The Gravity Probe B Detective Story · Page 7 The Gravity Probe B Detective Story Presentation to Dr. Turki Al-Saud – May 26, 2009 Actualities of GP-B z gyroscopes 106 times better

Page 1 The Gravity Probe B Detective StoryPresentation to Dr. Turki Al-Saud – May 26, 2009

Francis Everitt

May 26, 2009

The Gravity Probe B Detective Story

Dr. Turki Al-SaudVice President for Research Institutes

KACST

Presentation to


Geodetic EffectSpace-time curvature ("the missing inch")

Frame-dragging EffectRotating matter drags space-time ("space-time as a viscous fluid")

Orbiting Gyroscopes & Einstein

( ) ( ) ⎥⎦⎤

⎢⎣⎡ −⋅+×= ωRωRvR 23232

323

RRcGI

RcGMΩ

Quartz block

Gyro 1Gyro 2Star Tracking

TelescopeGuide

Star

Gyro 3Gyro 4Mounting

Flange

Mach

Thirring

Schiff

http://images.google.com/imgres?imgurl=http://aeiou.iicm.tugraz.at/aeiou.encyclop.data.image.t/t392376a.jpg&imgrefurl=http://aeiou.iicm.tugraz.at/aeiou.encyclop.t/t392376_ge.htm&h=400&w=267&sz=20&hl=en&start=35&um=1&tbnid=fqOmVPDhkEi7XM:&tbnh=124&tbnw=83&prev=/images%3Fq%3Dwalter%2Bthirring%26start%3D18%26ndsp%3D18%26svnum%3D10%26um%3D1%26hl%3Den%26sa%3DN


10/30 12/19 02/07 03/29 05/18 07/07

-10

-8

-6

arcs

ec

Gyro 1. NS Inertial Orientation

10/30 12/19 02/07 03/29 05/18 07/07-2

0

2

4

arcs

ec


10/30 12/19 02/07 03/29 05/18 07/070

2

4

6

arcs

ec


10/30 12/19 02/07 03/29 05/18 07/070

2

4

arcs

ec


Seeing GR in ‘Raw’ Data

Gyro 4: NS Inertial Orientation




Einstein expectation - 6571 ± 1*

4-gyro result (1σ) - 6578 ± 97 ≤ 97 marc-s/yr estimate based on gyro-to-gyro

disagreements & other systematics

SQUID noise limit (4-gyro)- 353 day continuous ± 0.12- segmented data ± 0.5 - 0.9

marc-s/yr

* -6606 + 7 solar geodetic + 28 ± 1 guide starproper motion

Geodetic effect

0.1 marc-sec/yr = 3.2 × 10-12 deg/hr –width of a human hair seen from 100 miles


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 4 +1 GP-B Challenges

Gyroscope (G) 107 times better than best 'modeled' inertial navigation gyrosTelescope (T) 103 times better than best prior star trackersG – T <1 marc-s subtraction within pointing rangeGyro Readout calibrated to parts in 105

Basis for 107 advancein gyro performance

ad hoc vs physics-basedModeling5th Challenge


Challenges 1 & 2: Gyro & Telescope

Detector Package

Si Diode Detector


gyro output

scale factors matched for accurate subtraction

Aberration -- Nature's calibrating signal for gyro scale factor Cg

telescope output

Dither -- Slow 60 marc-s oscillations injected into pointing system

Challenges 3 & 4: Matching & Calibration

Continuous accurate calibration of GP-B experiment

Orbital motion varying apparent position of star (vorbit/c + special relativity correction)

Earth around Sun -- 20.4958 arc-s @ 1-year periodS/V around Earth -- 5.1856 arc-s @ 97.5-min period


Actualities of GP-B

gyroscopes

106 times better than best inertial navigation gyroscopes

SQUID noise < expected

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

Gremlins, data grading & systematics

5th Challenge


A. Polhode-rate variationsA big surprise in early science phaseComplicates Cg determination

B. Misalignment torquesPointing to other stars gives

much-bigger-than-expected gyro drifts

C. Resonance torquesGyro-to-gyro comparisons reveal periodic jumps in individual gyro orientations

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

3 Gremlins

All due to one cause (patch effect)

Blue - Worden

Red - Santiago & Salomon

Polhode Period (hours)

Misalignment

Misalignment torque structure

-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

Roll-polhode resonance path


Roundness & Out-of-Roundness

Mechanical – Good & Essential1

Rotor ~ 5 x 10-7 Housing ~ 4 x 10-6

Electrical – Bad & Very Unexpected2

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

Large sideways forces from ‘patch effect’ voltages

Magnetic – Seemingly Bad, Miraculously Good!3Rotor ~ 0.4% - 5% of London Moment

I2I1

I3polhode ωs→

ωs→

6 Sept 2004

14 Nov 2004

Trapped Flux

Mapping

Gyro Contours

rotor surface

housing surface


3 Breakthroughs

1

2

3

Aug 2006: ‘Geometric’ Method [Gremlin B]

Aug 2007: Trapped Flux Mapping [Gremlins A & C]

Aug 2008: Full Torque Modeling [Gremlins B & C]


Breakthrough 1 [Aug ’06]

µ

The 2 MethodsGeometric: Change variables to plot rates against misalignment phase

component of relativity free of misalignment torques

Algebraic: Filtering machinery to explicitly model torques provides separation from relativity

• Annual aberration alters misalignment torque direction• A truly physical modeling process

A Geometrical Insight

Mac Keiser


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 μGTrapped Flux

Moment

MLMT

Ideal vs. Actual ML ReadoutRotorDynamics

Detailed Trapped Flux Mapping (TFM)

John Conklin Michael Dolphin Michael Salomon

3 K

ey S

tude

nts


Breakthrough 2 [Aug ’07]

TFM determines evolving polhode phase to 1° over the full mission

Resolves scale factor issueCritical input for torque analysis

– Prior to Aug ’07

– Initial TFM treatment

Accurate Cg Determination

batch processing, large scatter

100σ to 6σ to 2σTom Holmes


Gyro 3

Gyro 4

Gyro 1

Gyros 1, 3, 4 combined

GR prediction

After Breakthroughs 1 & 2 [Nov ’07]

GR prediction

Gyro 3

Gyro 4

Gyro 1



Breakthrough 3 [Aug 2008]

Treatment of roll-polhode term hinges on TFM

• Add resonance torque model to equations of motion

Resonance torqueMisalignment torqueRelativity

• Resonance condition


Resonance Torque Dynamics

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


N-S (Geodetic) E-W (Frame-dragging)

G1

G2

G3

G4

Full Model Results as of Dec ’08 - I


Full Model Results as of Dec ’08 - II


Gyro 3

Gyro 4

Gyro 1


GR prediction

After Breakthroughs 1 & 2 [Nov ’07]

GR prediction

Gyro 3

Gyro 4

Gyro 1



Full Model Results as of Dec ’08 - II

From once-per-orbit to 2-sec processing


RNS & RWE

Best so far for Gyro #4

Gravitational deflection of lightNearest approach to Sun

Date: March 11 Ecliptic Latitude: 22.1°

24.65-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 Geometric Results

Result to date

1

3

2

mas/yrR mas/yrR

WE

NS

14 7716 6631

±−=±−=

masbmasamasbmasa

WEWE

NSNS

13.061.0 12.011.0 14.036.0 14.065.1

±−=±−=±−=±−=


Are we done?• Current ‘2 floor’ 4-gyro result ~ 5 marcs/yr

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 marcs/yr (4 gyros combined)

Accurate integration requires time step << 1 orbit parallel processing


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 – Badr Alsuwaidan

Parallel processing speedspeed~ 10x faster (3 day analysis → overnight)requires computer cluster~ 10% modified/additional code – Majid Almeshari

Two simultaneous development activities

1

2

Co-PI Charbel Farhat


Serial 2-sec processing (segments 5, 6, 9) Aug ’09

Complete transition to parallel processing Oct ’09

Extension from 5, 6, 9 to all segments Dec ’09

Complete treatment of systematics Feb ’10

Grand synthesisapproach ~ 1 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


Heritage of GP-B for KACST-Stanford

Technologies

Vehicle & active control center(B. Muhlfelder)

Precision ATC(J. Mester)

STEP(P. Worden, J. Mester)

Documents

The Gravity Probe B Detective Story · Page 7 The Gravity Probe B Detective Story Presentation to Dr. Turki Al-Saud – May 26, 2009 Actualities of GP-B z gyroscopes 106 times better