Gravity Probe B – Testing General Relativity with Orbiting ... · Gravity Probe B – Testing...

GGI Workshop 2006 1GP-B T0083

Gravity Probe B – Testing General Relativitywith Orbiting Gyroscopes

Int’l Workshop on Precision Tests and Experimental Gravitation in SpaceGalileo Galilei Institute, Firenze, Italy; Sep 28-23, 2006

William Bencze, GP-B Program Managerfor the GP-B Team

GP-B T0082


Outline

• Gravity Probe B– Description of the experimental concept– Difficult requirements and key enabling technologies.– Status of post-flight data analysis

• STEP Mission Update


Testing GR with Orbiting Gyroscopes

( ) ( ) ⎥⎦⎤

⎢⎣⎡ −⋅+×= ωRωRvR 23232

323

RRcGI

RcGMΩ

Geodetic, ΩG Frame Dragging, ΩFD

Leonard Schiff’s relativistic precessions:

“If, at first, the idea is not absurd, then there

is no hope for it.”

- Albert Einstein

ddt

= ×s Ω sSpin axis orientation:


How Big is a 0.1 Milli-Arc-Second?

0.1 marc-sec

0.1 marc-sec = Angular width of

Lincoln’s eye in New York seen from Paris!


Einstein’s 2 1/2 TestsPerihelion Precession of Mercury

• GR resolved 43 arc-sec/century discrepancy.

Deflection of light by the sun• GR correctly predicted 1919 eclipse data.• 1.75 arc-sec deflection: Present limit 10-3

Gravitational Redshift: Equivalence Principle• Einstein’s “half test’ – Equivalence principle only• 1960 Pound-Rebka experiment (ground clocks)• 1976 Vessot-Levine GP-A (orbiting clocks): 2 × 10-4

Tests of General Relativity to date rely on astronomical measurements, not a laboratory

experiment under scientist's control.


102

10

1

0.1

0.01

6614

41

0.5

0.12

Geodetic effect <0.002% accuracy

Frame dragging<0.3% accuracy

GP-B requirement

Single gyro expectation

4 Gyro expectation(3x10-10 deg/√hr)

103

0.21m

arc-

s / y

r

103

104

105

106

107

108

109

1010

Best laser gyro (10-3 deg/hr)

Electrostatic vacuum gyro on Earth uncompensated (10-1 deg/hr)

Electrostatic vacuum gyro on Earth (torque modeling) (10-5 deg/hr)

Why a Space-based Experiment?

mar

c-s

/ yr

Spacecraft gyros(3x10-3 deg/hr)

Expected GP-B performance on orbit

Operation in 1g environment degrades mechanical gyro performanceLaser gyroscopes and other technologies fidelity too low for GP-B

Cold Atom Gyro (3x10-6 deg/√hr)(Kasevich 2006)


The “simplest experiment”

1. “Spinning Sphere” Perfect Gyros Drift < 0.1 marc-sec/yr– Perfect mass balance < 20 nm mass unbalance– Roundest spheres < 20 nm p-v– Gentle gyroscope suspension 200 mV – Gyroscope centering control ~ 1 nm– Precise initial gyro orientation < 10 arc-sec– Cross axis force control ~ 10-12 g cross-axis “drag free”– Spin down torques (gas drag) < 10-9 Pa – Rotor electrical charge < 15 mV– Orientation readout: low noise SQUIDS ~ 200 marc-sec/√Hz– Magnetic Shielding 240 dB shielding– Cryogenics, superfluid He dewar 2500 liter @ 1.8K

“No mission could be simpler than Gravity Probe B. It’s just a star, a telescope, and a spinning sphere.”

- William Fairbank, GP-B PI (ca. 1964)


The “simplest experiment” 2

2. Telescope – Accurate pointing < 0.1 marc-sec/yr– Precision vehicle pointing ~5 marc-sec– Low measurement noise ~ 34 marc-sec/√Hz– Mechanically “rock solid” Cryogenic quartz fabrication– Precise orbit Orbit trim with GPS monitoring

3. Guide Star – Inertial Reference < 0.1 marc-sec/yr– Optically “bright” 6 magnitude– Maximize frame dragging effects Near equator– Precise proper motion measurement VLBI – good radio source– Near extra-galactic radio source Quasar – distant inertial frame

A “simple” experiment …Indeed!


The Overall Space VehicleRedundant spacecraft processors, transponders.

16 Helium gas thrusters, 0-10 mNea, for fine 6 DOF control.

Roll star sensors for fine pointing.

Magnetometers for coarse attitude determination.

Tertiary sun sensors for very coarse attitude determination.

Magnetic torque rods for coarse orientation control.

Mass trim 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.


GP-B Launch - 20 April 2004

Fairing Installation

Launch!

Release from launch vehicle


The Science GyroscopesMaterial: Fused quartz, homogeneous to a few parts in 107

Overcoated with niobium.Diameter: 38 mm.Electrostatically suspended.Spherical to 10 nm – minimizes suspension torques.Mass unbalance: 10 nm – minimizes forcing torques.All four units operational on orbit.

Gyroscope rotor and housing halvesDemonstrated performance:

• Spin speed: 60 – 80 Hz.• 20,000 year spin-down time.


Drift-rate: Torque:

Moment of Inertia:

Requirement Ω < Ω0~ 0.1 marc-s/yr(1.54 x 10-17 rad/s)

On Earth (ƒ = 1 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

Drag-free eliminates mass-unbalance torque

and key to understanding of other

support torques

(ridiculous – 10 -4 of a proton!)

(unlikely – 0.1 of H atom diameter)

(straightforward – 100 nm)

“Perfect” Mass Balance Needed!

rδ CG

r sω

f

025

srrr f

ωδ< Ω

External forces acting through center of force,

different than CM

Demonstrated GP-B rotor: δrr < 3 x 10-7

22 5)(

sI

mr

mf rI

τ ωτ δΩ ===

Mass Balance Requirements:

Gyro

spin

axis


Sphericity Measurement

Talyrond sphericitymeasurements to ~1 nm

Typical measured rotor topology; peak-valley = 19 nm

If a GP-B rotor was scaled to the size of the Earth, the largest peak-to-valley

elevation change would be only 6 feet!


Flight Proportional Thruster Design

Propellant: Helium Dewar BoiloffSupply: 5 to 17.5 torr

• Cold gas (no FEEP!) proportional thruster; 16 units on space vehicle.

• Operates under choked flow conditions

• Pressure feedback makes thrust independent of temperature

3.5mm iaThrust

Location of thrusters on Space Vehicle

Thrust: 0 – 10 mNISP: 130 secMdot: 6-7 mg·s−1

Noise: 25 µN·Hz−1/2


Drag-free Operational Modes

• Suspended “accelerometer” mode– Measured gyro control effort nulled by space vehicle thrust.– Used during most of mission due to robustness, gyro safety.

• Unsuspended “free float” mode– SV chases gyro; nulls position signal.

21

Ms

21

ms

R

r

u

U

( )r R−


Drag Free Control for a Perfect Orbit

0 1000 2000 3000 4000 5000 6000-20

0

20

Gyr

o3 p

os (n

m)

Prime and Backup Drag Free operations, GP-B Gyro3 (VT=142273900)

XsvYsvZsv

0 1000 2000 3000 4000 5000 6000-0.1

0

0.1

Gyr

o3 C

E ( μ

N)

XsvYsvZsv

0 1000 2000 3000 4000 5000 6000-5

0

5

SV

tran

s fo

rce

(mN

)

seconds

XsvYsvZsv

Accelerometer mode

Suspension ONSuspension

OFF

Prime mode

Normal gyro

suspension

Demonstrated performance better than 10-11 g residual acceleration on drag free

gyroscope in measurement band

(12.9mHz ± 0.2mHz)Rejection ~ 10,000x

10-4

10-3

10-2

10-1

10010

-12

10-11

10-10

10-9

10-8

10-7

Drag-free control effort and residual gyroscope acceleration (2004/239-333)

Con

trol E

ffort

(g)

Frequency (Hz)

Gyro CE inertialSV CE inertial

Thruster Force

Residual gyro acceleration

Acc

eler

atio

n (g

)

SV

Thr

ust

(mN

)G

yro

cont

rol

effo

rt (μ

N)

Gyr

o P

ositi

on (n

m)

Gravity Gradient

thrust

Polhode frequency

Roll rate

Inertial space – Frequency domain

Drag free modes in operation

5x10-12 g in band~1.5x10-8 (m/s2)/√Hz 0.02mHz – 80 mHz


The Solution:London Moment Readout. A spinning superconductor develops a magnetic “pointer” aligned with its spin axis.

Magnetic field sensed by a SQUID, a quantum limited, DC coupled magnetic sensor.

SQUID electronics in Niobium carrier

72 1.14 10 GaussL s smcMe

ω ω−= − = − × ( )

Superconducting SQUID Readout

The Conundrum:How to measure with extreme accuracy the direction of spin of perfectly round, perfectly uniform, sphere with no marks on it?

Performance: measurement better than 200 marc-s/√Hz

Requirement


Science Instrument Assembly

Gyros 3 & 4

Gyros 1 & 2

Mounting flange

Quartz block

Star tracking

telescopeGuide starIM Pegasi

(HR 8703)

Stanford-developed silicate bonding technique to join

block and telescope.

12

34


Star Tracking Telescope

• Field of View: ±60 arc-sec.• Measurement noise: ~ 34 marc-s/√Hz

• All-quartz construction.• Cryogenic temperatures make a very stable

mechanical system.

Detector Package

Telescope in Probe

Image divider

Integrated Telescope

At focal plane:Image diameter 50 μm0.1 marc-s = 0.18 nm

Physical length 0.33 mFocal length 3.81 mAperture 0.14 m


Ultra-low Magnetic Field

• Magnetic fields are kept from gyroscopes and SQUIDs using a superconducting lead (Pb) bag– Mag flux = field x area.– Successive expansions of four

folded superconducting bags give stable field levels at ~ 10-7 G.

• AC shielding at 10-12 [ =240 dB! ] from a combination of cryoperm, lead bag, local superconducting shields & symmetry. Lead bag in Dewar

Expanded lead bag

Enables the readout system to function to its stringent

requirements


Cryogenic Dewar and Probe

• 2524 liter superfluid helium (1.82K dewar) • Porous plug phase separator.• Lifetime 17.3 months – longest lived dewar in

space.• Dewar boil-off gas used for attitude and

translation control of vehicle

Probe during assembly

Dewar

Gyro-scopes


Telescope Field of View 120 arc-sec

Guide Star SelectionCriteria:• Sufficiently close to equatorial

plane for maximum frame dragging signal

• Optically bright enough to meet the pointing requirement.

• Be a radio star to allow VLBI proper motion measurement

IM PegGuide Star

HR Peg (0.4°)

HD 216635 (1°)

0.5° FOV

±60 arc-sec telescope FOV

Palomar star map

22h53’02” +16°50’28” Mag 5.7 Optical diameter: ~1 marc-sec


Proper Motion Measurement via VLBI

• SAO measuring position of IM Peg via VLBI.

• Calibrated against extra-galaticobjects

• Defines a very precise distant inertial frame.

Very Large Array, Socorro, New Mexico

P re lim ina ry H R 8703 P os itions fo r P eak o f R ad io B righ tnessS o la r S ys tem B arycen tric , J2000 C oo rd ina te S ys tem

(R igh t A scens ion - 22h53m ) x 15 cos(D ec) (m as)32500325503260 03265032700

Dec

linat

ion

- 16o 5

0' 2

8'' (

mas

)

2 50

300

350

400

450

500

550

16.9 Jan 97 18.9 Jan 97

30.0 N ov 97 21.9 D ec 9727.9 D ec 97 1 .8 M ar 98

12.5 Ju l 98 8 .4 A ug 9817 .3 S ept 98 13 .8 M ar 99

15 .6 M ay 99 19.3 S ep t. 99

15 .0 D ec 91

22 .4 June 9313 .2 S ep t 93

24 .3 Ju ly 94

10.0 D ec 99 15 .6 M ay 00

7 .3 A ug 00 6 .1 N ov 007.1 N ov 00

29.5 June 0122.0 D ec 01

14 .7 A pr 02

20.2 O ct 01

History of IM Peg position since Dec 1991


3 Stages of In-flight Verification

A. Initial orbit checkout (121 days) – Re-verification of all ground calibrations.– Scale factors, thermal sensitivities, etc.– Disturbance measurements on gyros at low spin speed.

B. Science Phase (~ 11 months)– Exploiting the built-in checks (i.e. Nature's helpful variations).

C. Post-experiment tests (~ 1 month starting Aug 2005)– Refined calibrations through careful and deliberate enhancement

of disturbances, etc.

Mission Operations Center (MOC) at

Stanford University


One Orbit of Science Data

60.06 60.07 60.08 60.09 60.1 60.11-600

-400

-200

0

200

400

600Space vehicle pointing and SQUID3 output

60.06 60.07 60.08 60.09 60.1 60.11-300

-250

-200

-150

-100

Day of year, 2005

Indi

cate

d po

intin

g (m

illi-a

rc s

ec)

Space Vehicle Pointing

SQUID3 Output

Repeat every 97 minutes for a year......

Data processing:• Remove known (calibrate-able)

signals from SQUID signal to get at gyro precession.

Remove effects of:• Motional aberration of starlight.

• Parallax.

• Pointing errors; roll phase errors.

• Telescope/SQUID scale factors.

• Pointing dither.

• SQUID calibration signal.

• Scale factor variation with gyro polhode (trapped flux).

• Other systemic effects.

Guide star in view


Data Analysis: An Incremental Approach• Phase 1 – Day-by-day. (thru March 2006)

– Full year data grading; Instrument calibration.– Treatment of known features (e.g. aberration, pointing errors).– Result: first-cut “orientation of the day” per gyroscope.

• Phase 2 – Month-to-Month. (thru September 2006)– Identify and remove systematic effects.– Improve instrument calibrations through long-term trending.– Result: second-cut: “trend of the month” per gyroscope.

• Phase 3 – 1 Year Perspective. (thru April 2007)– Combine and cross-check data from all 4 gyroscopes – Incorporate measured guide star proper motion.– Result: Experimental results compared with predicted GR effects.

Follow-on

SAC13 SAC14

CY 2007SAC15

Analysis Phase 1

Analysis Phase 2

Analysis Phase 3

Mission OPS

PubPrep

PU

B

CY 2005 CY 2006

SAC Peer Review

Internal Science Result


Built-In Checks Assure Accurate Result• Structure of Data

– Predicted GR results: 6614.4 marc-sec Geodetic 40.9 marc-sec Frame-dragging

– Orbital aberration: 5185.6 marc-sec– Annual aberration: 20495.8 marc-sec– Gravitational deflection of light: 21.12 marc-sec peak (11 Mar 2005)– Parallax: ~ 10 marc-sec

• Scaling Verifications– Magnitudes & planar relations

of effects known

• Robustness further confirmed by agreement with

– Multiple data analysis approaches.– Gyro-to-gyro direct comparisons.

200 250 300 350 400 450 500 550 600 6500

5

10

15

20

25

Jan.01,2005

Time (Days) from Jan. 1, 2004

Def

lect

ion

(mas

)

Magnitude of Gravitational Deflection of Light by IM Pegasi

Gravitational deflection of starlight


• 4 gyros & SQUIDs with distinct characteristics – Different rotor & housing shapes, mass distributions, surface finish.– Different spin directions - 2 clockwise, 2 counterclockwise– Different spin speeds & polhode rates– Different acceleration environments (distances from drag-free point)

– Different magnetic fields & pressures

• Optical reference– Guide telescope – 2 separate optical images & detector assemblies – Roll reference – 2 roll axis star telescopes

Redundancy – with Variation

A POWERFUL VERIFICATION

4 gyros agreeing amid all these variations


What’s Taking so Long, Anyway?

• Overall, the GP-B spacecraft operated very well on orbit.• However, not perfectly:

– Out-of-spec pointing• Requires more careful telescope calibration.

– Polhode period damping – modelling• Modulates the gyro orientation angle readout scale factor. (systematic

error source)– Interference from onboard electronics system (ECU)– “Segmented” data from spacecraft anomalies.

• Knitting segments together requires care.– Need for “data grading” – 1 TB of science data!

All require time to understand, model, and remove…

…a lesson for other “simple”missions now in development


Satellite Test of the Equivalence Principle“STEP”

Program Update


Satellite Test of the Equivalence Principle

Dz

time

Orbiting drop tower experiment

Dz

Dz

time

F = ma mass - the receptacle of inertiaF = GMm/r2 mass - the source of gravitation

Newton’s Mystery

* More time for separation to build* Periodic signal


10-18

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

1700 1750 1800 1850 1900 1950 2000

Newton

Bessel

Dicke

Eötvös

Adelberger, et al.LLR

STEPα effect (min.)

DPV runaway dilaton (max.)

.

1 TeV Little String Theory

~ 5 x 10-13

100

Microscope

Space: > 5 Orders of Magnitude LeapSTEP Goal: 1 part in 1018


Proposed EP Tests in SpaceProposal Institution Accuracy Goal

SEE U. Tennessee UnspecifiedSatellite Energy Exchange

Microscope ONERA, OCA 10-15

CNES, ESA

Equivalence Harvard SAO, 10-15

Balloon drop test of EP IFSI Rome

GG Università di Pisa 10-17

Galileo Galilei

STEP Stanford U., NASA/MSFC, 10-18

Satellite test of EP European collaboration


STEP Mission Elements6 Month Lifetime• Sun synchronous orbit, I=97o• 550 Km altitude• Drag Free control w/ He Thrusters

Cryogenic Experiment• Superfluid Helium Flight Dewar• Aerogel He Confinement• Superconducting Magnetic Shielding

4 Differential Accelerometers• Test Mass pairs of different materials• Micron tolerances

Superconducting bearings• DC SQUID acceleration sensors• Electrostatic positioning system• UV fiber-optic Charge Control


• Fabricate prototype flight instrument– Differential accelerometer – Cryogenic electronics– Quartz block mounting structure

• Transfer critical GP-B technologies – SQUID readout– Drag-free thrusters– Electrostatic positioning system

• Integrated ground test of prototype flight accelerometer

Beginning 2nd year of 3 year Technology Program under NASA MSFC

STEP Status

Technology Program Goals:


GP-B: Over the Horizon

Dewar was depleted on 29 Sep 2005 –superconducting electronics ceased to function.

Systematic effects will be characterized and compensated for in 2006, followed by detailed data review by external experts.

Data analysis will continue to April 2007 when results will be published at the April APS meeting. (Jacksonville, Florida)


GP-B – An International Collaboration• Stanford University Development, Science Instrument, Management

C.W.F. Everitt PI, GP-B team Mission Operations, Data Analysis• Lockheed Martin Probe, Dewar, Spacecraft bus, Flight Software

GP-B teamResearch at Other Institutions

• Science Advisory CommitteeClifford Will chair

• Harvard Smithsonian Guide Star and Star Proper Motion StudiesIrwin Shapiro

• JPL Independent Science AnalysisJohn Anderson

• York University Guide Star and Star Proper Motion StudiesNorbert Bartel

• Purdue University Helium Ullage BehaviourSteve Collicot

• San Francisco State Gyroscope Read-out TopicsJim Lockhart

• National University of Ireland Proton MonitorSusan M.P. McKenna-Lawlor

• University of Aberdeen High Precision Homogeneity Measurement of QuartzMike Player

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