gravity probe b overview · gyro 1 3.0 μg gyro 2 1.3 μg gyro 3 0.8 μg gyro 4 0.2 μg trapped...

GPB Overview HEPL Seminar, June 17, 2009

Gravity Probe BOverview

Barry Muhlfelder

June 17, 2009

HEPL-AA Seminar


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


Launch: April 20, 2004 – 09:57:24

Stanford Mission Operations Center


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


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


The GP-B Gyroscope

• Electrical Suspension

• Gas Spin-up

• Magnetic Readout

• Cryogenic Operation


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


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


~ 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


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



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 )


Challenge 2: Sub-milliarc-s Star Tracker

Detector Package

Dual Si Diode Detector


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).


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


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


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


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


-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


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)


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)


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


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


Cos

ine

of R

oll F

requ

ency

(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


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


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


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


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


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


Cos

ine

of R

oll F

requ

ency

(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


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


Cos

ine

of R

oll F

requ

ency

(mV)


North

West

Approximate Scale:

50 mas

Jeff Kolodziejczak Alex SilbergleitMac Keiser Michael Heifetz Vladimir Solomonik


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


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


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


Full Model Results as of Dec ’08


Full Model Results as of Dec ’08 - II

Requires incorporation of systematic uncertainty evaluation


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

±−=±−=±−=±−=


Advanced Investigations of Systematics

• Improved science modeling• Exact treatment of readout nonlinearities

• Thermal correlations

• 2-sec processing

• Detailed gyro-to-gyro comparisons


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


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


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


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

gravity probe b overview · gyro 1 3.0 μg gyro 2 1.3 μg gyro 3 0.8 μg gyro 4 0.2 μg trapped...

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