Goddard Space Flight Center

Geodesy, Earth Science and 61A in the OSIRIS-Rex Asteroid Sample Return Mission

Dave Rowlands Terry Sabaka

Dave Rubincam Joseph Nicholas

Goddard Space Flight Center

•  OSIRIS-RExisaSampleRETURNMission

•  Naviga8onisthemostimportantthingforOREXmissionsuccess"SPACENAVIGATORS:TellingRocketScien9stswheretogosince1957.”Ourcode595navigators:MikeMoreau,KennyGetzandanner,DolanHighsmith

•  HowdoyounavigatetotheasteroidandbacktoEarth?

•  Onceinorbitaroundtheasteroid(Bennu),howdoyou(soRly)touchdown

toapredeterminedloca8on(TouchandGo…TAG)?•  Naviga8ondependsongeode8cobserva8onsandtheaccuratedetermina8onof

geode8cparameters(GEODYN)

GeodesyandNaviga8on

Goddard Space Flight Center

•  DeepSpaceOrbitDetermina8on

•  Determinetheposi8onandvelocityofOREXspacecraRatoneini8al"arc"epoch

•  Geode8cObserva8onsforDeepSpaceOrbitDetermina8on(ModeledinGEODYN)

•  LineofSightfromEarthtoOREXsatellite(distanceandvelocitymagnitude):

•  Range-roundtrip8meofflightfromasta8ontoandfromthesatellite

•  Doppler-averagerangerate

•  Posi8onofOREXOnSky

•  DeltaDOR:[Satellite!Sta8on#1wayrange]–[Satellite!Sta8on#2wayrange]

(Withclockcorrec8onfromstellar(quasar)VLBI)

GecngtoBennuandBacktoEarth

Goddard Space Flight Center

C*(Rela8veClockError)

SatellitePor8onofDeltaDORandErrorSources

2cmcanbe200minposi8onat1AUEOPErrors

AtmosphereErrors

ClockErrors

CorrectedbystellarVLBIpor8onoftheDDOR(15minutesbeforeandaRerthesatellitepor8on)

Goddard Space Flight Center

StellarVLBIPor8onofDeltaDOR(PureEarthScience)

61Ahasa“stellar”VLBIGroupProvidesEOPatcri8caljuncturesofplanetarymissionsProvidedouralgorithmsforthispor8onofDeltaDOR

Thispor8onofDeltaDORes8matesclockerrors

Goddard Space Flight Center

•  Determinetheposi8onandvelocityofBennuatoneini8al"arc"epoch

•  CameraObserva8onswhileSatelliteisapproachingBennu

•  SpacecraRposi8oniswelldetermined.Bennuseenasapointsource

Geode8cObserva8onsforBennuAsteroidEphemerisImprovement

DSN

Camera

Goddard Space Flight Center

•  RangeandDopplerobserva8onsonOREXwhenOREXisinorbitaroundBennu

DSN

Gravity

Geode8cObserva8onsforBennuAsteroidEphemerisImprovement

Goddard Space Flight Center

TheOSIRIS-RexLaserAl8meter(OLA)AScanningLidarthattakes3-Dpicturesin150secondscans

EachScan:•  150seconds@20,000Hz•  80mx80mswath•  5cmspots

Goddard Space Flight Center

•  OLAEnablesthes8tchingtogetherofaDEMfromthepointcloudsofeachscan

•  Sameideawithcamerasbutmorecomplicatedprocess(Stereophotoclinometry)

•  5Cameras(3science)2NavNACCam•  30cm/pixel

•  DEMsfrombothmethodsarerela8velyfreefromeffectsoforbitandpoin8ngerror

DigitalEleva8onModels(DEM)fromOLAandCameras

Goddard Space Flight Center

•  Providesstrongobserva8onalconstraintsrela8ngsatellitetoBennufixedframe

•  HoweverDEMerrorsdoaffectthemeasurementmodeling

•  OurGeodesyGrouphasthelongestexperienceusinglaseral8metryinorbitdetermina8onandgeode8cparameteres8ma8on(SLA,ICESat,ICESat-2)

DEMsEnableAl8meterRangeModeling

ModeledRangefromBennuRadiusandSatellitePosi8on

RadiusofBennufromDEM

Goddard Space Flight Center

•  CamerabasedDEMsyield"landmark"planetfixedcoordinates(recognizablepointsources)

•  LandmarkraytracedfromBennufixedcoordinatesthroughlenstolineandpixelcoordinates

DEMsEnableLandmarkModeling(CameraObserva8ons)

•  Providesstrongobserva8onalconstraintisrela8ngsatellitetoBennufixedframe

•  HoweverDEMerrorsdoaffectthemeasurementmodeling

(x,y,z)oflandmark

cameraLineandPixeloflandmark

Goddard Space Flight Center

Greatfororbit,gravityandspinstateevolu8onparameters

Al8meterCrossovers(differencedal8meterobserva8ons)

Thisdistanceisknown&providesaconstraint

OverlappingScansarematchedoffline

Goddard Space Flight Center

•  Twocameraimagesseesamelandmark

•  Raystracedfromlineandpixelineachcamera

•  Raysshouldintersect

CameraCrossovers

Greatfororbit,gravityandspinstateevolu8onparameters

Landmark(coordinatesdon’tmauer)

cameraEpoch1

Epoch2

Goddard Space Flight Center

Geode8cParametersatBennurequiredforTAGPart1:ParametersforDEM

RadiusofBennufromDEMfromCenterofFigure(CoF)

•  OffsetofDEMoriginfromBennucenterofmass(al8metryandCamera)(LongExperiencein61AfromEarthScience)

•  DEMScale(al8meterranges)•  LandmarkCoordinates(cameradata)

SatellitecoordinatesfromCenterofMass(CoM)

Offset

Goddard Space Flight Center

•  GravityField(allmeasurementtypes)

•  Satellitetrajectory

•  BennuSpin/Orienta8onState(allmeasurementtypes)•  ForTAGweneedtoconnecttheBennubodytothe

iner8alframe•  Thismeansconnec8ngBennuorienta8ontoiner8al

J2000frame

Geode8cParametersatBennurequiredforTAGPart2:OtherParameters

Goddard Space Flight Center

Orienta8onofBennu

Z

X

Y

Weneedtodeterminetheorienta8onoftheBennubody-fixedaxesintheJ2000frame

RAandDecofbodyfixedNorthPole

W:angulardistanceofprimemeridianfrominer8alXaxis

ω3

ω1

ω2

Goddard Space Flight Center

Bestcasescenario:RA,DECofpoleconstant,However,Bennumayhavewobble.WhatisWobble?Twowaystolookatit:(1)angularmo8onaboutallaxes(2)spinaxischangesloca8ononthesurfaceofBennuEitherwayRA,DECandWwillhaveperiodicmo8onPeriodwillbelessthanmeanspinratePerioddependsonmomentsofiner8aofBennuNeedadynamicmodelthatwillallowustocomputea"trajectory"ofRA,DEC,W

DeterminingOrienta8onParameters

W

constant(likeaspinningglobeonapedestal)

Goddard Space Flight Center

EulerRota9onalEqua9onsofMo9on

Rota%ngBody-FixedFrame:

!R(t) = [R(t)ω(t)]×R(t)!ω(t) =M −1[T (t)−ω(t)×Mω(t)]

PrincipalAxisFrame:

!ω1!ω2!ω3

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟=

[T1 − (M3 −M2 )ω2ω3] /M1[T2 − (M1 −M3)ω3ω1] /M2[T3 − (M2 −M1)ω1ω2 ] /M3

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟, M =

M1 0 00 M2 00 0 M3

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

R : 3x3 matrix whose columns are body-fixed axes in inertial frame

ω j : Angular velocity about j-th axis, ω = ω1 ω2 ω3( )T

M : 3x3 matrix of moments of inertia of body

Tj : Torque on j-th axis, T = T1 T2 T3( )T

Goddard Space Flight Center

Ini8alizingthe"trajectory"-Ini8alstate:[-Ini8alvalues[RA0,Dec0andW0]yieldini8alvaluesforR(t)(unitvectorsforbodyfixedaxisinJ2000)att=t0-Ini8alvalues-Withini8alvaluesofR(t)andω1,ω2,ω3att=t0andwithmomentsofiner8a,integra8oncanbegin-Integra8onyieldsR(t)whichyieldsRA,DECandWatanyepoch

RA,DecandW“trajectory”computa8on

RA0, Dec0, W0, RA0 Dec0, W0

RA0, Dec0, and W0

yieldω1,ω2andω3

]

att=t0

Goddard Space Flight Center

Wedevelopedcompanionvaria8onalequa8ons.Theseyieldpar8alsof[RA,Dec,W]atanyepochwithrespectto12parameters(6ini8alstateparametersand6moments)36varia8onalpar8alderiva8vesfor12es8matedparameters[RA,Dec,W]trajectoryneededtomodelmeasurements(measurementsareafunc8onof[RA,Dec,W])Sowecanobtainpar8alsofmeasurementsWRT12es8matedorienta8onparameters

RA,DecandW“trajectory”refinement

Goddard Space Flight Center

Goal:DeterminehowwellBennufixedcoordinatesofsatellitecanbepredictedinthecaseBennuhasawobbleSimulate108hoursofOREXinorbitaroundBennuwitha1degreewobble("Truth"trajectoryforBennuorienta8onandOREXorbit)Simulatetrackingdatafor72hoursusing"truth"OREXorbitandBennuorienta8ontrajectoriesCamera(landmarkandlandmarkcrossovers)~1000obsAl8meter(rangesandcrossovers)~200,000obsDSNDopplerandRange~1000obsRecoverOREXorbitandBennuorienta8onparametersusing72hoursofdataErrorsinmodelsandsimulatedobserva8onsincludedforrealismComparerecoveredOREXBennu-fixedtrajectoryin36hoursaRersolu8onRecoveredOREXtrajectorymatches"truth"onBennubodyatthe1meterlevel

GEODYNSimula8ontoTestRecoveryofOrienta8on;1degreeWobbleCase(Is1MeterGeoloca8onPossible?)