Gravity Probe B Experiment

1
Gravity Probe BExperiment Results

• John W. Conklin
• Stanford University
• ICGC 2007, IUCAA, Pune

2
Overview

• The Gravity Probe B experiment
• Spacecraft payload
• Launch flight operations
• A million things went right but 2 surprises
• Data analysis adventure
• Challenges and their resolutions
• Current best results
• The Gravity Probe B team

3
Relativity Mission Concept
If, at first, the idea is not absurd, then there
is no hope for it." A. Einstein
4
GP-B Instrument Concept

• 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 biases

Guide star IM Pegasi
Gyros 2 1
Star tracking telescope
Fused quartz block(metrology bench)
Mounting flange
Gyros 4 3
5
Gravity Probe B History

• 1957 Sputnik Dawn of the space age
• 1959 L. Schiff conceives of orbiting gyro
  experiment as a test of General Relativity
• 1961 L. Schiff W. Fairbank propose gyro
  experiment to NASA
• 1972 1st drag-free spacecraft TRIAD/DISCOS
• 1975 SQUID readout system developed
• 1980 Rotor machining techniques perfected
• 1998 Science instrument assembled
• 2002 Spacecraft payload integrated
• 2004 Launch and vehicle operations
• 2005 End of data collection He depletion
  Sept.
• 2007 Preliminary results presented at April APS
• 2008? Final results

6
Seeing General Relativity Directly
Red Raw flight dataBlue With torque modeling
(4 gyros co-processed)
Gyro 1. NS Inertial Orientation
Gyro 1 NS Inertial Orientation
-6
(arcsec)
-8
Geodetic effect marcsec/yr
-10
Einstein expectation 65711 4-gyro result
(1s) 6632 43 for 85 day processing(12
Dec 04 - 4 Mar 05) SQUID noise
limit (4-gyro) - 353 day continuous
0.12 - segmented data 0.5 0.9
10/30
12/19
02/07
03/29
05/18
07/07
Gyro 2 NS Inertial Orientation
Gyro 3 NS Inertial Orientation
6606 7 solar geodetic 28 1 GS proper
motion
Gyro 4 NS Inertial Orientation
1 marc-sec/yr 3.2?10-11 /hr(width of a human
hair seen from 10 miles)
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The CP-B Challenge

1. Gyroscope (G) 107 times better than best
   'modeled' inertial navigation gyros
2. Telescope (T) 103 better than best star trackers
3. G T lt 1 marcsec subtraction in pointing range
4. Gyro readoutcalibrated to 10-5

• Space
• Drag-free
• Roll spacecraft
• Cryogenics
• Magnetic readout shielding
• Thermal mechanical stability
• Ultra-high vacuum

8
Challenge 1 lt 10-11 /hr Classical Drift

• Seven near zeros
• Rotor inhomogeneities lt 10-6 (met)
• Drag-free (cross-track) lt 10-11 g (met)
• Rotor asphericity lt 10 nm (met)
• Magnetic field lt 10-6 gauss (met)
• Pressure lt 10-12 torr (met)
• Electric charge lt 108 electrons (met)
• Electric dipole moment 0.1 Vm (issue)

4.
2.
3.
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The GP-B Gyroscope

• 38 mm diameter rotor
• Fused quartz body
• niobium coating
• Fused quartz housing
• 6 circular suspension electrodes
• Superconductingpickup loop
• He spin-up channel
• UV electricdischarge system

"Everything should be made as simple as possible,
but not simpler." A. Einstein
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Gyro London Moment Readout
Pickup loop connection

• Requirements / goals
• SQUID noise 190 marcsec/Hz1/2
• Centering stability lt 50 nm
• DC trapped flux lt 10-6 gauss
• AC shielding gt 1012

DC SQUID package
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Challenge 2 sub-marcsec Telescope

• All fused quartz construction
• Physical length 35 cm
• Optical characteristics
• Focal length 3.9 m
• Aperture 14 cm
• Readout noise
• lt 34 marcsec/?Hz
• Pointing accuracy
• lt 0.1 marcsec

Primary Mirror
Secondary Mirror
Dual Si Diode Detector
Tertiary Mirror
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Challenges 3, 4 Matching Calibration

gyro output
telescope output

• Dither Slow 60 marcsec oscillations injected
  into pointing system
• Scale factors matched for accurate subtraction
• Aberration (Bradley 1729) Natures calibrating
  signal for gyro readout

• Orbital motion
• Varying apparent position of star (vorbit/c
  special relativity)
• Earth around Sun
• 20.4958 acrsec (1 yr period)
• Spacecraft around Earth
• 5.1856 arcsec (97.5 min period)

Continuous accurate calibration of GP-B experiment
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Guide Star IM Pegasi

• Selection criteria
• Close to equatorial plane
• Optically bright
• Radio star
• Proper motion measurement
• SAO measures GSposition via VLBI
• Calibrated againstextra-galacticsource (quasar)
• Defines very precisedistant inertial frame

Very Large Array, New Mexico
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GP-B Cryogenic Payload
Payload in ground testing at Stanford, August
2002
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GP-B Spacecraft

• Redundant spacecraft processors, transponders.
• 16 Helium gas thrusters, 0-10 mN ea. (6 DOF
  control)
• Magnetic torque rods for coarse orientation
  control
• Roll star sensors for fine pointing
• Magnetometers for coarse attitude determination
• Tertiary sun sensors for very coarse attitude
  determination
• Mass trim mechanism 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

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Launch 20 April, 2004 095724
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Boeing Luck
100 m from pole
Delta II 3s orbit
x
GP-B orbit
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Flight Operations
Gaylord Green
Anomaly room
Marcie Smith
Mission Operations Center
Marcie Smith (NASA Ames) Kim Nevitt (NASA
MSFC) Rob Nevitt (NavAstro) Brett Stroozas
(NavAstro) Lewis Wooten (NASA MSFC) Ric Campo
(Lockheed Martin) Jerry Aguinado (LM)
many more
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Gyro On-Orbit Initial Liftoff
Initial gyro levitation and de-levitation using
analog backup system
Suspension release
Rotor Position (µm)
Initial suspension
David Hipkins (HEPL) Yoshimi Ohshima (A/A)
Steve Larsen (LM) Colin Perry (LM)
many more
Gyro bouncing
Time (sec)
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1st Near ZeroMass Unbalance
Gyro 1 36 hr polhode period
lt 3?10-6
David Satniago (Physics) Michael Salomon (A/A)
Mass Unbalance (nm)
Gyro 1 2 3 4
Prelaunch estimate 18.8 14.5 16.8 13.5
On-orbit data 10.1 4.8 5.4 8.2
Paul Shestople Michael Dolphin (A/A)
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2nd Near Zero Drag-free

• Proportional thruster
• He boil off gas (Reynolds No 10)

Dan DeBra, John Bull (A/A), J-H Chen (A/A),
Yusuf Jafry (A/A), Jeff Vanden Beukel LM
Gravity gradient
Roll rate
Acceleration (m/sec2)
Cross-axis avg. 1.1 x 10-11 g
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Gyro Readout Performance On-Orbit
Peak-to-peak 24 arcsec
Gyro 3
Gyro Experiment Duration(days) SQUID Readout Limit (marc-s/yr)
1 353 0.198
2 353 0.176
3 353 0.144
4 340 0.348
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5th Near Zero Ultra-Low Pressure
Low Temperature Bakeout (ground demonstration)
GP-B Cyropump
Gyro spindown periods on-orbit
John Lipa, John Turneaure (Physics) students
adsorption isotherms for He at low temperature,
Eric Cornell, (undergrad honors thesis)
Gyro Before Bakeout (yr) After Bakeout (yr)
1 50 15,800
2 40 13,400
3 40 7,000
4 40 25,700
pressure 10-14 torr( patch-effect dampings)
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On-Orbit Verification 3 Phases

• Initial Orbit Checkout 128 days
• Re-verification of all ground calibrations
• Disturbance measurements on gyros low spin
• Science phase 353 days
• Exploiting built-in checks
• Natures helpful variations
• Post-experiment tests 46 days
• Refined calibrations through deliberate
  enhancement of disturbances, etc.

Surprise A Polhode-rate variations ? affect Cg
determinations Surprise B Larger than expected
misalignment torques Two mutually
reinforcing gremlins
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Surprise A Polhode Rate Variations

• 10-13 W power dissipation for spin axis motion
  from I1 (min) to I3 (max) in 1 year D. DeBra
• Model adds dissipation term to Euler eqns.
• No change in angular momentum alignment
• True energy dissipation with excellent fit to
  observed dissipation curves
• Rotor asymmetry parameter Q2determinations A.
  Silbergleit

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Polhode, Trapped Flux Cg

• Actual London moment readout
• Scale factor Cg modulated at polhode frequencies
  by trapped magnetic flux
• Two methods of determining Cg history
• Fit polhode harmonics to LF SQUID signal
• Direct computation by Trapped Flux Mapping

London field at 80 Hz 57.2 µG
Gyro 1 3.0 µG Gyro 2 1.3 µG Gyro 3
0.8 µG Gyro 4 0.2 µG
Trappedfields
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Surprise B Larger than Expected Misalignment
Torques

• Pointing to series of real virtual guide stars
• Duration 12 hours to 2 days
• Misalignment range 0.1 7

Drift-rate azimuthal linear to lt 2up to 1500
arcsec misalignment
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Patch Effect Detective Story

• Pre-launch investigation
• Rotor electric dipole moment field gradient in
  housing
• Kelvin probe measurements
• Contact potentialdifferences 100 mV
• Mitigated / eliminated by grainsize, lt 1 µm ltlt
  30 µm gap
• On-orbit observations
• Large misalignment torques
• Spin-down rates not consistent gas damping
• Z-bias acceleration 10-8 N modulated at polhode
  freq.
• and polhode damping
• Hypothosis
• Patch effect fields (surface layer with variable
  electric dipole moment density) on rotor AND
  housing interact

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GP-B Data Analysis Team
John Lipa
John Turneaure
Dan DeBra
Karl Stahl
Mike Adams
Sasha Buchman
Bill Bencze
Michael Heifetz
Bruce Clarke
Dave Hipkins
Tom Holmes
Mac Keiser
Jeff Kolodziejczak
Jie Li
Yoshimi Ohshima
Paul Shestople
Students
Vladimir Solomonik
Paul Worden
Alex Silbergleit
Barry Muhlfelder
Jonathan Kozaczuk Shannon Moore John Conklin
Michael Dolphin Matthew Tran Gregor Hanuschak Ed
Fei Michael Salomon Sara Smoot
Peter Boretsky
Suwen Wang
David Santiago
John Goebel
Francis Everitt, PI
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Geometric Separation of R µ Drifts

• Relativity, R
• Fixed direction ininertial frame
• Misalignment drift
• Torque ? to ?
• Drift ? to ?
• M. Keiser observation
• Component of R ? free of misalignment torques
• Component of R ? ? provideshistory of torque
  coefficient k
• ? modulated over year byannual aberration

Defines truly physical modeling process
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Geometric Approach

• Original mission concept
• ?? L t-3/2, t mission length
• Simple geometric approach
• ??g v2 L T-1 t-1/2,T batch length

Gyro 1 2 3 3
Original 0.198 0.176 0.144 0.348
Simple Geometric 19.8 17.6 14.4 33.5

• Power of geometric approach
• Clear proof of relativity separation
• Diagnostic tool for other potential
  disturbances
• Need to find way to recover t-3/2 dependence
• Algebraic Integral Geometric filtering
  procedures

32
Geometric vs. Algebraic Processing

• 1. Geometric, rate based
• Torque-free component of R determined from e.g.
  5-day batch-averaging
• 1.5. Integral geometric, orientation based
• Integral form of 1. ? Orientation over months
• Includes estimation for component ? to ?
• 2. Algebraic orientation based
• Also utilizes geometrical relationships, but with
• Explicit torque models continuous estimation /
  filtering
• Requires detailed history of gyro misalignment
  angle
• Status of methods 1. 2. as of April APS meeting

Geodetic effect 6638 97 marc-s/yr Frame-draggi
ng no definitive result
Geometric
Geodetic effect 6595 20 marc-s/yr Frame-draggi
ng tantalizing glimpses
Algebraic
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GSV/GSI Misalignment
Long-term mean uncertainty through mission lt 10
marcsec
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Data Analysis Adventure (since April 2007)

• May through August
• Progressive development use of algebraic
  machinery
• Consistent Floor 1 / Floor 2 processing
• Gyro orientation profiles based on 5-day moving
  window
• Common relativity, roll-phase offset vehicle
  pointing inputs for 4 gyros
• Some encouraging results but limitations lead to
  intensive investigation of 45-day period (1 Jan -
  15 Feb 2005)
• Trapped Flux Mapping (the event of August 17)
• Insertion of TFM Polhode Phase into Algebraic
  Method
• Immediate dramatic improvement to 45-day results
• Successful extension to 85-day period

Transition from interesting glimpses to robust
results
35
TFM Advances Since APS meeting

• TFM Use HF SQUID data to
• Solve for gyro motion (polhode spin)
• Fit magnetic potential (linear)
• Compute Cg
• Gyro motion
• Spin speed to 10 nHz(x1000 improvement)
• Spin-down 1 pHz/s(x100 improvement)
• Polhode Phase 2(x100 improvement)
• Magnetic potential

Gyro 1
µ gauss-cm
36
Scale Factor Cg (10 Nov 2004)
Independent determination agrees to lt 0.1 of
total Cg
37
Algebraic 4-gyro Relativity Estimate
  Earth Solar Geodetic Proper Motion Net Expected
NS -6606 7 28 1 -6571 1
EW -39 -16 -20 1 -75 1
85-day result RNS -6632 43 marc-s/yr RWE
-82 13 marc-s/yr
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Data Analysis Path to Completion

• Extended Algebraic results to 270-307 day period
• Make Integral Geometric method fully functional
  cover same period
• Final critical evaluation of systematics

• Expected / hoped for (!) final accuracy
• t -3/2 going from 85 to 307 days ? 6.8x
  improvement
• Cg from full TFM ? 2x improvement
• Proper treatment of systematics ? 1 to 2
  marcsec/yr final limit

Final double blind comparison with HR8703
proper motion data
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International Collaboration

• Stanford University Development, SI,
  Management,C.W.F. Everitt PI, GP-B team Mission
  Ops, Data Analysis
• Lockheed Martin Probe, Dewar, Spacecraft
  busGP-B team Flight software
• NASA
• Other Institutions
• Science Advisory CommitteeCliff Will chair
• Harvard Smithsonian Star Proper motion
  studiesIrwin Shapiro
• JPL Independent Data AnalysisJohn Anderson
• York University Star Proper motion studies
  Norbert Bartel
• Perdue University Helium Ullage BehaviorSteve
  Collicot
• San Francisco State Gyroscope readout topicsJim
  Lockhart
• National University of Ireland Proton
  monitorSusan M. P. McKenna-Lawlor
• University of Aberdeen Precision Quartz
  Homogeneity Mike Player Measurement