarEcliptic’ (JSE) with ‘Jupiter Solar Equatorial’ coordinates (JSE) that was used forotherGalileowork.IfyouseeJSEitcouldbeJSSorJSO–becareful!

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ReferencesBagenal, F., T. E. Dowling, and W. B. McKinnon (Eds.), Jupiter: Planet, Satellites,

Magnetosphere,CambridgeUniversityPress,2004.Connerney,J.E.P.,ThemagneticfieldofJupiter:Ageneralizedinverseapproach,J.

Geophys.Res.,86,7679-7693,DOI:10.1029/JA086iA09p07679,1981.Connerney, J. E. P.,M.H. Acuna,N. F. Ness, and T. Satoh,Newmodels of Jupiter’s

magnetic field constrained by the Io flux tube footprint, J.Geophys.Res.,103,11,929–11,940,1998.

Connerney, J. E. P., Planetary Magnetism, in Treatise in Geophysics, Volume 10:PlanetsandSatellites,G.Schubert,T.Spohn(eds),Elsevier,Oxford,UK,2007.

Fränz, M., and D. Harper, Heliospheric coordinate systems, Planetary and SpaceScience,50(2),217–233,doi:10.1016/S0032-0633(01)00119-2,2002.

Hapgood,M.A.,Spacephysicscoordinatetransformations-Auserguide,Planetaryand Space Science (ISSN 0032-0633), 40, 711–717, doi:10.1016/0032-0633(92)90012-D,1992.

Hess,S.L.G.,B.Bonfond,P.Zarka,andD.Grodent,ModeloftheJovianmagneticfieldtopology constrained by the Io auroral emissions, J.Geophys.Res.,116, 5217,2011.

Higgins, C. A., T. D. Carr, and F. Reyes, A new determination of Jupiter’s radiorotationperiod,Geophys.Res.Lett.,23,2653–2656,1996.

Higgins,C.A.,T.D.Carr,F.Reyes,W.B.Greenman,andG.R.Lebo,AredefinitionofJupiter’srotationperiod,J.Geophys.Res.,102,22,033–22,042,1997.

Ridley,V.A.,R.Holme,ModelingtheJovianmagneticfieldanditssecularvariationusing all availablemagnetic field observations,Modeling the Jovianmagneticfieldanditssecularvariationusingallavailablemagneticfieldobservations,J.Geophys.Res.Planets,121,doi:10.1002/2015JE004951,2016.

Russell,C.T.,Z.J.Yu,andM.G.Kivelson,TherotationperiodofJupiter,Geophys.Res.Lett.,28,1911–1912,2001.

Yu, Z. J., and C. T. Russell, Rotation period of Jupiter from the observation of itsmagneticfield,Geophys.Res.Lett.,36,20,202,2009.

Joy, S.P., Mafi, J.N., GO JUP POS GLL TRAJECTORY JUPITER CENTEREDCOORDINATESV1.0,GO-J-POS-6-SC-TRAJ-JUP-COORDS-V1.0,NASAPlanetaryDataSystem,2002.