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Page 1 GPB Overview HEPL Seminar, June 17, 2009
Gravity Probe BOverview
Barry Muhlfelder
June 17, 2009
HEPL-AA Seminar
Page 2 GPB Overview HEPL Seminar, June 17, 2009
Geodetic EffectSpace-time curvature ("the missing inch")
Frame-dragging EffectRotating matter drags space-time ("space-time as a viscous fluid")
The Relativity Mission Concept
( ) ( ) ⎥⎦⎤
⎢⎣⎡ −⋅+×= ωRωRvR 23232
323
RRcGI
RcGMΩ
Quartz block
Gyro 1Gyro 2Star Tracking
TelescopeGuide
Star
Gyro 3Gyro 4Mounting
Flange
Page 3 GPB Overview HEPL Seminar, June 17, 2009
Launch: April 20, 2004 – 09:57:24
Stanford Mission Operations Center
Page 4 GPB Overview HEPL Seminar, June 17, 2009
Quartz Block
Measurement of Gyroscope Orientation Relative to Position of Guide Star
Gyro
Gyro Electronics TelescopeElectronics
Telescope
Roll Star Reference
HR8703(IM PEG)
SQUID
Roll: 77.5 seconds
gyroProbe
Telescope
GuideStar
Dewar
Bill Fairbank– “It’s just a star, a
telescope, & a spinning sphere”
spin axis
Page 5 GPB Overview HEPL Seminar, June 17, 2009
Space- reduced support force, "drag-free" - roll about line of sight to star
Cryogenics- magnetic readout & shielding- thermal & mechanical stability- ultra-high vacuum technology
The GP-B ChallengeGyroscope (G) 107 times better than best 'modeled' inertial navigation gyrosTelescope (T) 103 times better than best prior star trackersGyro Readout calibrated to parts in 105
G – T <1 marc-s subtraction within pointing range
Basis for 107 advancein gyro performance
Page 6 GPB Overview HEPL Seminar, June 17, 2009
The GP-B Gyroscope
• Electrical Suspension
• Gas Spin-up
• Magnetic Readout
• Cryogenic Operation
Page 7 GPB Overview HEPL Seminar, June 17, 2009
Seven Near Zeros
• "Drag-free" (cross track) < 10-11 g met
• Rotor inhomogeneities < 10-6 met
• Rotor asphericity < 10 nm met
• Magnetic field < 10-6 gauss met
• Pressure < 10-12 torr met
• Electric charge < 108 electrons met
• Electric dipole moment 0.1 V-m issue
Challenge 1: < 10-11 deg/hr Classical Drift
6
4
53
2
1
Page 8 GPB Overview HEPL Seminar, June 17, 2009
GP-B Performance
Space improves gyro accuracyby > 50,000,000!
Why go to space?
Gyroscope drift ≤ 0.05 marcsec/yr
Readout error effect≤ 0.08 marcsec/yr
Guide star uncertainty≤ 0.09 marcsec/yr
Page 9 GPB Overview HEPL Seminar, June 17, 2009
~ 5 x 10-7
drift-rate for the drag-free GP-B< 0.01 marc-s/yr
Drift-rateTorqueMoment of Inertia
Ω = T / Iωs
T = M ƒ δrI = 2/5 Mr2
ƒ
δr
requirement Ω < Ω0 ~ 0.1 marc-s/yr
δrr ƒ < vs Ω0
25
vs = ωsr = 950 cm/s (80 Hz)
(1.54 x 10-17 rad/s)
On Earth (ƒ = g)
Standard satellite (ƒ ~ 10-8 g)
GP-B drag-free (ƒ ~ 10-12 gcross- track average)
< 5.8 x 10-18
< 5.8 x 10-10
< 5.8 X 10-6δrr
δrr
δrr
δrr
Drag-free eliminates mass-unbalance torque -- and key to understanding/quantification of other support torques
(ridiculous)
(unlikely)
(straightforward)
Mass-Unbalance & Drag-Free
All GP-B rotors mass unbalance < 10 nm (2 cm radius) or
Page 10 GPB Overview HEPL Seminar, June 17, 2009
Mass Unbalance & Drag Free On-orbit Results
Acc
eler
atio
n (m
/sec
2 )
0 20 40 60 80 100 120
-10
0
10
Science Gyro Position
Pos
ition
(nm
)
0 20 40 60 80 100 120-100
-50
0
50
100Science Gyro Control Effort
Forc
e (n
N)
0 20 40 60 80 100 120-5
0
5Space Vehicle Thrust
Minutes Since 08/22/2005 18:05
Forc
e (m
N)
Vehicle XVehicle YVehicle Z
Vehicle XVehicle YVehicle Z
Vehicle XVehicle YVehicle Z
Drag free off
Drag free on
10-4
10-3
10-2
10-1
10010
-11
10-10
10-9
10-8
10-7
10-6
Frequency (Hz)
Con
trol
effo
rt, m
/sec
2
Gyro 1 - Space Vehicle and Gyro Ctrl Effort - Inertial space (2005/200, 14 days)
X Gyro CE
X SV CE
2×Orbit
Cross-axis avg.1.1 x 10-11 g
Gravity gradient Roll
rate
0 20 40 60 80 100 120 140 160 1800
1
2
3
4
5
6
7
Elapsed Minutes since Vt = 147228407.1 s
Am
plitu
de (n
m)
Sample Polhode Period, Gyro 1
Rotor Mass Unbalance < 10 nm for all gyros
Drag Free (cross-track 10-11 g )
Page 11 GPB Overview HEPL Seminar, June 17, 2009
Challenge 2: Sub-milliarc-s Star Tracker
Detector Package
Dual Si Diode Detector
Page 12 GPB Overview HEPL Seminar, June 17, 2009
Telescope Detector Signals from IM Peg Divided by Rooftop Prism
-2
0
2
4
6
8
10
12
14
0 100 200 300 400 500 600
Sample Sequence
ST_SciSlopePX_B ST_SciSlopeMX_B
Star Tracking Telescope: On-Orbit
Feedback control maintains spacecraft pointing at balance pt
(~20 marcsec inertially).
Page 13 GPB Overview HEPL Seminar, June 17, 2009
Challenge 3: Gyro Readout
SQUID noise 190 marc-s/√HzCentering stability < 50 nmDC trapped flux < 10-6 gaussAC shielding > ~ 1012
Requirement
“SQUID” 1 marc-s in 5 hours
4 Requirements/Goals
Page 14 GPB Overview HEPL Seminar, June 17, 2009
Challenge 3: Gyro Readout Calibration
Peak to peak ~ 24 arc-sec
Aberration
Measurement System
Aberration: A Natural Calibration
Orbital motion varying apparent position of star Cause: transverse velocity of telescope to starlight
(vorbit/c + special relativity correction)
S/V around Earth -- 5.1856 arc-s @ 97.5-min periodEarth around Sun -- 20.4958 arc-s @ 1-year period
zero aberration pt.
max. aberration
Page 15 GPB Overview HEPL Seminar, June 17, 2009
G – T <1 marc-s subtraction within pointing range
gyro output
scale factors matched for accurate subtraction
telescope output
Dither -- Slow 60 marc-s oscillations injected into pointing system
Challenge 4: Gyro-Telescope Matching
How do we subtract imperfect telescope pointing from the gyro signal?
Scale factor matching allows G-T subtraction to < 1 marcsec
Page 16 GPB Overview HEPL Seminar, June 17, 2009
Actualities of GP-B
gyroscopes105 times better than best inertial navigation gyroscopes
SQUID noise < expected
Trapped magnetic flux meets spec
excellent charge control & centering stability
τ's ~ 7200 to 26,100 years
telescopesuperb overall performance
dewarbeats design hold time
orbit within 100 m of ideal
polhode rate variation
misalignment torque
resonance torque
Less than idealGood
segmented data
interference from ECU
out-of-spec pointing
Systematics & data grading
New Challenge
Page 17 GPB Overview HEPL Seminar, June 17, 2009
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5Sine and Cosine at Roll Frequency, Gyro 2, Res 277
Cos
ine
of R
oll F
requ
ency
(mV)
Sine of Roll Frequency (mV)
North
West
Approximate Scale:
50 mas
A. Polhode rate variations affect scale factor (Cg) determinations
Discovered in early science phaseAlex Silbergleit talk July 1
B. Misalignment torquesDiscovered in post-science
calibration phaseMac Keiser talk next week
C. Roll-polhode resonance torquesDiscovered during data reduction phaseMac Keiser talk next week
Polhode Period (hours) vs Elapsed Time(days) since January 1, 2004
Mean WE Misalignment
Mea
n N
S
Mis
alig
nmen
t
1000200030004000
30
210
60
240
90
270
120
300
150
330
180 0
0 500100015002000250030003500400000.5
11.5
22.5
33.5
4
Drif
t Rat
e M
agni
tude
Challenge 5: Data Analysis Subtleties
All due to one physical cause (patch effect)
Blue - Worden
Red - Santiago & Salomon
Polhode Period (hours)
Misalignment
Misalignment torque structure
Roll-polhode resonance path
Page 18 GPB Overview HEPL Seminar, June 17, 2009
Evolving Polhode Impact onActual London Moment Readout
Trapped fields
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
Trapped flux contributes to readout scale factor• Expected prior to launch• Adds to London Moment scale factor• Trapped flux scale factor modulated by body dynamics (polhode)• Evolving polhode prevents averaging or other simple analysis technique
Trapped Flux Moment
MLMT
GyroDynamics(spin & polhode)
Page 19 GPB Overview HEPL Seminar, June 17, 2009
Trapped Flux Mapping: Cg DeterminationI3
I2I1
ωs→
ωs→
6 Sept 2004
14 Nov 2004
polhodeTFM determines evolving polhode
phase to 1° over the full missionFully resolves gyro scale factorCrucial input for torque analysis
Nov. 2007, Gyro 1, Fit residuals = 14% Aug. 2008, Gyro 1, Fit residuals = 1%
Alex Silbergleit John Conklin Mac Keiser(Ballhaus AA award)
Page 20 GPB Overview HEPL Seminar, June 17, 2009
Pre-launch investigationRotor electric dipole moment + field gradient in housing100 mV contact potentials mitigated by minute grain size,
0.1 μm << 30 μm rotor-electrode gap
Kelvin probe measurements on flat samples
On-orbit discoveries (Sasha Buchman talk next week)Polhode damping (July 2004)Drag-free z acceleration ( Sept. 2004)Spin down rate > gas damping (Feb. 2005)Misalignment torques (Aug. 2005)
Roll-polhode resonance torques (Jan. 2007)
Post-launch ground-based investigationsWork function profile via UV photoemission Detailed analytical modeling
SEM image of rotor Nb film average grain size 0.1 μm
0.20.250.3
0.350.4
0.450.5
0.550.6
0.65
12 3 4
56
789101112
1314
1516
17181920
21222324
2526
2728
293031323334
3536
3738 39 40
Work function polar plot
The GPB 'Patch Effect' History
rotor surface
housing surface
Page 21 GPB Overview HEPL Seminar, June 17, 2009
Origin of Misalignment & Resonance Torque
1. Expand rotor & housing potentials• Using spherical harmonics
2. Derive stored energy• Laplace’s equation • Between rotor & housing
3. Find torque: Derivative of the energy • WRT angles defining the spin orientation• Spin average
Roll ave. torque proportional & perpendicular to misalignmentNon roll averaged torque when polhode harmonic = roll freq.
These torques follow directly from randomly distributed patch potentials
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5Sine and Cosine at Roll Frequency, Gyro 2, Res 277
Cos
ine
of R
oll F
requ
ency
(mV)
Sine of Roll Frequency (mV)
North
West
Approximate Scale:
50 mas
Mean WE Misalignment
Mea
n N
S
Mis
alig
nmen
t
1000200030004000
30
210
60
240
90
270
120
300
150
330
180 0
0 500100015002000250030003500400000.5
11.5
22.5
33.5
4
Drif
t Rat
e M
agni
tude
Misalignment
Misalignment torque structure
Roll-polhode resonance path
Page 22 GPB Overview HEPL Seminar, June 17, 2009
Treating Misalignment TorqueThe 2 Methods
Algebraic: Filtering machinery to explicitly model torques provides separation from relativity
Geometric: Plot rates against misalignment phase Φcomponent of relativity free of misalignment torques
• Drift rate free of torque parallel to misalignment
• Annual aberration alters torque direction• Over time provides geodetic & FD measurement
• A truly physical modeling process
A Geometrical Insight
Mac Keiser
.
UnperturbedNS drift geodetic Unperturbed
linear combination
UnperturbedEW drift (FD)Φ
Gyro misalignment & unperturbed relativity measurement
Page 23 GPB Overview HEPL Seminar, June 17, 2009
0 1 2 3 4 5 6- 4 0
- 3 5
- 3 0
- 2 5
- 2 0
- 1 5
- 1 0
- 5
0
5
1 0
NS
(arc
-s)
G y r o 1 M i s a l i g n m e n t - 2 0 0 5 / 0 0 1 - 0 0 : 0 1 : 0 8 . 0 - 4 O r b i t s
G S VG S I
0 1 2 3 4 5 6- 4 0
- 3 5
- 3 0
- 2 5
- 2 0
- 1 5
- 1 0
- 5
0
5
1 0
t i m e ( h o u r s )
WE
(arc
-s)
-40 -35 -30 -25 -20 -15 -10 -5 0 5 10-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
WE (arcs)
NS
(arc
s)
GYRO 1 Misalignment - 2005/001-00:01:08.0 - 4 Orbits
GSI
GSV
NS & WE vs time NS vs WE
GSVGSI
GSIGSV
• Required to remove effect of misalignment torque
• Science gyroscopes provide precision misalignment information when guide star occulted
Continuous Guide-Star Valid / Guide-Star Invalid misalignment history
Obtaining Continuous Misalignment History
Page 24 GPB Overview HEPL Seminar, June 17, 2009
Early Methods for treating Resonance Torque
1.66 1.67 1.68 1.69 1.7 1.71 1.72 1.73 1.74 1.75
x 108
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
Time (seconds) spans March 1- July 1
Drif
t rat
e
(arc
sec
/yr)
Gyro #2 West/East Drift Rates
Blue: Resonances not mitigated (SAC 15)Red: Resonances mitigated (SAC 16) Vertical dotted: Resonance times
1. Excise data during resonancesBlue curve shows large drift during resonancesRed curve eliminates spikes by excising data
2. Model drift during resonancesA unique drift rate during eachA separate drift rate elsewhere
Page 25 GPB Overview HEPL Seminar, June 17, 2009
Gyro 3
Gyro 4
Gyro 1
Gyros 1, 3, 4 combined
GR prediction
Early Results [Nov ’07]
GR prediction
Gyro 3
Gyro 4
Gyro 1
Gyros 1, 3, 4 combined
Page 26 GPB Overview HEPL Seminar, June 17, 2009
Resonance Torque Modeling LimitationsIssue: High sensitivity for resonance torque modeling (2007)
• Leading term in experiment error (relativity rate scatter)
First result based upon excluding data within resonance periods
Second result: 3x smaller (but still large) sensitivity by linear fit during resonance periods
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5Sine and Cosine at Roll Frequency, Gyro 2, Res 277
Cos
ine
of R
oll F
requ
ency
(mV)
Sine of Roll Frequency (mV)
North
West
Approximate Scale:
50 mas
5660 5680 5700 5720 5740 5760-2
-1
0
1
2Cosine of Roll After Removing DC and Linear Drift, Gyro 2, Res 277
mV
5660 5680 5700 5720 5740 5760-2
-1
0
1
2Sine of Roll
mV
Orbit Number
Gyroscope 2 From: May 10, 2005, 2amTo: May 15, 2005, 5 pm
1 day
50 mas
Next step: Once per orbit model improves sensitivity & experiment error
Modeled
drift
Actual
Drift
Page 27 GPB Overview HEPL Seminar, June 17, 2009
Improved Resonance Torque Modeling
Path predicted from rotor & housing potentials• Roll averaging fails when ωr = nωp
• Orientations follow Cornu spiral
• Magnitude & direction depend on patch distribution, roll & polhode phasesat resonance
Example: Gyro 2, Resonance 277 – Oct 25, ’04
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5Sine and Cosine at Roll Frequency, Gyro 2, Res 277
Cos
ine
of R
oll F
requ
ency
(mV)
Sine of Roll Frequency (mV)
North
West
Approximate Scale:
50 mas
Jeff Kolodziejczak Alex SilbergleitMac Keiser Michael Heifetz Vladimir Solomonik
Page 28 GPB Overview HEPL Seminar, June 17, 2009
The Science Equations [Aug 2008]
Treatment of roll-polhode term hinges on TFM
• Add resonance torque model to equations of motion• Follows directly from randomly distributed patch potentials
Resonance torqueMisalignment torqueRelativity
• Resonance condition
Page 29 GPB Overview HEPL Seminar, June 17, 2009
Resonance Torque Modeling Implementation
Torque coefficients tied to gyro body
TFM provides accurate body dynamics profile• γp φp (in addition to readout scale factor)
• TFM: body fixed trapped flux as marker
• Torque model uses TFM polhode
• Requires accuracy for tracking high order polhode harmonics
Body dynamics determined from TFM is KEY
Page 30 GPB Overview HEPL Seminar, June 17, 2009
N-S (Geodetic) E-W (Frame-dragging)
G1
G2
G3
G4
(note: different y-axis scale for N-S vs. E-W)
Full Model Results as of Dec ’08
Page 31 GPB Overview HEPL Seminar, June 17, 2009
Full Model Results as of Dec ’08
Page 32 GPB Overview HEPL Seminar, June 17, 2009
Full Model Results as of Dec ’08 - II
Requires incorporation of systematic uncertainty evaluation
Page 33 GPB Overview HEPL Seminar, June 17, 2009
RNS & RWE – Gyro #4
Gravitational deflection of light
24.6487-day guide star orbital motion
-50 0 50 100 150 200 250-5
0
5
10
15
20North-South Deflection of Light
milli
-arc
-sec
-50 0 50 100 150 200 250-10
0
10
20West-East Deflection of Light
milli
-arc
-sec
Time (days) from Jan. 1, 2005
0.17 20.1 ±=λ
Independent SuperGeometric Results
Result to date
1
3
2
mas/yrRmas/yrR
WE
NS
14 7716 6631
±−=±−=
masbmasamasbmasa
WEWE
NSNS
13.061.0 12.011.0 14.036.0 14.065.1
±−=±−=±−=±−=
Page 34 GPB Overview HEPL Seminar, June 17, 2009
Advanced Investigations of Systematics
• Improved science modeling• Exact treatment of readout nonlinearities
• Thermal correlations
• 2-sec processing
• Detailed gyro-to-gyro comparisons
Page 35 GPB Overview HEPL Seminar, June 17, 2009
Are we done?• Current ‘2 floor’ 4-gyro result ~ 5 marcs/yr (statistical uncertainty)
once-per-orbit time step3 out of 10 segments (158 days vs. 333 days)limited by
• Fundamental & operational limitsSQUID noise 0.14 – 0.35 marcs/yr (gyro dependent)Covariance ~ 1-2 marcs/yr (4 gyros combined)
Accurate integration requires time step << 1 orbit parallel processing
9 marcs p-p
variation
Gyro 2: Orientation EW (worst case example)
Note: noiseless trajectory shown.
Noise must be added for complete evaluation
Page 36 GPB Overview HEPL Seminar, June 17, 2009
Advanced (2-sec) Filter Development
Serial processing accuracyaccuracybuilt on 4-years’ experience with 2-floor (once per orbit) filteraccurately models the physical phenomenahas passed truth test
Parallel processing speedspeed~ 10x faster (3 day analysis → overnight)requires computer cluster~ 10% modified/additional code
Talk by Michael Heifetz July 29
Two simultaneous development activities
1
2
Co-PI Charbel Farhat
Michael Heifetz Badr Alsuwaidan Majid Almeshari John Conklin Vladimir Solomonik
Page 37 GPB Overview HEPL Seminar, June 17, 2009
Upcoming GPB Talks
June 24 Sasha Buchman Evidence for patch effectMac Keiser Torques & analysis treatment
July 1 Alex Silbergleit Trapped flux mapping
July 29 Michael Heifetz Data Analysis Past, Journey
Page 38 GPB Overview HEPL Seminar, June 17, 2009
Serial 2-sec processing (applied to data subset) Aug ’09
Complete transition to parallel processing Oct ’09
Extension from 5, 6, 9 (applied to full data set) Dec ’09
Complete treatment of systematics Jan ’10
Blind test against SAO guide star orbital motion Feb ’10
Grand synthesis of Geometric & Algebraic resultsapproach ~ 1-2 marcs/yr 4-gyro limit Jun ’10
Path to Completion
Final results to be announced at Fairbank Workshop onFundamental Physics & Innovative Engineering in Space Aug ’10