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The Determination Of The R otational State Of C elestial Bodies

scuola di ingegneria aerospaziale dottorato di ricerca in ingegneria aerospaziale XXIV ciclo. The Determination Of The R otational State Of C elestial Bodies. R. Meriggiola Advisor : Prof. Luciano Iess. Roma, 3 Aprile 2012. Planetary Interior Structure Revealed by Spin Dynamics.

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The Determination Of The R otational State Of C elestial Bodies

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  1. scuola di ingegneria aerospaziale dottorato di ricerca in ingegneria aerospaziale XXIV ciclo The DeterminationOfThe Rotational State OfCelestialBodies R. Meriggiola Advisor: Prof. Luciano Iess Roma, 3 Aprile 2012

  2. PlanetaryInteriorStructureRevealedbySpin Dynamics Precession Polarmotion Interior Moment ofInertia obliquity seasonal mass redistribution Chandler’s Wobble free corenutations solid/fluidoutercore Librations eccentricityequatorialbulge determination of rotational state of celestial bodies

  3. RotationalModels (t) - Right Ascension (t) - Declination Standard model Pole Location IAU Model • Precession – nutation terms • Librationsonlyfor Moon precession (sinusoidal) termsincluded Developedmodels ExtendedModel W(t) - Prime Meridian  - Spin Rate Rotation • improvedaccuracy • polarmotionincluded LibrationModels • IAU modifiedversion • Librationsincluded precession (sinusoidal) termsincluded determination of rotational state of celestial bodies

  4. CurrentlyAppliedTechniques Observationof the Earth Radio tracking • opticalastrometricobservations • satellite tracking • laser ranging • GPS • VLBI • Radio tracking of Mars landers • Range/Doppler observables accuracy : 0.001 – 0.005 as accuracy: 0.13 as Ground-based Radar Imaging from orbit • Based on the correlation of receivedspeckles • Margot et al., 2007 Mercury Libration Experiment • Based on repeatedobservations of the sameregion • Magellan (Venus) • Cassini (Titan) • BepiColombo (Mercury) accuracy: 6 as accuracy: 1 - 36 as determination of rotational state of celestial bodies

  5. ImagingFromOrbitTechnique Pattern Matching 105° E 105° E 73° S 73° S Cross-over detection Apparentshift on the surface  = R2 – R1 Rotational RegistrationError pi Parameters Observables LeastSquaresFit A = M(pi,t2)r2,A – M(pi,t1)r1,A …. …. N = M(pi,t2)r2,N – M(pi,t1) r1,N determination of rotational state of celestial bodies

  6. Pattern Matching Menrva Crater on Titan SIFT features (Univ. of Bologna) ImageRegistration - Cassini SAR imagesofTitan determination of rotational state of celestial bodies

  7. Rotational State Determination Software Input Core Output W Matrix Residuals Error budget Rotationalmodel Dr LeastSquares Estimator EstimatedParameters r1, r2 t1, t2 Ancillary Information PartialDerivatives Tiepointinertial direction (r1,r2) Observationepoch (t1,t2) Propagated pole at a referenceepoch • A simulatedobservablesgeneratorwasdevelopedtoperformsimulations • Software validation: extensivesimulations (noiseless, gaussian, systematics) determination of rotational state of celestial bodies

  8. TitanObservedFromCassini Cassini SAR • Cassini RADAR imaging • > 71 Titanflybys • SAR Imager, altimeter, radiometer, scatterometer • HGA diameter: 4 m • SAR imager: 13.78 GHz, • resolution: 0.175  1.4 km Operative sequencefor a Cassini RADAR flyby (Elachiet al., 2005) Titan Atmosphere • N2, Methane dense atmosphere (50% more thanEarth) Surface • icyshellwithliquidhydrocarbonrivers and lakes. Dunes can easilydetected. Surface temperature about 94 K. • hydrologiccyclebased on hydrocarbons SAR false colourimaging of Ligeia Mare determination of rotational state of celestial bodies

  9. Goalsof the Experiment Cassini state 1 Obliquity Stiles et al. 2008:  = 0.3 deg • Occupancyof a Cassini state • MoIfromobliquity • information on the interiorstructure • core-shelldecoupling Laplace pole Orbit pole Spinaxis InteriorofTitan Spin Rate Stileset al., 2010: ( =22.5773 deg/day) • Iesset al., 2012: evidenceof a sub-surfaceocean • Atmospericaltorqueacting on a coredecoupledfrom the shell? • Non-synchronousrotation? determination of rotational state of celestial bodies

  10. Data Processing • Georeferenced BIDR images at 256 pxl/deg (175 m) resolution • Conversionfromoblyquecylindricaltogeographical lat/lonprojection • Stereographicprojectionforpolarflybys • Visual detection ofcrossovers and selectionof ROI (Regions-of-Interest) • Used pattern matching algorithm: 2D cross-correlation • 243 producedtiepointswithregistrationerrorsbetween 400 m and 40 km • Heightcorrectionsprovidedby JPL Green – Prime Mission Blue – ExtendedMission determination of rotational state of celestial bodies

  11. Pattern Matching • Severalobservationswith a t > 1000 days • distributionof the correlationindex (I) for cross-over pairs • > 60% ofobservationshas a correlationindex > 0.3 T55 flyby – f25 T56 flyby – f25 determination of rotational state of celestial bodies

  12. Models and Estimation Cases IAU, NAV Models • NAV model: based on IAU, includesupdatedcoefficients and nutation terms(i = 2…N) • Case A: linear approximation valid for the observation epoch • Case B: estimated amplitude of the precessionterms determination of rotational state of celestial bodies

  13. Residuals • 8 outliersdetected • detected a 4 km bias for T3, T7, T21, T41, T61 data • improvementsintroducing a periodicterminto Prime Meridian formulation • No improvements are observed for all models determination of rotational state of celestial bodies

  14. SpinRate and NSR NSR rotationabsent • estimatedcompatible at 3-level (worst case) withsynchronousvalue • sameresultsobtainedforall the estimates • residual NSR is 0.02° Estimatedvalues determination of rotational state of celestial bodies

  15. Pole Location and Cassini State Solutions are compatiblewith the occupancyof a Cassini state • Obliquity = 0.31 deg • Precessionterms • Deviation ( 2°) for the estimated pole (IAU) • Largerdeviationsfor NAV model estimate due to nutation terms • Unknownaccuracyof the Laplace pole determination of rotational state of celestial bodies

  16. Pole Location and Obliquity Estimate at AVG observationepoch • Averaged pole location (2004-2009) • resultscompatiblewithprevious estimate IAU, NAV models • modelto propagate the spinaxismotion • center ofprecession Laplace pole • differencebetween IAU and NAV estimatedobliquity due to the nutations Obliquity  = 0.31 ± 0.005deg determination of rotational state of celestial bodies

  17. Geophysicalimplications: Obliquity • Estimated= 0.31°  0.005° • + • Cassini state 1 -0.14 MoIfromobliquity (Bills and Nimmo, 2008) rotation gravity (gravityfieldinferredfrom (Iess et al., 2010) • disagreementwithgravity data/ unphysicalvalue • inferredfromsurfacemeasurements • differentiatedinteriorstructure MoI = 0.62 determination of rotational state of celestial bodies

  18. GeophysicalImplications: Spin Rate Measured NSR • NSR variesbetween +0.02 deg/year and -0.02° deg/year • A signinversionisobservedbetween prime and extendedmission • Similartrend(amplitude and sign) waspredictedbyKaratekinet al. (2008) • Seasonalvariationsofspin rate  atmospherictorqueacting on a shelldecoupledfrom the core Seasonalvariationsof (Karatekinet al.,2008) determination of rotational state of celestial bodies

  19. BepiColombo Rotation Experiment Goalsof the experiment • Investigationof the interiorofMercury • MoIfromobliquity (Cassini state) • Librations moltencoreofMercury Librations in longitude Solidcore Fluidcore BepiColombo MPO and HRIC • Launch at 2015, orbitinsertion at 2022 • polarorbit (400 x 1508 km - 2.3 hrperiod) • three-axisstabilized – nadir pointing • High ResolutionImagingChannel (Optical) • resolution: 5 m at pericenter • swathwidth at periapsis: 21km (3.2°) determination of rotational state of celestial bodies

  20. Error Budget • Target: 1 arcsec accuracy (librations) • Systematicerrors (8 m) • Veryperformant pattern matching • Attitudedeterminationis the mostrelevanterror source determination of rotational state of celestial bodies

  21. Rotation Experiment Simulator Modules Simulations • attitude • image georeferencing • generation of the observables • Estimator • attitude error • registration error • error-free preliminary simulations determination of rotational state of celestial bodies

  22. Conclusions and Future Work Models and Methods • reviewofcurrentrotationalmodels • Extendedrotationalmodel • IAU modifiedmodel (librationterms) • reviewof the technique • selectionof pattern matching algorithms • Estimator: RSDS software Mercury Rotation Experiment Titan Rotation Experiment • data processing • estimationofspin rate and obliquity • occupancyof a Cassini state 1 • differentiatedstructureof the interior • seasonalvariationsofspin rate • Future Work • Nutations and librations estimate • end-to-endexperiment simulator • modeling of the errorsources • Future Work • experimentsimulations determination of rotational state of celestial bodies 22 determination of rotational state of celestial bodies

  23. Abstracts & Conferences NASA/ESA/ASI Cassini PSG – RADAR Team Meeting , London, Giugno 2011 Talk: “TitanGravity and Rotation” Autori: L. Iess, R. Meriggiola, P.Racioppa, NASA – Titan Surface Workshop, Caltech, 26 – 27 Agosto 2009 Talk: “Titan Rotation” Authors: L. Iess, R. Meriggiola NASA – Cassini Radio Science Team Meeting , JPL, 23 Ottobre 2009 Talk: “TitanGravity and Rotation” Autori: L. Iess, J.W. Armstrong, S.W.Asmar, R.Jacobson, R. Meriggiola, P.Racioppa, N.Rappaport,D.J. Stevenson, B. Stiles, P. Tortora ESA BepicolomboGeodesdy and GeophysicsWorking Group, Berlino, 03 Luglio 2010 Poster: “MORE: Recovery of Mercury gravity field and MPO Orbit” Authors: A. Genova, M. Marabucci, L. Iess, R. Meriggiola EGU General Assembly , Vienna, 7 Aprile 2011 Abstract: “Simulations of BepiColombo's Mercury Rotation Experiment” Authors: P. Tortora,A. Bevilacqua, L. Carozza, A. Genova, A. Gherardi, L. Iess, R. Meriggiola, A. Palli, P. Palumbo, M. Zusi NASA/ESA/ASI Cassini PSG – RADAR Team Meeting , ESTEC (Noordwijck), Giugno 2011 Talk: “Summary of activities with Cassini RADAR data in Rome” Authors: R. Orosei, L. Iess, M. Langhans, J.I. Lunine, R. Meriggiola, G. Mitri, F. Tosi EPSC 2011 , Nantes, 2-7 Ottobre 2011 Abstract: “Image Processing Simulations for the BepiColombo Rotation Experiment” Authors: A. Palli,, A. Bevilacqua, L. Carozza, A. Genova, A. Gherardi, L. Iess, R. Meriggiola, P. Palumbo, P. Tortora, M. Zusi AGU Fall Meeting 2011 , San Francisco, 5-9 Dicembre 2011 Abstract: “The rotation of Titan by latest Cassini data” Authors: R. Meriggiola, L. Iess, B.W. Stiles determination of rotational state of celestial bodies 23

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