The Relativity Mission, Gravity Probe B Results and Lessons … · 2013. 4. 16. · The Relativity...

48
1 The Relativity Mission, Gravity Probe B Results and Lessons Learned Sasha Buchman for the GP-B team Q2C, Quantum to Cosmos #5 Köln, October 9 th 2012

Transcript of The Relativity Mission, Gravity Probe B Results and Lessons … · 2013. 4. 16. · The Relativity...

Page 1: The Relativity Mission, Gravity Probe B Results and Lessons … · 2013. 4. 16. · The Relativity Mission, Gravity Probe B Results and Lessons Learned Sasha Buchman for the GP-B

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The Relativity Mission, Gravity Probe B

Results and Lessons Learned

Sasha Buchman for the GP-B team

Q2C, Quantum to Cosmos #5

Köln, October 9th 2012

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Outline

1. Experiment description

2. Patch effects

3. Data models and analysis techniques

4. Results, uncertainties and cross-checks

5. Lessons learned

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Gravity Probe B Concept

eee

FD ωRωR

R

Rc

IGΩ

232

3

vRRc

MGΩ e

G

322

3

Guide STAR

IM Pegasi

HR 8703

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Expected Gyroscope Behavior

Newton

Newton

Geodetic effect*

(-6571 marcsec/yr)

Frame-dragging effect*

(-75 marcsec/yr)

*includes solar GR effects and guide star motion

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The Science Instrument

Nothing could be simpler then GP-B;

just a gyroscope and a telescope

William Fairbank

Telescope Quartz Block Gyro 4

Science Instrument Assembly

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GP-B Gyroscope Requirements

1 marcsec/yr = 3.2×10-11 deg/hr = 1.5 10-16 rad/sec

Electrostatic gyro

uncompensated

(10-1 deg/hr)

Electrostatic gyro

with modeling

(10-5 deg/hr)

39 Frame dragging effect

0.50 GP-B requirement

~10-6

102

10

1

10-1

10-2

103

6,606 Geodetic effect

103

104

105

106

107

108

109

1010

Laser gyro

(10-3 deg/hr)

marc

sec/y

r

Spacecraft gyros

(3x10-3 deg/hr) m

arc

sec/y

r

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Ensuring Gyro Performance

1. Optimize Geometry

I. Gyro asphericity R/R < 10-6

II. Gyro mass unbalance dMU/R < 10-6

III. Housing asphericity RH/RH < 10-5

2. Reduce Environmental Disturbances

I. Residual acceleration atrans < 10-11 ms-2

II. Magnetic field B < 10-10 T

III. Gas pressure P < 10-11 Pa

IV. Electric charge Q < 10-11 F

V. Patch effects dpatch < 10-6 m

3. Shift Frequency and Average Signal

I. Roll satellite 77.5 s

II. Use polhode averaging ~ 3,000 s

III. Multiple gyroscopes (4) 4 gyros

4. Use Natural Calibrations

I. Daily aberration ~ 5 arcsec

II. Yearly aberration ~ 20 arcsec

5. Ground Testing Capability 10 ms-2 to 10-11 ms-2

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Gyro Description

Components

Rotor

Housing

Read-out loop

Spin-up nozzle

UV fixtures

Suspension cables

Read-out cable

Functionality

Electrostatic suspension

Capacitance rotor position

Forcing charge measurement

London moment read-out

Helium spin-up

Cryogenic operations

UV charge management

Gap = 32.5 m

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Gyro Spin-up

Differential Pumping Requirement:

1) spin channel ~ 10 torr (sonic velocity)

2) 2) electrode area < 10-3 torr

Gyro f (Hz) df/dt

(μHz/hr) (yr)

1 79.4 0.57 15,900

2 61.8 0.52 13,600

3 82.1 1.30 7,200

4 64.8 0.28 26,400

0 0.5 1 1.50

10

20

30

40

50

60

70

80

90

100

Time (hours)

Spin

rate

(H

z)

Gyro 1

Gyro 2

Gyro 3

Gyro 4

Gyro 1 spun-up last; spin-up

of one gyro causes spin

down of the other gyros

0 0.5 1.0 1.5 Time (hours)

Spin

Speed (

Hz)

100

80

60

40

20

0

Spin-up half

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London moment read-out with dc SQUIDs

Superconducting pickup on gyroscope housing

< 8 10-29 J/Hz (<50 0/ Hz) at 5 mHz 200 marcsec/ Hz (5 10-11 G/ Hz )

London Moment Read-Out

A spinning superconductor

develops a magnetic “pointer”

aligned with its spin axis

)(GssLe

mcB

71014.1

2

Requirement

Read-out half

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Gyroscope Readout Single Orbit

0 10 20 30 40 50 60-6

-5.8

-5.6

-5.4

-5.2

-5Output of SQUID Readout Electronics, Gyroscope 3, Orbit 6200, June 15, 2005

Ou

tpu

t(V

olt

s)

0 10 20 30 40 50 60

-6

-4

-2

0

2Optical Aberration due to Orbital Motion

Arc

Sec

Time (minutes) After Acquisition of Guide Star

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Post Science Calibration Anomaly

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

Angle of Misalignment (degrees)

Dri

ft R

ate

(as

/da

y)

Magnitude of Drift Rate vs. Angle of Misalignment

Gyro 1

Gyro 2

Gyro 3

Gyro 4

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The Patch Effects:

1.Gyro acceleration along the roll axis

2.Gyro acceleration at spin frequency

3.Gyro spin down

4.Gyro polhode damping

5.Misalignment torque

6.Resonance torque

7.Charge measurement bias

The Patch Effect

Explanation of anomalies: Patch Effect

Mechanical, magnetic, suspension effects ruled out

Variation of electric potential over the surface

Can arise due to the polycrystalline structure

Can be affected by presence of contaminants

Patch fields present on gyro and housing walls

Cause forces and torques between surfaces

d

Gyro surface

Housing surface

Schematic of surfaces with patches

Complicate

Data analysis

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3 Complications due to Patch Effect I

Misalignment Torques

Proportional to spin to roll angle

Magnitude up to 2.5 arcsec/yr

Orthogonal to misalignment plane (roll & spin axes)

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3 Complications due to Patch Effect II

Polhode damping

Caused by power dissipation in housing resistances to ground

Changes trapped flux orientation to the spin axis

Complicates scale factor Cg determination

Time (days from Day #1; Apr. 20, 2004)

Polh

ode P

eriod (

hours

)

140 190 240 290 340 390 440

140 190 240 290 340 390 440 140 190 240 290 340 390 440

140 190 240 290 340 390 440

Time (days from Day #1; Apr. 20, 2004)

Gyro

1

Gyro

4

Gyro

3

Gyro

2

4

3

2

1

20

15

10

5

1.8

1.7

1.6

5.5

5.0

4.5

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3 Complications due to Patch Effect III

Gyro 2 per orbit orientation

142 139 140 141 145 144 143 138 146

sEW

res. m

EW

orienta

tion,

s EW (

arc

sec)

Date (2005)

Roll-polhode Resonance Torque

‘Jumps’ occur when harmonic of polhode rate coincident with roll rate

Up to 200 marcsec discontinuities in data

Long term oscillatory behavior polhroll ff

m 1

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Raw & Processed Flight Data (Gyro 2)

Jan 8 Jan 28 Feb 17 Mar 9 Mar 29 Apr 18 May 8

Jan 8 Jan 28 Feb 17 Mar 9 Mar 29 Apr 18 May 8

date (2004)

–0.5

0.0

0.5

1.0

1.5

2.0

1.64

1.66

1.68

1.70

1.72

1.74

EW

orienta

tion (

arc

sec)

NS

orienta

tion (

arc

sec)

EW uniform drift

NS uniform drift

Gyro 2, orientations – Newtonian torques

–1

+1

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Gyroscope Performance

700 marcs

Patch effects

1 marcsec/yr = 3.2×10-11 deg/hr = 1.5 10-16 rad/sec

Electrostatic gyro

uncompensated

(10-1 deg/hr)

Electrostatic gyro

with modeling

(10-5 deg/hr)

39 Frame dragging effect

0.50 GP-B requirement

102

10

1

10-1

10-2

103

6,606 Geodetic effect

103

104

105

106

107

108

109

1010

Laser gyro

(10-3 deg/hr)

marc

sec/y

r

Spacecraft gyros

(3x10-3 deg/hr) m

arc

sec/y

r

~ 1%

Data Analysis

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Science Data Segments and Anomalies

Aug Sept Oct Nov Dec Jan Feb

Mar Apr May Jun Jul Aug Sept

2004 2005

2005

5 - Jan 20

Solar Flare

9 - roll

notch filter

6, 7,8 -

computer reboots

Segment 9 Segment 10

Segment 6 Segment 5

Calibration

4 - roll

notch filter

3 - bad

GPS config

2 - SRE

Safemode

1 - Gyro 3

Analog Backup

Spinup &

Alignment Complete Gyros 1, 2, 3

Gyro 4

Segment 2 Seg. 3

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Two Foundations of the Data Analysis

1. Spectral separation

a) Rotor spin ~ 60 Hz - 80 Hz (changing with time)

b) Spacecraft roll = 12.9 mHz (from on-board star trackers)

c) Spacecraft orbit = 0.17 mHz (from on-board GPS)

d) Rotor polhode ~ 0.1 mHz (changing with time)

e) Earth’s orbit = 31.7 nHz (from JPL Earth ephemeris)

General Relativity acts at zero-frequency

2. Trapped magnetic flux Enables determination of a) & d)

1. + 2. + model of patch effect & gyro dynamics

allow separation of relativistic & Newtonian effects

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Sources of Experiment Uncertainty

1. Statistical

– Covariance matrix (or Fisher info) provided by 2-sec Filter

– Quantifies uncertainty related to:

• measurement noise

• a priori information

• Model (including the number of parameters estimated)

2. Systematic

A. Parameter sensitivity

• Quantifies uncertainty associated with choice of number of parameters estimated

B. Unmodeled effects

• e.g. uncertainty of solar geodetic effect, guide star motion

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Mitigation of Systematic Effects

Source Magnitude

of Effect Analysis

Contribution

to total error

Misalignment torque ~ 500 mas/yr Physical

Model

~5 mas/yr EW

~15 mas/yr NS

Resonance torque ~ 500 mas/yr Physical Model ~4 mas/yr

Other classical torques < 1 mas/yr Not modeled < 1 mas/yr

SRE variations ~ 100 mas/yr Taylor

expansion

~4 mas/yr EW

~12 mas/yr NS

Gyro scale factor ~ 100 mas/yr Physical Model

TFM

~1 mas/yr EW

~2 mas/yr NS

Other readout errors < 1 mas/yr Not modeled < 2 mas/yr

Telescope readout ~ 1 mas/yr Not modeled ~1 mas/yr

Guide Star Motion ~ 1 mas/yr Not modeled ~1 mas/yr

ECU noise 10% data Data excluded ~2 mas/yr

TOTAL ~700 mas/yr

(GR ~6600 mas/yr)

~8 mas/yr EW

~20 mas/yr NS

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GP-B Results

Relativistic Drift Rate Estimates rNS (mas/yr) rWE (mas/yr)

Gyro 1 -6,588.6 31.7 -41.3 24.6

Gyro 2 -6,707.0 64.1 -16.1 29.7

Gyro 3 -6,610.5 43.2 -25.0 12.1

Gyro 4 -6,588.7 33.2 -49.3 11.4

Joint result -6,601.8 18.3 -37.2 7.2

GR Prediction -6,606.1 0.1 -39.2 0.1

Contributions to Experiment Uncertainty rNS (mas/yr) rWE (mas/yr)

Statistical uncertainty 16.8 5.9

Systematic uncertainty

Parameter Sensitivity 7.1 4.0

Solar geodetic effect 0.3 0.6

Telescope readout 0.5 0.5

Other readout uncertainties <1 <1

Other classical torques <0.3 <0.4

Guide star proper motion

uncertainty 0.1 0.1

Total uncertainty 18.3 7.2

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Low & High Frequency SQUID Data

LF SQUID channel (780 Hz LP filter4 Hz LP filter gain)

– 5 Hz continuous

HF SQUID channel (780 Hz LP filter)

– 106 “snapshots” over 1 year

(2200 Hz, ~ 2 sec duration)

SQUID

Pick-Up

Loop

RFR

CFLL Electronics

A/D

A/D

780 Hz

Low Pass

Filter

4 Hz

Low Pass

Filter

Gain

VF

D/A

ROC

D/A

VRCV

RO

ITIFIC

IO

MF

MI

IL

ROF

to A/Dto A/D

Voltage

Divider

VR

Gyro 1 HF “snapshot”, 10 Nov. 2004

LF

channel

HF

channel

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nbCZ rEWrNSg sincos

SQUID & Telescope Readout

Gyros 4 & 3

Gyros 2 & 1

Telescope

Guide Star

(IM Pegasi)

North (inertial) ^ s ^

NSe

EWe

r

S/C x-axis

• Telescope measures

• SQUID measures = –

s ^

SQUID readout in Volts

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Time-varying Scale Factor, Cg

TF

g

LM

g

SRE

gg CCCC

Due to London Moment

Constant to ~10–5

Not modeled

Due to Trapped Flux

& polhode motion

Varies by up to10–2

Modeled to <10–4 by TFM

Due to SQUID Readout

Varies by up to 10–3

Modeled to < 10–4

3 independent sources of evidence for SRE variations of up to 10–3

Injected calibration signal

Flux slipping

Aberration of starlight

Inclusion of SRE model improves segment-to-segment consistency

nbCZ rEWrNSg sincos

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Gyroscope Equations of Motion (NS, EW)

Relativity

Misalignment torque

Roll-polhode resonance torque

nbCZ rEWrNSg sincos

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Data Analysis Tools

High Frequency Analysis

Low Frequency

Analysis

Trapped Flux Mapping (TFM)

Results evaluation

2-second Filter

(Geometric Analysis: cross-check)

Scale factor, polhode parameters

Relativity estimates

+ a few hundred other parameters

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Trapped Flux Mapping

Express trapped magnetic potential

in spherical harmonics

Transform TF fixed in body by

Euler rotation to inertial frame

1. About 3-axis by p (polhode phase) 2. About 2-axis by p (polhode angle)

3. About 3-axis by – s (“spin” phase)

Trapped Flux Mapping:

1. Nonlinear estimation of rotor

dynamics, p(t), p(t), s(t)

2. Linear fit for coefficients of

spherical harmonic , Alm, l odd

Rotor body-fixed frame

I3

I2 I1

Trapped magnetic potential

Tra

pp

ed M

ag

netic P

ote

ntia

l (V

)

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Trapped Flux Mapping (HF Analysis)

Parameter Error

Angular velocity, 10 nHz

~ 10–10

Polhode phase, p ~ 1

Rotor orientation ~ 2

Trapped magnetic potential ~ 1%

Gyroscope scale factor, CgTF ~ 10–4

I3

I2

Path of spin axis in gyro body

I1

I3

I2 I1

Trapped magnetic potential

^ s

Gyro 1

Re

lative C

g v

ari

atio

ns

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The 2-second Filter (LF Analysis)

• LF SQUID data sampled every 2 sec over 1 yr ( 4)

• Nonlinear simultaneous estimation of

– Relativistic drift, scale factor, torque coeffs., telescope params., …

• Batch least-squares fit (Bayesian)

– Iterative linearization & linear least squares fit

– Sigma point algorithm for Jacobian computation

• Robust convergence & unbiased uniform drift estimates

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Choosing Baseline Number of Parameters

r NS (m

as/y

r)

rWE (mas/yr)

0 terms 1 term

2 terms 3 terms

5 terms

4 terms

6 terms

baseline

sensitivity

• Low frequency scale

factor variations

• Trapped flux part of

scale factor

• Low freq. misalignment

torque coefficient

• Polhode harmonics of

torque coefficient

• Telescope scale factor

Relevant Sub-models

Criteria: increase number of terms until rNS, rWE 0.5

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Parameters & Data Segments & Data Points

• 6 data segments 4 gyros analyzed independently

– Consistency of 24 gyro-segments verifies model accuracy

• 6 segments analyzed together for each gyro

– Most precise result due to nonlinearities

• Linear combination of 4 gyros

– Final experiment result

Gyro 1 Gyro 2 Gyro 3 Gyro 4

No. parameters 154 662 139 272

No. days of data 200.7 219.7 188.8 241.7

No. 2 s data points 8.7 × 106 9.5 × 106 8.2 × 106 10.4 × 106

Number of parameters & days of data & data points per gyro

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Individual Gyro & Joint Results & GR Prediction

All ellipses are 95% confidence

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Cross-checks

1. Consistency of analysis approaches

2. Segment-to-segment consistency

3. Gyro-to-gyro consistency

4. Measurement of Guide Star bending by the Sun

5. Others …

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East-West Orientation (arbitrary units)

No

rth

-So

uth

Orie

nta

tio

n (

arb

itra

ry u

nits)

-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

Co

sin

e o

f R

oll F

req

uen

cy (

mV

)

Sine of Roll Frequency (mV)

North

West

Approximate Scale:

50 mas

Roll-polhode Resonance Torque

Electrostatic model predicts Euler spiral motion when

harmonic of polhode = roll frequency

Unique behavior clearly seen in “raw” data

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Misalignment torque

Geometric method is torque model independent

Consistent with 2-second Filter with explicit model

From 2-sec Filter

From Geometric method

(model independent)

Gyro 3

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Gyro 4 Per-segment Results without SRE Model

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Gyro 4 Per-segment Results with SRE Model

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Segment-to-Segment Consistency

Gyro 1 Gyro 2

Gyro 3 Gyro 4

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Consistency Among Analysis Approaches

Geometric method less model independent

– Uses geometry to eliminate misalignment torque from data

– Reduced precision relative to 2-second Filter

-1500 -1000 -500 0 500 1000

-7500

-7000

-6500

-6000

-5500

rEW

(marcsec/yr)

r NS (

ma

rcse

c/y

r)

5

6

9

10

Gyro 4, segments

5, 6, 9, 10

Geometric

2-sec Filter

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Gravitational Deflection of Starlight

• As a cross-check, Geometric method inverted to estimate guide

star deflection by the Sun

• Modified gyro rate equations

• GR predicted deflection:

21.7 mas

• GP-B estimate:

21 7 mas

-50 0 50 100 150 200 250-5

0

5

10

15

20North-South Deflection of Light

mill

i-a

rc-s

ec

-50 0 50 100 150 200 250-10

0

10

20West-East Deflection of Light

mill

i-a

rc-s

ec

Time (days) from Jan. 1, 2005

)(

)(

tddt

dkR

dt

ds

tddt

dkR

dt

ds

WENSWEWE

NSWENSNS

Page 44: The Relativity Mission, Gravity Probe B Results and Lessons … · 2013. 4. 16. · The Relativity Mission, Gravity Probe B Results and Lessons Learned Sasha Buchman for the GP-B

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Credibility of the Result

1. Models based on the physics of the experiment

2. Clear separability of relativity from classical effects

3. Parameter sensitivity

• Result NOT from any particular choice of parameters

4. Verification through consistency of results

• Gyro-to-gyro

• Segment-to-segment

5. Agreement between separate approaches

• For both intermediate parameters and relativity estimates

GP-B result -6,601.8 18.3 -37.2 7.2

GR Prediction -6,606 0.1 -39.2 0.1

Page 45: The Relativity Mission, Gravity Probe B Results and Lessons … · 2013. 4. 16. · The Relativity Mission, Gravity Probe B Results and Lessons Learned Sasha Buchman for the GP-B

45

Lessons Learned

A. Large gaps and no disturbances to TM

B. The more data the better

C. COMPLEX SPACE EXPERIMENTS DO WORK

Page 46: The Relativity Mission, Gravity Probe B Results and Lessons … · 2013. 4. 16. · The Relativity Mission, Gravity Probe B Results and Lessons Learned Sasha Buchman for the GP-B

46

Thank you for your attention

Page 47: The Relativity Mission, Gravity Probe B Results and Lessons … · 2013. 4. 16. · The Relativity Mission, Gravity Probe B Results and Lessons Learned Sasha Buchman for the GP-B

47

UV Charge Management Concept

UV Electrode

UV Lamp Assembly

Rotor charge controlled via UV excited electrons

Charge rates ~ 0.1 pC/day

Continuous measurement at the 0.1 pC level

Control requirement: 15 pC

Gyro

1 C

harg

e (

pC

)

0.2 0.6 1.0 1.4 1.8

Day of year, 2004 (+221)

450pC (on levitation)

100 pC

0 pC

70 pC/hour

discharge

Discharge of Gyro1 after levitation

450

400

350

300

250

200

150

100

50

0

-50

Page 48: The Relativity Mission, Gravity Probe B Results and Lessons … · 2013. 4. 16. · The Relativity Mission, Gravity Probe B Results and Lessons Learned Sasha Buchman for the GP-B

48

Gyro

Pote

ntial (m

V)

300 350 400 450 500 550-15

-10

-5

0

5

MEASURED GYRO CHARGE (mV)G

YR

O 1

300 350 400 450 500 550

-5

0

5

10

15

GY

RO

2

300 350 400 450 500 550

-5

0

5

10

GY

RO

3

300 350 400 450 500 550

-20

-15

-10

-5

0

5

GY

RO

4

Day of Year 2004

G #1

G #2

G #3

G #4

300 350 400 450 500 550

300 350 400 450 500 550

300 350 400 450 500 550

Day of Year 2004

300 350 400 450 500 550

0

-10

10

0

10

0

0

-10

-20

UV Charge Management Results

Discharge I Discharge II 1 pC 1 mV

Cgyro = 1 nF