The Design and On-orbit Performance of the Relativity Mission Gyroscopes

Transcription

1 The Design and On-orbit Performance of the Relativity Mission Gyroscopes Sasha Buchman, Stanford University Symposium on Gyro Technology 2010 Karlsruhe, September 21 st

2 2 642 km Guide Star IM Pegasi (HR 8703) Geodetic Effect 6,606 marcsec/yr deg/hr v R R c M G Ω e G Frame-Dragging Effect 39 marcsec/yr deg/hr e e e FD ω R ω R R R c I G Ω Gravity Probe B Concept e e e R c GL v R R c GM Ω ˆ ˆ ˆ

3 GP-B Gyroscope Requirements marcsec/yr marcsec/yr 1 marcsec/yr = deg/hr = rad/sec Electrostatic gyro uncompensated (10-1 deg/hr) Spacecraft gyros (3x10-3 deg/hr) Laser gyro (10-3 deg/hr) ,606 Geodetic effect 39 Frame dragging effect Electrostatic gyro with modeling (10-5 deg/hr) GP-B requirement 3

4 GP-B Gyroscope Requirements marcsec/yr marcsec/yr 1 marcsec/yr = deg/hr = rad/sec Electrostatic gyro uncompensated (10-1 deg/hr) Spacecraft gyros (3x10-3 deg/hr) Laser gyro (10-3 deg/hr) ,606 Geodetic effect 39 Frame dragging effect Electrostatic gyro with modeling (10-5 deg/hr) GP-B requirement GP-B Gyro Design 4

5 The Science Instrument Gyro4 Quartz Block Telescope Science Instrument Assembly Nothing could be simpler then GP-B; just a gyroscope and a telescope William Fairbank 5

6 Probe, Dewar, and Satellite 6

7 GP-B Launch April 20 th

8 Ensuring Gyro Performance 1. Optimize Geometry I. Gyro asphericity R/R < 10-6 II. Gyro mass unbalance r/r < 10-6 III. Housing asphericity R H /R H < Reduce Environmental Disturbances I. Residual acceleration a trans < ms -2 II. Magnetic field B < T III. Gas pressure P < Pa IV. Electric charge Q < F V. Patch effects d patch < 10-6 m 3. Shift Frequency from dc and Average Signal I. Roll satellite 77.5 s II. Use Polhode averaging ~ 3,000 s III. Multiple gyroscopes (4) 4 gyros 4. Use Natural Calibrations I. Daily aberration ~ 5 arcsec II. Yearly aberration ~ 20 arcsec 5. Ground Testing Capability 10 ms -2 to ms -2 8

9 Gyro Description Components Rotor Housing Read-out loop Spin-up nozzle UV fixtures Suspension cables Read-out cable Functionality Electrostatic suspension Capacitance rotor position Forcing charge measurement London moment read-out Helium spin-up Cryogenic operations UV charge management 9

10 Why Gyros in Space? r ƒ External forces through CF, different than CM Requirement Ω < Ω 0 ~ 0.1 marcs/yr (1.5 x rad/s) Drift-rate: Torque: Moment of Inertia: s mf r I I (2 5) mr 2 r 2 r s r 5 f 0 Mass Unbalance Requirements limits on r On Earth (ƒ = 10 ms -2 ) δr < m (unrealistic) Standard satellite (ƒ ~ 10-7 ms -2 ) δr < m (unlikely) GP-B drag-free cross- track average (ƒ ~ ms -2 ) δr < 10-7 m (achievable) 10

11 Rotor Fabrication I Fused quartz 1.9 cm radius Homogeneity < 1 ppm Sphericity < 1 ppm Polishing system Roundness measurement Holder for homogeneity measurement <10-6 8,848 m above sea level Profile of optical path difference: nm 2.4 m above mean surface Surface Profile 19 nm peak-valley Gyro profile scaled to Earth size 11

12 Rotor Fabrication II Nb film 1.3 m (50 inch) Nb Coating Uniformity <2% Mass unbalance < 1 ppm I/I < Gyro in backscattering machine Coating process rf sputtering 2 layers 32 location faces & vertices of icosahedron Mass Unbalance (nm) 20 nm requirement Gyro Pre-Flight Estimate On-Orbit Data Requirement Nb coating thickness Measured at 32 points backscattering 147 Pm, 2.62 yr, 0.224MeV Coating Mass Unbalance Results for 20 Gyros 12

13 Gyro Housing Fabrication Radius 1.9 cm Sphericity < 10 ppm 6 Electrodes in 3 Orthogonal Pairs 5 Turn Read-out Loop Channel and Ti Nozzle for Spin-up 7-layer Ti-Cu Electrode Coating 3-layer Ti-Cu-Ti Support and Spin-up Lands Coatings Ti Film For Bare Quartz Spin-up half Read-out half Lands and Electrodes Coatings Three Layer Film Seven Layer Film SEM Micrographs 1 m 1 m 13

14 Spin Spin Speed rate (Hz) (Hz) Gyro Spin-up Differential Pumping Requirement: 1) spin channel ~ 10 torr (sonic velocity) 2) 2) electrode area < 10-3 torr Gyro 1 spun-up last; spin-up of one gyro causes spin down of the other gyros Gyro 1 Gyro 2 Gyro 3 Gyro 4 Gyro Spin Speed (Hz) df/dt (μhz/hr) Spindown (yr) , , , , Time (hours) 14

15 Gyro1 Charge (pc) UV Charge Management Concept Rotor charge controlled via UV excited electrons Charge rates ~ 0.1 pc/day Continuous measurement at the 0.1 pc level Control requirement: 15 pc UV Electrode Discharge of Gyro1 after levitation pC (on levitation) 70 pc/hour discharge 0 pc 100 pc Day of year, 2004 (+221) UV Lamp Assembly 15

16 UV Charge Management Results Gyro Potential (mv) GYRO 1 GYRO 4 GYRO 2 GYRO Discharge I MEASURED GYRO CHARGE (mv) G # G # G # G # Day of Year Day of Year 2004 Discharge II 1 pc 1 mv C gyro = 1 nf 16

17 London Moment Read-Out London moment read-out with dc SQUIDs Superconducting pickup on gyroscope housing < J/Hz (<50 0 /Hz) at 5 mhz 200 marcsec/hz ( G/ Hz ) A spinning superconductor develops a magnetic pointer aligned with its spin axis Requirement 2mc BL s e f s pt Hz 17

18 Gyroscope Readout Single Orbit Output(Volts) Arc Sec Output of SQUID Readout Electronics, Gyroscope 3, Orbit 6200, June 15, Optical Aberration due to Orbital Motion Time (minutes) After Acquisition of Guide Star 18

19 Excellent Gyro Performance 1. Optimize Geometry I. Gyro asphericity R/R < 10-6 II. Gyro mass unbalance r/r < 10-6 III. Housing asphericity R H /R H < Reduce Environmental Disturbances I. Residual acceleration a trans < ms -2 II. Magnetic field B < T III. Gas pressure P < Pa IV. Electric charge Q < F V. Patch effects d patch >> 10-6 m 3. Shift Frequency from dc and Average Signal I. Roll satellite 77.5 s II. Use Polhode averaging Variable III. Multiple gyroscopes (4) 4 gyros 4. Use Natural Calibrations I. Daily aberration ~ 5 arcsec II. Yearly aberration ~ 20 arcsec 5. Ground Testing Capability 10 ms -2 to ms -2 19

20 Polhode Period (hours) Unexpected Polhode Damping Gyro 2 Gyro 1 Gyro 4 Gyro 3 polhode path of the pole (Greek) [torque-free motion] The curve produced by the angular velocity vector on the inertia ellipsoid 4 L between I 1 & I L between I 2 & I L between I 2 & I L between I 1 & I 2 L between I 2 & I L between I 2 & I Time (days from Day #1; Apr. 20, 2004) Time (days from Day #1; Apr. 20, 2004) I 3 I2 I1 20

21 Misalignment Torque Anomaly Drift Rate (as/day) 4 Magnitude of Drift Rate vs. Angle of Misalignment Gyro Gyro 2 3 Gyro 3 Gyro Angle of Misalignment (degrees) 21

22 The Patch Effect Explanation of anomalies: Patch Effect Mechanical, magnetic, suspension effects ruled out Variation of electric potential over the surface Can arise due to the polycrystalline structure Can be affected by presence of contaminants Patch fields present on gyro and housing walls Cause forces and torques between surfaces The Patch Effects: 1.Gyro acceleration along the roll axis 2.Gyro acceleration at spin frequency 3.Gyro spin down 4.Gyro polhode damping 5.Misalignment torque 6.Resonance torque 7.Charge measurement bias d Complicate Data analysis Schematic of surfaces with patches Gyro surface Housing surface 22

23 3 Complications due to Patch Effect I Polhode Period (hours) Gyro 2 Gyro 1 Gyro 4 Gyro 3 Polhode damping Caused by power dissipation in housing resistances to ground Changes trapped flux orientation to the spin axis Complicates scale factor C g determination Time (days from Day #1; Apr. 20, 2004) Time (days from Day #1; Apr. 20, 2004) 23

24 3 Complications due to Patch Effect II Misalignment Torques Caused by interaction of patches on gyro and housing Proportional to spin to roll angle Magnitude up to 2.5 arcsec/yr Orthogonal to misalignment plane (roll & spin axes) 24

25 EW orientation, s EW (arcsec) 3 Complications due to Patch Effect III Roll-polhode Resonance Torque Caused by interaction of patches on gyro and housing Jumps occur when harmonic of polhode rate coincident with roll rate Up to 200 marcsec discontinuities in data Long term oscillatory behavior Gyro 2 per orbit orientation m r s EW res. m P Date (2005) 25

26 Expected Gyroscope Behavior Newton Geodetic effect* (-6571 marcsec/yr) Newton Frame-dragging effect* (-75 marcsec/yr) *includes solar GR effects and guide star motion 26

27 Flight Data (Gyro 2) 27

28 GP-B Gyroscope Requirements marcsec/yr marcsec/yr 1 marcsec/yr = deg/hr = rad/sec Electrostatic gyro uncompensated (10-1 deg/hr) Spacecraft gyros (3x10-3 deg/hr) Laser gyro (10-3 deg/hr) ,606 Geodetic effect ~ 1,000 Patch effects 39 Frame dragging effect Electrostatic gyro with modeling (10-5 deg/hr) GP-B Gyro Design 28

29 Two Foundations of the Data Analysis 1. Spectral separation a) Gyro spin ~ 60 Hz - 80 Hz (changing with time) b) Spacecraft roll = 12.9 mhz (from on-board star trackers) c) Spacecraft orbit = 0.17 mhz (from on-board GPS) d) Gyro polhode ~ 0.1 mhz (changing with time) e) Earth s orbit = 31.7 nhz (from JPL Earth ephemeris) General Relativity acts at zero-frequency 2. Trapped magnetic flux modeling Enables determination of frequency of Gyro spin & Gyro polhode 1 & 2 + model of patch effects and gyro dynamics allow separation of relativistic from Newtonian effects 29

30 Trapped Flux Mapping Trapped Magnetic Potential (V) Express trapped magnetic potential in spherical harmonics Transform TF fixed in body by Euler rotation to inertial frame 1. About 3-axis by p (polhode phase) 2. About 2-axis by p (polhode angle) 3. About 3-axis by s ( spin phase) Rotor body-fixed frame Trapped Flux Mapping: 1. Nonlinear estimation of rotor dynamics, p (t), p (t), s (t) 2. Linear fit for coefficients of spherical harmonic, A lm, l odd I 3 I 1 I 2 Trapped magnetic potential 30

31 Relativity & Newtonian Torque Model Relativity Misalignment torque Roll-polhode resonance torque 31

32 Flight Data (Gyro 2) Apply Torque Model 32

33 Newtonian Effects Removed EW orientation (arcsec) NS orientation (arcsec) Gyro 2, orientations Newtonian torques NS uniform drift Jan 8 Jan 28 Feb 17 Mar 9 Mar 29 Apr 18 May 8 EW uniform drift +1 1 Jan 8 Jan 28 Feb 17 Mar 9 Mar 29 Apr 18 May 8 date (2004) 33

34 Gyro 1 Drift Estimates: Consistent 95% confidence ellipses Seg. 2-3 Seg. 10 Seg. 9 Seg. 5,6,9,10 Seg. 5-6 NS / EW observability varies due to annual aberration 34

35 Four-Gyroscope Results: Consistent 95% confidence ellipses Gyro 2 Gyro 4 Gyro 1 Gyros 1,2,3,4 Gyro 3 35

36 GP-B Gyroscope Requirements marcsec/yr marcsec/yr 1 marcsec/yr = deg/hr = rad/sec Electrostatic gyro uncompensated (10-1 deg/hr) Spacecraft gyros (3x10-3 deg/hr) Laser gyro (10-3 deg/hr) ,606 Geodetic effect ~ 1,000 Patch effects 39 Frame dragging effect Expected GP-B Electrostatic gyro with modeling (10-5 deg/hr) GP-B Gyro Design improvement over previous gyroscopes 36

37 Looking to the Future The towering figure of Einstein provides a tempting target for physicists of all stripes. He would perhaps look with approval on these efforts to go beyond his theories. The Search for Relativity Violations Alan Kostelecky Scientific American

38 Expected Experiment Accuracy Primarily depends on treatment of 2 systematic effects: ECU, SRE Covariance analysis (including nearly all systemati effects) Parameter optimization + additional data = additional 10% Analysis excludes ~15% of potentially valuable data (i.e. outliers) Misalignment Torque Coeff. r NS (mas/yr) [% GR] r EW (mas/yr) [% GR] Upper Bound 21 [0.3%] 12 [30%] Complete Treatment of ECU Noise 13 [0.2%] 7 [18%] Complete Treatment of ECU Noise & SRE variations 6 [0.1%] 4 [10%] All results to date consistent with GR (within 3), but not yet at final experiment accuracy 38

39 Data Analysis Time-line Pre-launch data analysis completely rewritten (almost) Data Analysis timeline Launch 20 April 2004 Post science calibration 15 August 2005 Helium depletion September 2005 Geometric separation of misalignment torque August 2006 Trapped Flux Mapping August 2007 Complete Torque Modeling August 2008 Complete (2-second) data processing August 2009 Release of Science Results (NASA HQ) 13 October

40 Geometric Method (from SAC 15) Drift Rate Drift Rate Data simulated for illustration purposes Misalignment Drift Uniform Drift Radial component of Misalignment Drift Misalignment Angle Phase (degrees) (deg) Radial Component of Uniform Drift Misalignment Angle Phase (degrees) (deg) Radial Component of Drift Rate Contains NO Contribution from Misalignment Drift Magnitude and Direction of Uniform (Relativistic) Drift Rate May Be Determined From Variation of Radial Component with Misalignment Phase 40

41 Low & High Frequency SQUID Data LF SQUID channel (780 Hz LP filter 4 Hz LP filter gain) 5 Hz continuous HF SQUID channel (780 Hz LP filter) 10 6 snapshots over 1 year (2200 Hz, ~ 2 sec duration) V RO V RC Voltage Div ider 780 Hz Low Pass Filter 4 Hz Low Pass Filter Gain A/D A/D V R D/A to A/D D/A to A/D V F Gyro 1 HF snapshot, 10 Nov R OF I O R OC I C R C I F R F FLL Electronics HF channel LF channel I T SQUID M I M F I L Pick-Up Loop 41

42 Science Signals Telescope measures S/C pointing: ^ SQUID measures misalignment: = ^ s s ^ ^ ê NS North (inertial) S/C x-axis r Gyros 2 & 1 Science telescope ^ ê EW Guide Star (IM Pegasi) Gyros 4 & 3 42

43 Trapped Flux & Readout Scale Factor Trapped Magnetic Potential (V) Gyro 1 polhode ˆ I 3 6 Sept 2004 s ~ 1% ˆ I 1 ˆ I 2 43

44 Trapped Flux & Readout Scale Factor Trapped Magnetic Potential (V) Gyro 1 ˆ I 3 s 4 Oct 2004 ˆ I 1 ˆ I 2 44

45 Trapped Flux & Readout Scale Factor Trapped Magnetic Potential (V) Gyro 1 ˆ I 3 s 14 Nov 2004 ˆ I 1 ˆ I 2 45

46 Trapped Flux & Readout Scale Factor Trapped Magnetic Potential (V) Gyro 1 ˆ I 3 s 20 Dec 2004 ˆ I 1 ˆ I 2 46

47 Trapped Flux & Readout Scale Factor Trapped Magnetic Potential (V) Gyro 1 ˆ I 3 s 20 Feb 2005 ˆ I 1 ˆ I 2 47

48 Trapped Flux & Readout Scale Factor Trapped Magnetic Potential (V) Gyro 1 ˆ I 3 s 26 June 2005 ˆ I 1 ˆ I 2 48

49 Trapped Flux Mapping (August 2007) Relative C g variations Parameter Angular velocity, Error 10 nhz ~ I 3 s ^ Polhode phase, p ~ 1 Rotor orientation ~ 2 Trapped magnetic potential ~ 1% Gyroscope scale factor, C g TF ~ 10-4 I 1 I 2 Path of spin axis in gyro body I 3 Gyro 1 I 1 I 2 Trapped magnetic potential 49

50 Modeling Patch Effect Torques 1. Arbitrary rotor & housing potentials (spherical harmonics) 2. Rotate to common frame, spin average 3. Solve Laplace s equation between rotor & housing Energy stored in E-field Patch effect torque: (a) roll averaged torque and (b) torque at 1 st harmonic of roll significant Guide Star ^ s ^ p s s ^ Spacecraft dynamics p Rotor dynamics 50

51 Misalignment Torque (Roll Averaged) NS misalignment (arcsec) Guide Star ^ Torque Drift Proportionality coefficient: k( p, p ) s ^ Relativity fixed in inertial frame Aberration spectrally separates misalignment torque Torque-induced drift N Misalignment angle E µ y R Misalignment Phase Uniform Radial Precession (Relativity) NS vs. EW misalignment, EW misalignment (arcsec) 51

52 Roll-polhode Resonance Torque Cosine of Roll Frequency (mv) North-South Orientation (arbitrary units) Torque at 1 st roll harmonic significant during resonance Electrostatic model predicts: 1.5 Sine and Cosine at Roll Frequency, Gyro 2, Res North Defines Cornu spiral Requires accurate p (t) Provided by TFM West -1 Approximate Scale: 50 mas Sine of Roll Frequency (mv) East-West Orientation (arbitrary units) 52