GP-B/Aero-Astro1Data AnalysisSeptember 30, 2008 • StanfordGP-B Experiment and Data Analysis ChallengesMichael HeifetzGP-B/ Aero-Astro2October 21, 2008 • StanfordData Analysis• Geodetic Effect– Space-time curvature ("the missing inch")• Frame-dragging Effect– Rotating matter drags space-time ("space-time as a viscous fluid")The Relativity Mission Concept( ) ( )−⋅+×= ωRωRvR23232323RRcGIRcGMΩQuartz blockGyro 1Gyro 2Star Tracking TelescopeGuide StarGyro 3Gyro 4Mounting FlangeLeonard SchiffGP-B/ Aero-Astro3October 21, 2008 • StanfordData AnalysisBrief History of Gravity Probe B1957 Sputnik – Dawn of the space age1958 Stanford Aero-Astro Department created1959 L. Schiff conceives of orbiting gyro experiment as a test ofGeneral Relativity1961 L. Schiff & W. Fairbank propose gyro experiment to NASA1972 1stdrag-free spacecraft: TRIAD/DISCOS1975 SQUID readout system developed1980 Rotor machining techniques perfected1998 Science instrument assembled2002 Spacecraft & payload integrated2004 Launch and vehicle operations2005 End of data collectionStart of Data Analysis2007 Preliminary results presented at April APS meeting2008 -2009 Final resultsGP-B/ Aero-Astro4October 21, 2008 • StanfordData AnalysisSpacecraft gyros(3x10-3deg/hr)1021010.10.0139Frame dragging<0.3% accuracy1036606Geodetic effect <0.002% accuracymarcsec/yr0.5GP-B requirement104105106107108109Best laser gyros (1x10-3deg/hr)Best mechanical gyros on Earth(10-2deg/hr)Electrostatically suspended gyroscope (ESG) on Earth with torque modeling(10-5deg/hr)Why a Space-Based Experiment?marcsec/yrBest terrestrial gyroscopes 1,000,000 times worse than GP-BOperation in 1g environment degrades mechanical gyro performanceLaser gyroscopes and other technologies fidelity too low for GP-B1 marcsec/yr = 3.2x10-11 deg/hrGP-B/ Aero-Astro5October 21, 2008 • StanfordData AnalysisGP-B Instrument ConceptGyros 4 & 3Gyros 2 & 1Fusedquartz block(metrology bench)Star tracking telescopeGuide starIM Pegasi• Operates at ~ 2 K with liquid He• Rolls about line of sight to Guide Star– Inertial pointing signal at roll frequency– Averages body-fixed classical disturbance torques toward zero– Reduces effect of body-fixedpointing biasesGP-B/ Aero-Astro6October 21, 2008 • StanfordData AnalysisThe GP-B Science Gyroscope Material: Fused quartz, homogeneous to a few parts in 107 Overcoated with Niobium. Diameter: 38 mm. Electrostatically suspended. Spherical to 10 nm – minimizes suspension torques. Mass unbalance: <10 nm – minimizes forcing torques. All four units operational on orbit.Gyroscope rotor and housing halvesIf a GP-B rotor was scaled to the size of the Earth, the largest peak-to-valley elevation change would be only 2 meters!Demonstrated performance:• Spin speed: 60 – 80 Hz.• <1 µHz/hr spin-down. "Everything should be made as simple as possible, but not simpler." – A. EinsteinGP-B/ Aero-Astro7October 21, 2008 • StanfordData AnalysisReadout and Gyro Scale FactorScale Factor Calibration using guide star light aberrationallows conversion of measurement (volts) to angle (arcsec)Aberration: Vehicle motion causes star’s apparent position to varyS/V around Earth -- 5.1856 arc-s @ 97.5-min periodPeak to peak ~ 24 arc-secHow to measure the spin direction of a perfect spinning sphere?GP-B/ Aero-Astro8October 21, 2008 • StanfordData Analysis19 Redundant spacecraft processors, transponders.  16 Helium gas thrusters, 0-10 mNea, for fine 6 DOF control. Roll star sensors for fine pointing. Magnetometers for coarse attitude determination. Tertiary sun sensors for very coarse attitude determination. Magnetic torque rods for coarse orientation control. Mass trim to tune moments of inertia. Dual transponders for TDRSS and ground station communications. Stanford-modified GPS receiver for precise orbit information.  70 A-Hr batteries, solar arrays operating perfectly.GP-B Spacecraft6.4 m 3240 kgGP-B/ Aero-Astro9October 21, 2008 • StanfordData AnalysisθApparent Guide StaraberrationGuide StarGSeˆEWeˆNSeˆτˆµrsˆ-gyro spin axis orientation-vehicle roll axis orientation- gyroscope misalignmentsˆτˆµrRelativity: slopes of (Geodetic) and (Frame- dragging) (significantly more complex problem))(tsNS)(tsEWnoisebiasrEWEWrNSNSgSQUIDssCtZ+++Φ−++Φ−=][)sin()()cos()()(δϕτδϕτSQUID ReadoutDataRoll Phase DataTelescope Data, Orbital and AnnualAberrationsScale FactorGyro orientation trajectory and - straight lines )(tsNS)(tsEWSurprise B: Patch Effect Torque-calibrated based on orbital and annual aberrationδϕ,gCSurprise A: variationsgC‘Simple’ GP-B Data AnalysisPointing Error via TelescopeGP-B/ Aero-Astro10October 21, 2008 • StanfordData AnalysisThree Cornerstones of Estimation (Filtering) MethodInformationTheoryFilter Implementation: Numerical TechniquesGyroscope Motion: Torque ModelsUnderlyingPhysicsSQUID Readout Signal Structure: Measurement ModelsUnderlyingPhysics,EngineeringGP-B/ Aero-Astro11October 21, 2008 • StanfordData AnalysisData Analysis Structure: ‘Two-Floor’ ProcessingTorque ModelingSQUID Readout ProcessingGyro Orientation Time HistoryData Analysis BuildingFirst FloorSecond FloorRelativityMeasurementFull Information MatrixGP-B/ Aero-Astro12October 21, 2008 • StanfordData AnalysisReadout Scale Factor: γCgModel002 20 0( ) 1 ( )cos( ( )) ( )sin( ( )) ,, , ( ) tan( / 2).Ng g n p n pnK Kn k n kn nk n nkk kC t C a n t b n ta a b b tγ γε ε ε ε ε γ== =  = + Φ + Φ   = = =∑∑ ∑Harmonic expansion in polhode phase withcoefficients that depend on polhode angleTrapped Flux Mapping (TFM)- Polhode phasepΦ- Polhode angleγblue –an(t)and bn(t)red - fit to ε(t) 0000ΦpI3I1I2γωrGyro principle axes of inertiaand instant spin axis positionGP-B/ Aero-Astro13October 21, 2008 • StanfordData AnalysisFirst Floor: SQUID Readout Data ProcessingSQUID DataSQUID No-bias SignalNonlinear Least-Squares Estimator(No Torque Modeling)Roll PhaseDataAberrationDataData GradingτµBatch length: 1orbitBias EstimatorCg(tk*)CT(tk*)δφ(tk*)ResidualsPointing/Misalign. Computation TelescopeDataRoll PhaseDataAberrationDataOUTPUT:PointingGSV/GSIPolhode PhaseDataTrapped Flux MappingPolhode AngleDataFull Information MatrixGyro Orientation(1 point/orbit)State Vector EstimatesgCγGyro Scale Factor ModelLet’s look at the gyro orientation profiles…G/T MatchingGP-B/ Aero-Astro14October 21,