1

Gravity Probe B: Instrument and Data Reduction

Mac KeiserSLAC Summer Institute

July 25, 2005

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Topics

Design of Gravity Probe B Payload and Spacecraft

On-Orbit Performance

Data Reduction

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Gravity Probe B Design Challenges

1. Design a gyroscope where the drift rate due to classical torques is less than 0.3 mas/yr.

2. Measure the gyroscope spin axis orientation relative to a metrology reference frame to an accuracy of 1 masin 5 hr.

• Noise • Calibration

3. Determine the orientation of the metrology reference frame relative to distant inertial space to an accuracy of better than 0.15 mas/yr.

• Measure metrology reference frame relative to guide star• Measure proper motion of guide star

4. Ensure than there are numerous cross checks for that may be used to eliminate potential systematic errors.

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Conventional vs. GP-B Gyroscopes

1 marcsec/yr = 3.2 × 10-11 deg/hr

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Performance Improvements Classical Torques

Support Dependent Torques− Reduce the Forces Required to Support the Rotor.

• Place the Gyroscope in a Satellite – 10-8 g.• Use Drag-Free Control For the Satellite – 10-11g .• Carefully Select the Orbit to Reduce the Effects of Gradients

in the Earth’s Gravitation Field 10-11g.− Improve the Sphericity and Mass Unbalance of the Rotor <

25 nm.− Choose the Appropriate Spin Speed – 60 -180 Hz

Support-Independent Torques– Residual Gas Pressure < 3 x 10-10 Torr– Electric Charge on the Rotor < 15 nC– Residual Magnetic Field < 10 µG

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Gravity Probe B Gyroscopes

• Rotor (63g, 1.91cm radius)– Fused Quartz Substrate

• Density Homogeneity < 4×10-6• Asphericity < 30 nm

– Niobium Coating • Thickness – 1.25 µm• Uniformity < 10 nm

– Rotor to Housing Gap – 31 µm• Housing

– Cavity • Asphericity < 250 nm

– Cu/Ti Electrodes for Electrostatic Suspension

– Spin Up Channel with Raised Cu Lands

– Electrodeposited 4 turn superconducting pickup loop

– Conducting Ground Plane– UV Fibers and Electrodes for

Charge Control

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Electrostatic Suspension System

Backup Controller Electronics

Switch

Gyro

Bridge

Arbiter & Mode Register

Multi-Level AmplifierSpinup (750V)

Science Mission(45V)

SM High Backup

SM Low Backup

Flight Computer (RAD6000)

Spin-up

Science Mission(SM)

Spin-up Backup

D/AA/DGFAB

GFAB

4kVrelay

Requirements in Science Mode:Readout Noise < 0.1 nm/√HzCentering Stability at Roll < 0.3 nmControl Voltage 0.2 vStability of Control Voltage < 3 × 10-5

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Gyroscope Readout

• London Moment of a Spinning Superconductor

– Aligned with Instantaneous Spin Axis

• 4 Turn Pickup Loop • Superconducting Cable• DC SQUID and SQUID

Readout Electronics– Noise < 190 mas/√Hz at

Satellite Roll Period• Superconducting

Magnetic Shields– Residual Magnetic Field

< 9 µGauss– Attenuation of External

Magnetic Fields > 2 1012 “SQUID” 1 marc-s in 5 hours

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TelescopeDimensions:

Physical length 0.33 mFocal length 3.81 mAperture 0.14 m

Properties: Field of View 1 arc minStrehl Ratio(695nm) 30%Noise 50 mas/√Hz

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Quartz Block and Science Instrument Assembly

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Low Temperature Probe

Sintered Titanium Cryopump

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Liquid Helium DewarLow Field Technology• flux = field x area• successive expansions give stable field levels ~10-7 gauss•10-12 [ =120 dB! ] ac shielding through combination of cryoperm, lead bag, local superconducting shields & symmetry

• Dewar Capacity 2300 L Superfluid He• Boil-Off Gas Used for Proportional Thrusters

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Spacecraft• 16 Helium gas thrusters, 0-10 mN ea, for fine 6 DOF control.

• Mass trim to tune moments of inertia.

• Roll star sensors for fine pointing.

• Dual transponders for TDRSS and ground station communications.

• Modified GPS receiver for precise positioning and timing information.

• Laser ranging corner cube is a backup and cross-check for orbit determination.

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Topics

Design of Payload and Spacecraft– Classical Torques are Significantly Smaller than

the Relativisitic Effects– Gyroscope and Telescope Readouts are Possess

Sufficient Resolution and Signal-to-Noise– Carefully Controlled Environment

On-Orbit Performance

Data Reduction

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Launch April 20, 2004, 9:57 am PDT

• Boeing Delta II Rocket from Vanderburg Airforce Base

• One Second Launch Window– Target Orbit – Polar with Guide

Star in Plane of Orbit to within 0.0250

– Provisions Made to Adjust Orbit with Helium Thrusters

• Launched to the South Over the Pacific

• Within 1 hour, Cameras Attached to Second Stage Showed All Four Solar Arrays Fully Deployed

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Orbit Injection

Required Final Orbit Area

Orbit achieved ~100 mfrom the pole

x

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Initial Gyro Levitation and De-levitationAnalog Backup Electrostatic Suspension System

0 2 4 6 8 10 12-40

-30

-20

-10

0

10

20

30

Time (sec)

Pos

( µm

)

Gyro2 Position Snapshot, VT=135835310.3

Initial suspension Suspension release

Gyro “bouncing”

Rot

or P

ositi

on (µ

m)

Time (sec)

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Low Frequency SQUID NoiseMeasured On-Orbit

10-4

10-3

10-2

10-1

10-6

10-5

10-4

frequency (Hz)

PSD

( Φ0/ √

Hz)

LOW FREQUENCY NOISE - SQUID 1 - 5/23/04 0945 Z + 21.75 Hours

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Gyroscope Spinup

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

time (minutes)

Spin

Spe

ed (H

z)

Gyro 4 Spin-Up - 7/13/04 - 2004:195:20:00 Z

Final Gyroscope Spin Speeds

Gyro 1 – 79.394 Hz

Gyro 2 – 61.821 Hz

Gyro 3 – 82,110 Hz

Gyro 4 – 64.853 Hz

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Low Temperature Bakeout and Gyroscope Spin-Down Rate

Low Temperature Bakeout

Gyroscope Spin Down Time Constant (yr)

Gyro #1 ~ 50 15,800Gyro #2 ~ 40 13,400Gyro #3 ~ 40 7,000Gyro #4 ~ 40 25,700

before bakeout after bakeout

Demonstrates pressure less than ~1.5 x 10-11 torr

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Measured Mass Properties of Gyroscope Rotors

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

Mass Unbalance (nm) from Measured Displacement at Spin Frequency

Gyro # 1 2 3 4

Prelaunch Estimate 18.8 14.5 16.8 13.5

On-orbit data 10.5±0.5 6.9±0.2 5.6±0.2 9.1±0.2

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Telescope Performance

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

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Transverse Acceleration with Drag-Free Control

Proportional thrusterHe boil off gas – Reynolds number ~ 10 !!

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

el(g

)

Demonstrated accelerometer (drag free) performance better than 10-11 g DC to 1 Hz

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Attitude and Translation Control: Acquiring Star

Acquisition time ~ 110 s

RMS pointing ~ 90 marc-s

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Topics

Gravity Probe B Payload and Spacecraft

On-Orbit PerformanceGravity Probe B is working as Planned

Data Reduction

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Schematic Diagram of Science Instrument Assembly

Quartz Block

Gyro

Gyro Electronics TelescopeElectronics

Telescope

Roll Star Reference

HR8703(IM PEG)

Roll –1 to 3 minutes

☼

SQUID☼

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Pointing Dither and Stellar Aberration

Dither -- Slow 30 marc-s oscillations injected into pointing system

gyro outputtelescope output{

scale factors matched for accurate subtraction

Aberration -- Nature's calibrating signal for gyro readout

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

Continuous accurate calibration of GP-B experiment

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Gyroscope and Telescope ReadoutsOrbit 5786 (of 6736 as of 12:00 N GMT 7/21/05)

70 80 90 100 110 120 130-1

-0.5

0

0.5

1Gyroscope 4 Signal, May 18, 2005

Volts

70 80 90 100 110 120 130-1

-0.5

0

0.5

1Telescope Y-Axis Pointing Error, May 18, 2005

Dim

ensi

onle

ss

Time (min)

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Combined Gyroscope

and Telescope Signals

70 80 90 100 110 120 130-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (min)

Volts

Combined Gyroscope 4 and Telescope Signals, May 18, 2005

( )[ ] bAWEANSCz rWErNSg ++++++= )sin()()cos( δφφδφφ

Measurements:

z – Combined gyroscope and telescope signals

φr – Measured satellite roll phase

ANS, AWE – North-South and West-East Components of Stellar Aberration

Parameters:

NS, WE – North-South and West-East Orientation of Gyroscope Spin Axis

Cg – Gyroscope Readout Scale Factor

δφ - Roll Phase Offset, angle between measured roll phase and normal to pickup loop

b - bias

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Three Phases of In-Flight Verification

A. Initial orbit checkout (121 days) – re-verification of all ground calibrations [scale factors,

tempco’s etc.]– disturbance measurements on gyros at low spin

speedB. Science Phase (~ 11+ months)

– exploiting the built-in checks [Nature's helpful variations]

C. Post-experiment tests (~ 3 weeks)– refined calibrations through deliberate enhancement

of disturbances, etc. […learning the lesson from Cavendish]

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Five Modes of Verification

• A heavily instrumented payload and spacecraft

• Redundancy – with variation

• Built-in calibrations/natural variations

• Error enhancement

• End-around checks

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Proper Motion of Guide Star

• Guide Star, HR 8703• Declination, 16.840• Visual Brightness, 5.7• Radio Source

– 0.5 to 40 mJy1 Jy =10-26 W/(m2Hz)

• VLBI Measurements of Proper Motion

• Harvard -Smithsonian Center for Astrophysics and York University

• 4 VLBI Observations per year

• 1991 through 2005

Very Large Array, Socorro, New Mexico

Preliminary HR 8703 Positions for Peak of Radio BrightnessSolar System Barycentric, J2000 Coordinate System

(Right Ascension - 22h53m) x 15 cos(Dec) (mas)3250032550326003265032700

Dec

linat

ion

- 16o

50'

28'

' (m

as)

250

300

350

400

450

500

550

16.9 Jan 97 18.9 Jan 97

30.0 Nov 97 21.9 Dec 9727.9 Dec 97 1.8 Mar 98

12.5 Jul 98 8.4 Aug 9817.3 Sept 98 13.8 Mar 99

15.6 May 99 19.3 Sept. 99

15.0 Dec 91

22.4 June 9313.2 Sept 93

24.3 July 94

10.0 Dec 99 15.6 May 00

7.3 Aug 00 6.1 Nov 007.1 Nov 00

29.5 June 0122.0 Dec 01

14.7 Apr 02

20.2 Oct 01

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Precession RatesPredicted by General Relativity

( ) ( ) ⎥⎦

⎤⎢⎣

⎡−⋅+×∇=Ω ee RR

RRc

GIc

ωωφ 23223

23 v

Geodetic Effect Frame Dragging Effect

Terrestial 6.6 arc sec/yrPerpendicular to orbital plane

Solar 19.2 mas/yrPerpendicular to Ecliptic

Terrestial 42 mas/yrParallel to Earth’s rotation axis

VelocityEarth’s Ephemeris

VelocityGPS and Lunar Range Meaurements

Gradient of TerrestialGravitational Potential

Position - GPS GME, J2

PositionGPS

Rotation RateIERS

GIE – Known to 10-6

Gradient of SolarGravitational Potential

Position – Earth’s Ephemeris GMS

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Status and Plans

April 20, 2004 Launch

August 28, 2004 Completion of Initialization Phase, Spinup of Gyroscopes,Start of Science Data Collection

August 1, 2005 Planned Start of Calibration Phase

September 1, 2005 Liquid Helium Expected to Run Out

Late 2006 Release of Data and Results

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Gravity Probe B: Instrument and Data ReductionTopicsGravity Probe B Design ChallengesConventional vs. GP-B GyroscopesPerformance Improvements Classical TorquesGravity Probe B GyroscopesElectrostatic Suspension SystemGyroscope ReadoutTelescopeQuartz Block and Science Instrument AssemblyLow Temperature ProbeLiquid Helium DewarSpacecraftTopicsLaunch April 20, 2004, 9:57 am PDTOrbit InjectionInitial Gyro Levitation and De-levitation Analog Backup Electrostatic Suspension SystemLow Frequency SQUID Noise Measured On-OrbitGyroscope SpinupLow Temperature Bakeout and Gyroscope Spin-Down RateMeasured Mass Properties of Gyroscope RotorsTelescope PerformanceTransverse Acceleration with Drag-Free ControlAttitude and Translation Control: Acquiring StarTopicsSchematic Diagram of Science Instrument AssemblyPointing Dither and Stellar AberrationGyroscope and Telescope ReadoutsOrbit 5786 (of 6736 as of 12:00 N GMT 7/21/05)Combined Gyroscope and Telescope SignalsThree Phases of In-Flight VerificationFive Modes of VerificationProper Motion of Guide StarPrecession RatesPredicted by General RelativityStatus and Plans