Gravity Probe B Data Analysis Challenges, Insights, and Results

Transcription

1 Gravity Probe B Data Analysis Challenges, Insights, and Results Mac Keiser April 15, 27 April 15, 27 Jacksonville, FL 1

2 Topics Data Analysis Strategy and Methods Challenges and Insights Trapped Magnetic Flux and Slowly Changing Polhode Path Misalignment Torque Offsets in Gyroscope Spin Axis Orientation at Predictable Times Present Status and Future Prospects April 15, 27 Jacksonville, FL 2

3 Data Collection Strategy and Limits on Potential Systematic Errors American Physical Society Meeting Initialization Phase Science Data Collection Phase Calibration Phase Launch April 2, 24 Gyroscopes Spun Up and Aligned August 29, 24 Aug. 15, 25 Liquid Helium Depeleted Sept. 29, 25 Initialization Phase Instrument Calibration Science Data Collection Phase Redundancy Internal Cross-Checks Calibration Phase Deliberate Enhancement of Disturbing Effects April 15, 27 Jacksonville, FL 3

4 Science Data Collection: Measurement of Gyroscope Spin Axis Orientation Relative to Guide Star ΔGyro Pointing = ΔTelescope Pointing- ΔStar (2 axes resolved by roll telescopes) Gyro SQUID Quartz Block Roll Star Reference Telescope Roll Period 77.5 seconds HR873 (IM PEG) Gyro Electronics Telescope Electronics April 15, 27 Jacksonville, FL 4

5 Gyroscope Readout Single Orbit Data Analysis Procedure: 1. Find Ratios to Telescope to Gyroscope Scale Factors Using Attitude Errors 2. Combine Gyroscope and Telescope Signals 3. Calibrate Combined Signals Using Orbital Aberration Vo lts Combined Gyroscope 3 and Telescope Signals, Orbit 62, June 15, Arc s ec Optical Aberration Orbital due Abe to Satellite s rratio n Orbital Motion Time (min) Afte r Acquis ition of Guide Star April 15, 27 Jacksonville, FL 5

6 Gyroscope Spin Axis Gyroscope Spin Axis London Moment, Trapped Flux, and Polhode Motion London Moment Magnetic Field London Mome nt Field Trapped Trapped Magentic Magnetic Field Field Polhode Period (hr) Elapsed Time Since 1-Jan-24 (days) London Moment Readout: Rotating Superconductor Develops Dipole Field Aligned with Instantaneous Spin Axis Field at Surface of Rotor for Gyroscope Spinning at 8 Hz: 57.2 μg Trapped Magnetic Field: Body-Fixed Gyroscope 1 3. μg Gyroscope μg Gyroscope 3.8 μg Gyroscope 4.2 μg Polhode Motion and Damping: Polhode Motion: Motion of spin axis within the body along the polhode path (Euler s Equations) Damping: Slow Relaxation of Polhode Path toward maximum moment of inertia April 15, 27 Jacksonville, FL 6

7 Data Analysis in Presence of Trapped Magnetic Flux and Polhode Motion Scale Factor Modulation, Gyro 1, Harm Impact on Data Analysis 3 1. Scale Factor is Modulated at Harmonics of Polhode Frequency Magnitude of Modulation ~ 1% 2. Amplitude and Phase of Scale Factor Modulation Slowly Changes 3. Constant (Zero Frequency) Component Slowly Changes Solution: Divide data into batches with length up to 75 orbits (5 days) For Each Batch Estimate» Modulation Coefficients at Known Polhode Period» Constant Component of Scale Factor Time (days), Since Jan. 1, 24 April 15, 27 Jacksonville, FL 7 % % % % Gyro 1 Scale Factor Modulation Time (days) since Jan. 1, 24 Gyro 4 Scale Factor Modulation Scale Factor Modulation, Gyro 4, Harm Time (days), Since Jan. 1, 24 Time (days) since Jan. 1, 24

8 History of Gyroscope Spin Axis Orientation Relative to the Apparent Position of the Star 15 Gyroscope Spin Axes Orientation in Orbital Plane 25 Gyroscope Spin Axes Orientation Perpendicular to Orbital Plane South-North (arc sec) Gyro 1 Gyro 2 Gyro 3 Gyro 4 Jan.1,25 Flight Data Eas t-wes t (arc s ec) Gyro 1 Gyro 2 Gyro 3 Gyro Time (days), Since Jan. 1, Time (days), Since Jan. 1, 24 Maximum Differences Between Apparent and True Guide Star Positions North-South West-East Annual Aberration 11. arc sec 19.1 arc sec Parallax 3 milli-arc sec 5 milli-arc sec Deflection of Starlight 19 milli-arc sec 15 milli-arc sec April 15, 27 Jacksonville, FL 8

9 Changes in Gyroscope Spin Axis Orientation Elliptical Path Due to Annual Aberration 15 1 Gyros cope Spin Axe s Re lative to Appare nt Guide Star Pos ition Gyro 1 Gyro 2 Gyro 3 Gyro 4 South-North (arc sec) Eas t-we s t (arc s e c) April 15, 27 Jacksonville, FL 9

10 History of Gyroscope Spin Axis Orientation Relative to the True Position of the Star 8 Gyroscope Spin Axis Orientation in Orbital Plane 8 Gyroscope Spin Axis Orientation Perpendicular to Orbital Plane 6 6 Orientation (arc sec) Gyro 3 Gyro 2 Gyro 4 Orientation (arc sec) Gyro 2 Gyro 1 Gyro 3 (offset -2 arc sec) -8 Gyro 1-8 Gyro 4 (offset -3 arc sec) Time (days), Since Jan. 1, Time (days), Since Jan. 1, 24 Proton Flux, Jan. 2, 25, Measured by GOES Satellite April 15, 27 Jacksonville, FL 1

11 Calibration Phase Discovery of a Misalignment Torque 19 Maneuvers to nearby stars or virtual stars Maximum misalignment 7 degrees Majority of maneuvers at 1 degree or less American Physical Society Meeting Maneuvers included variety of operating conditions for gyroscope suspension system and spacecraft translation control Electrostatic Suspension System Operated with» Voltages Applied to Electrodes Modulated at 2 Hz» DC Voltages Applied to Electrodes Deliberate Acceleration of the Spacecraft Along Roll Axis and Perpendicular to the Roll Axis Change in spacecraft roll period (77.5 sec to 12 sec) Calibration phase lasted from Aug. 15 through depletion of liquid helium on Sept. 29, 25. April 15, 27 Jacksonville, FL 11

12 Gyro 3 Misalignment Torques Calibration Phase Mean Rate (marc-s/day) vs. Mean Misalignment (arc-s) Mean North-South Misalignment Drift Rate Magnitude (arc sec/day) Gyro 3, Drift Rate Magnitude vs. Mean Misalignment k = 2.5 arc sec/day/degree Mean West-East Misalignment Mean Misalignment (arc sec) For gyroscope 3 drift rate is azimutal to measurement accuracy drift rate increases linearly with the misalignment angle up to 15 arc sec. April 15, 27 Jacksonville, FL 12

13 All Gyroscopes Calibration Phase Mean Rate (marc-s/day) vs. Mean Misalignment (arc-s) American Physical Society Meeting Mean North-South Misalignment Gyroscope 1 Gyroscope Gyroscope 3 Gyroscope Mean North-South Misalignment Mean West-East Misalignment Mean West-East Misalignment April 15, 27 Jacksonville, FL 13

14 Summary of Calibration Phase Results Drift rate is perpendicular to misalignment Torque coefficients as large as 2.5 as/day/deg Stability of misalignment torque coefficient Gyroscope 3:» Gyroscope 3: Consistent calibration-phase results» Offset following solar flare is consistent with magnitude of misalignment torque» Sign of Torque Coefficient has changed from solar flare to calibration phase Other gyroscopes:» Evidence for variation in torque coefficient during calibration phase Most Plausible Explanation: Interaction of patch effect fields on the gyroscope rotor with patch effect fields on the housing. April 15, 27 Jacksonville, FL 14

15 Data Analysis in the Presence of Misalignment Torques Data simulated for illustration purposes Misalignment Drift Radial Component of Drift Rate Contains NO Contribution from Misalignment Drift Uniform Drift Radial component of Misalignment Drift Misalignment Angle (degrees) Radial Component of Uniform Drift American Physical Society Meeting Magnitude and Direction of Uniform (Relativistic) Drift Rate May Be Determined From Variation of Radial Component with Misalignment Phase April 15, 27 Jacksonville, FL 15 Drift Rate Drift Rate Misalignment Angle (degrees)

16 An Additional Observation: Offsets in Gyroscope Spin Axis Orientation American Physical Society Meeting -1.6 Gyros cope 1 Orie ntation Pe rpe ndicular to Orbital Plane -1.7 Arc Sec Freq. (Hz) Sate llite Roll Fre que ncy 43rd Harm o nic 42nd Harmonic Time (days), Since Jan. 1, 24 Data is Not Used in Analysis When an Harmonic of Polhode Frequency Coincides with Satellite Roll Frequency April 15, 27 Jacksonville, FL 16

17 Relativistic Drift Rate All 4 Gyroscopes Least Squared Fit for Sinusoidal Component, All Gyroscopes Gyro 1 Gyro 2 Gyro 3 Gyro 4 Drift Rate (mas /day) Consistency between gyroscopes and data runs better than 1 mas/year Mis alignm e nt Phas e (de g ) April 15, 27 Jacksonville, FL 17

18 A complementary data analysis approach: Algebraic Method Method: Determine Gyroscope Spin Axis Orientation from Short-Term Analysis Simultaneously Estimate Relativistic Drift Rate and Misalignment Torque Coefficient Using Known History of Satellite Roll Axis Orientation Geometric Method Algebraic Method Short Term Analysis Information for Long Term Analysis Additional Information Needed Long Term Analysis 1 to 75 orbits Modulation of Scale Factor at Polhode Frequency Gyroscope Drift Rate Misalignment between satellite roll axis and gyroscope spin axis Relativistic Drift Rate and Misalignment Torque 1 to 5 orbits Modulation of Scale Factor at Polhode Frequency Gyroscope Spin Axis Inertial Orientation Inertial Orientation of Satellite Roll Axis Relativistic Drift Rate Misalignment Torque Polhode Variations of Scale Factor Continuous Dynamic Estimation of Gyroscope Orientation Two Complementary Data Analysis Methods Provide Valuable Cross- Checks and Additional Insight April 15, 27 Jacksonville, FL 18

19 Preliminary Results: Algebraic Method June 26 Frame- Dragging from GR December 26 Error Ellipses Show Statistical Error Only March 27 Geodetic from GR April 15, 27 Jacksonville, FL 19

20 Initial Geodetic Effect Results 'Geometric 'Algebraic' Full Year 158 days 85 days 82 days 41 days 1σ statistical error only ± ± ± ± ± 7 Separate gyro, ~ 5-day batches Combined gyro processing, continuous filtering Progress in modeling with algebraic approach evident SQUID noise limit Net expected ± 1 * [marc-s/yr] ± 97 Residual gyro-to-gyro inconsistencies due to incomplete modeling ~ 1 marc-s/yr * Earth -666, solar geodetic +7, proper motion +28 ± 1 net expected ± 1 April 15, 27 Jacksonville, FL 2

21 Summary Solutions to Difficulties in Data Analysis Have Been Found 1. Trapped Flux and Changing Polhode Path Solution: Estimate Modulation and Constant Components of Scale Factor for Batches up to 75 orbits long. 2. Misalignment Torques Two Complementary Solutions: Geometric and Algebraic Methods 3. Offsets in Gyroscope Positions When Harmonics of Polhode Frequency Coincide with Satellite Roll Frequency Solution: Do not use data near resonances All Four Gyroscopes are Consistent with One Another and with Drift Rate Predicted by General Relativity to better than 1 mas/yr. Formal Statistical Error is Significantly Smaller than Typical Inconsistencies Between Gyroscopes or Between Data Runs April 15, 27 Jacksonville, FL 21

22 Methods for Improving Consistency of Results Trapped Magnetic Flux and Polhode Motion 1. Include temporal variation of scale factor modulation 2. Use known polhode path 3. Trapped Flux Mapping 4. Crosschecks;» Annual Aberration» Flux Slipping Misalignment Torques 1. Provide for slowly changing torque coefficient and misalignment 2. Tighten Limits on Misalignment Torques due to Incomplete Roll Averaging Offsets in Gyroscope Spin Axis Orientation When Harmonics of Polhode Coincide with Roll Frequency 1. Compare data with physical model 2. Include additional terms in data analysis or modify data selection criteria April 15, 27 Jacksonville, FL 22

23 Acknowledgements April 15, 27 Jacksonville, FL 23