Gravity Probe B Testing General Relativity with Orbiting Gyroscopes - - PowerPoint PPT Presentation

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Gravity Probe B – Testing General Relativity with Orbiting Gyroscopes

Int’l Workshop on Precision Tests and Experimental Gravitation in Space Galileo Galilei Institute, Firenze, Italy; Sep 28-23, 2006 William Bencze, GP-B Program Manager for the GP-B Team

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Outline

• Gravity Probe B

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

• STEP Mission Update

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Testing GR with Orbiting Gyroscopes

( ) ( )

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⋅ + × = ω R ω R v R

2 3 2 3 2

3 2 3 R R c GI R c GM Ω

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

d dt = × s Ω s

Spin axis orientation:

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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!

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Einstein’s 2 1/2 Tests

Perihelion 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.

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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 0.21

marc-s / yr

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

• n Earth (torque

modeling) (10-5 deg/hr)

Why a Space-based Experiment?

marc-s / yr Spacecraft gyros (3x10-3 deg/hr)

Expected GP-B performance on orbit Operation in 1g environment degrades mechanical gyro performance Laser gyroscopes and other technologies fidelity too low for GP-B

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

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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)

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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!

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The Overall Space Vehicle

Redundant spacecraft processors, transponders. 16 Helium gas thrusters, 0-10 mN ea, 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

• rientation 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

• perating perfectly.

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GP-B Launch - 20 April 2004

Fairing Installation

Launch!

Release from launch vehicle

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The Science Gyroscopes

Material: 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 halves

Demonstrated performance:

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

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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 g cross- track average) < 5.8 x 10-18 < 5.8 x 10-10 < 5.8 X 10-6

δr r δr r δr r

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!

r δ

CG

r

s

ω

f

2 5

s

r r r f ω δ < Ω

External forces acting through center of force, different than CM

Demonstrated GP-B rotor:

δr r

< 3 x 10-7

2

2 5)

(

s

I mr

mf r I

τ ω

τ δ Ω = = =

Mass Balance Requirements:

Gyro spin axis

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Sphericity Measurement

Talyrond sphericity measurements 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!

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Flight Proportional Thruster Design

Propellant: Helium Dewar Boiloff Supply: 5 to 17.5 torr

• Cold gas (no FEEP!)

proportional thruster; 16 units

• n space vehicle.
• Operates under choked flow

conditions

• Pressure feedback makes

thrust independent of temperature

3.5mm ia

Thrust Location of thrusters on Space Vehicle Thrust: 0 – 10 mN ISP: 130 sec Mdot: 6-7 mg·s−1 Noise: 25 µN·Hz−1/2

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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.

2

1 Ms

2

1 ms R

• r
• u
• U
• (

) r R −

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Drag Free Control for a Perfect Orbit

1000 2000 3000 4000 5000 6000

• 20

20 Gyro3 pos (nm) Prime and Backup Drag Free operations, GP-B Gyro3 (VT=142273900) Xsv Ysv Zsv 1000 2000 3000 4000 5000 6000

• 0.1

0.1 Gyro3 CE (μN) Xsv Ysv Zsv 1000 2000 3000 4000 5000 6000

• 5

5 SV trans force (mN) seconds Xsv Ysv Zsv

Accelerometer mode Suspension ON Suspension 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

10 10

• 12

10

• 11

10

• 10

10

• 9

10

• 8

10

• 7

Drag-free control effort and residual gyroscope acceleration (2004/239-333) Control Effort (g) Frequency (Hz) Gyro CE inertial SV CE inertial

Thruster Force

Residual gyro acceleration

Acceleration (g) SV Thrust (mN) Gyro control effort (μN) Gyro Position (nm)

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

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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

7

2 1.14 10 Gauss

L s s

mc M e 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

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Science Instrument Assembly

Gyros 3 & 4 Gyros 1 & 2 Mounting flange Quartz block Star tracking telescope Guide star IM Pegasi

(HR 8703)

Stanford-developed silicate bonding technique to join block and telescope.

1 2 3 4

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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 μm 0.1 marc-s = 0.18 nm Physical length 0.33 m Focal length 3.81 m Aperture 0.14 m

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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

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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

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Telescope Field of View 120 arc-sec

Guide Star Selection

Criteria:

• 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 Peg Guide 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

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Proper Motion Measurement via VLBI

• SAO measuring position of

IM Peg via VLBI.

• Calibrated against extra-galatic
• bjects
• Defines a very precise distant

inertial frame.

Very Large Array, Socorro, New Mexico

P relim inary H R 8703 P ositions for P eak of R adio B rightness S olar S ystem B arycentric, J2000 C oordinate S ystem

(R ight A scension - 22h53m ) x 15 cos(D ec) (m as)

32500 32550 32600 32650 32700

Declination - 16

• 50' 28'' (mas)

250 300 350 400 450 500 550

16.9 Jan 97 18.9 Jan 97 30.0 N ov 97 21.9 D ec 97 27.9 D ec 97 1.8 M ar 98 12.5 Jul 98 8.4 A ug 98 17.3 S ept 98 13.8 M ar 99 15.6 M ay 99 19.3 S ept. 99 15.0 D ec 91 22.4 June 93 13.2 S ept 93 24.3 July 94 10.0 D ec 99 15.6 M ay 00 7.3 A ug 00 6.1 N ov 00 7.1 N ov 00 29.5 June 01 22.0 D ec 01 14.7 A pr 02 20.2 O ct 01

History of IM Peg position since Dec 1991

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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

• f disturbances, etc.

Mission Operations Center (MOC) at Stanford University

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One Orbit of Science Data

60.06 60.07 60.08 60.09 60.1 60.11

• 600
• 400
• 200

200 400 600 Space 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

Indicated pointing (milli-arc sec)

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

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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-

• n

SAC13 SAC14

CY 2007

SAC15 Analysis Phase 1 Analysis Phase 2 Analysis Phase 3 Mission OPS Pub Prep PUB

CY 2005 CY 2006

SAC Peer Review Internal Science Result

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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

• f effects known
• Robustness further confirmed

by agreement with

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

200 250 300 350 400 450 500 550 600 650 5 10 15 20 25 Jan.01,2005 Time (Days) from Jan. 1, 2004 Deflection (mas) Magnitude of Gravitational Deflection of Light by IM Pegasi

Gravitational deflection of starlight

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• 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

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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

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Satellite Test of the Equivalence Principle “STEP” Program Update

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Satellite Test of the Equivalence Principle

Dz time

Orbiting drop tower experiment

Dz Dz time

F = ma mass - the receptacle of inertia

F = GMm/r2

mass - the source of gravitation Newton’s Mystery {

* More time for separation to build

* Periodic signal

{

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10

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• 10

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• 8

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• 6

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10-2

1700 1750 1800 1850 1900 1950 2000

Newton Bessel Dicke Eötvös Adelberger, et al. LLR

STEP

α effect (min.) { DPV runaway dilaton (max.) . 1 TeV Little String Theory ~ 5 x 10-13

100

Microscope

Space: > 5 Orders of Magnitude Leap

STEP Goal: 1 part in 1018

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Proposed EP Tests in Space

Proposal Institution Accuracy Goal SEE

• U. Tennessee

Unspecified Satellite 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

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STEP Mission Elements

6 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

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• 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:

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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)

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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 team Research at Other Institutions

• Science Advisory Committee

Clifford Will chair

• Harvard Smithsonian

Guide Star and Star Proper Motion Studies Irwin Shapiro

• JPL

Independent Science Analysis John Anderson

• York University

Guide Star and Star Proper Motion Studies Norbert Bartel

• Purdue University

Helium Ullage Behaviour Steve Collicot

• San Francisco State

Gyroscope Read-out Topics Jim Lockhart

• National University of Ireland

Proton Monitor Susan M.P. McKenna-Lawlor

• University of Aberdeen

High Precision Homogeneity Measurement of Quartz Mike Player