1. Parker Lowe 4/17/2018 California Institute of Technology
Gravity Probe B
Parker Lowe
4/17/2018
California Institute of Technology

2. What is Gravity Probe B
Satellite-based experiment to test GR by measuring spacetime curvature near Earth via gyroscopes
Small changes in spin axis from GR effects
Fundamentally: “A star, a telescope, and a spinning sphere.” –Bill Fairbank
Conducted by NASA and Stanford University

3. Image credit: NASA

4. Image credit: NASA, Lockheed Martin- Russ Underwood

5. Overview Purpose: Testing General Relativity Geodetic Effect
Frame Dragging
Experimental Setup and Methods
London Moment Gyroscopes
Reference Telescope
SQUID
“Near Zeroes”
Data and Results
Data
Significance
Second space-gravity measurement
Politics
Spinoffs

6. General Relativity Refresher
GR: generalizes special relativity and Newton’s universal gravitation to describe gravity as geometric property of spacetime
Schwarzschild Metric: Solution to Einstein Field EQ’s for the field outside a circular mass
How to reconcile with quantum physics (quantum gravity)- still unknown
Special relativity:
Laws of physics invariant in inertial frames
Speed of light in a vacuum same for all observers

7. General Relativity Predictions
Two previously unverified predictions:
Geodetic Effect
The effect of curved spacetime on a moving vector
Frame Dragging
The effect of rotating mass on the curvature of spacetime
Both effects contribute to changes in spin of the gyroscopes

8. Rendering of Geodetic and Frame Dragging Effects (J.P. Ekels)
Image credit: Stanford GP-B Official Site

9. Geodetic Effect Derivation (Short)
Derivation of precession from Schwarzschild metric:
Standard metric w/ c=G = 1.
Introduce rotating coord. syst. by substituting
Transform to rotating frame: B = sin^2(theta)
Lots of algebra: accumulated precession for one orbit:

10. Geodetic Effect Animation
Image credit: The Physics Mill

11. Geodetic Effect
Testing: Observe how precession of gyroscope angular momentum matches this prediction
Need very sensitive gyroscopes and measurement equipment
Will elaborate on sensitivity levels required

12. Frame Dragging Mathematics
Kerr Metric, Boyer-Lindquist Coordinates
See Wikipedia for more info on the derivations

13. Frame Dragging Tested the same way as the geodetic effect
Precession of the angular momentum axis of the gyroscope
Smaller effect requires higher levels of precision to measure compared to geodetic effect

14. Measurement Philosophy
Elegant design: N-S deviation would only be caused by geodetic perturbation, while E-W deviation includes frame-dragging effects

15. Image credit: Stanford

16. Experimental Setup Why space? The gyroscopes The telescope The probe
Image credit: Stanford

17. Why Space?
“In the realm of black holes and the universe, the language of general relativity is spoken, and it is spoken loudly. But in our tiny solar system, the effects of general relativity are but whispers.” –Kip Thorne
High levels of sensitivity required necessitate low background noise
Caveat: One second launch window for perfect polar orbit, necessary to decompose spin signals

18. “Near-Zeroes” High precision requires reduction of background noise
Seven key constraints
Three on gyro rotors
Four on the cryogenic laboratory environment
Constraints such that compound error signal will be less than the signal to be measured

19. Near-Zeroes: Table Table: Stanford (Einstein.Stanford.edu)
Experimental Variable
Tolerance Requirements
Tolerances Achieved During Mission
Gyroscope Rotor Near Zeros
Mechanical Sphericity
50 nanometers (2 microinches)
<10 nanometers (< 0.4 microinches)
Material Homogeneity
3 parts in 106
3 parts in 107
Electrical Sphericity
5 parts in 107
<5 parts in 107
Probe Environment Near Zeros
Temperature
1.95 kelvin (-271.2° Celsius or ° Fahrenheit)
1.8 kelvin (-271.4° Celsius or ° Fahrenheit)
Non-Gravitational Residual Acceleration
Less than g
Less than 5 x g
Background Magnetic Field
10-6 gauss
Less than 10-7 gauss
Probe Pressure
10-11 torr
Less than torr
Table: Stanford (Einstein.Stanford.edu)

20. Gyroscope Design
Unique sphere design of 1.5in pure fused quartz coated with niobium
Most spherical objects created by humans at time
Significant constraints
Image credit: Popular Science

21. Gyroscope Sphericity
Image credit: Stanford

22. Gyroscope Drift Rate ESG: Electrically Suspended Gyroscope
Space required
Image credit: C. W. F. Everitt 2006

23. Gyroscope Function
Spinning superconductor generates magnetic field along rotation axis (London moment)
Measured by SQUIDs and averaged to determine angular momentum vector
Averaging introduces some issues to discuss later

24. Gyroscope Suspension (GSS)
Spun up by helium gas and suspended by superconducting electrodes
Operates from 1 to 10^-8 Gs
15,000 nm range of motion within cavity to orient along spin channel, calibrate, and center upon beginning measurement

25. Gyroscope Drag-Free
Gyroscopes suspended inside interior of satellite, not in contact after spin-up: true shielded orbit!
Drag-Free: Spacecraft shields gyros from solar weather and “chases” them via sensor feedback system
Solar weather an issue that appears later as well

26. Drag-Free Data:
Image credit: Stanford, C. W. F. Everitt 2009

27. Gyroscope Issues
Three Newtonian issues compromised gyroscope performance and accuracy (systematic errors)
1. Damped polhode motion
2. Misalignment Torques
3. Roll-polhode resonance torques

28. Damped Polhode Motion
Akin to football wobble: rotation between 2 stable axes
Rotatonal Motion of an Object around Its Three Principal Axes of Inertia
Principal Axis of Minimum Inertia Simulation
Principal Axis of Maximum Inertia Simulation
Principal Axis of Interm. Inertia Simulation
Stable Rotation
Unstable Rotation
Image credit: Einstein.Stanford.edu, “Polhode Motion”

29. Damped Polhode Motion
Affects gyroscopes due to surface mass inhomogeneity
Dissipates due to
Internal energy dissipation
10^-16 W, interface between rotor and niobium coating, gas damping
External torques with resonant frequency

30. Damped Polhode Motion: Gyro 1
Early Mission
Mid Mission
Late Mission
Large Polhode Path
Moderate Polhode Path
Very Small Polhode Path
Image credit: Einstein.Stanford.edu, “Polhode Motion”

31. Misalignment Torques
Occurs when spacecraft is not aligned with gyroscope
Caused by electrostatic patches on the gyroscopes interacting with the spacecraft
Geometrically related to spacecraft deflection angle so can be filtered out

32. Roll-Polhode Resonance Torques
“Offsets in orientation of gyroscopic axis tend to occur when a harmonic of the gyroscope polhode frequency is equal to the satellite roll frequency”
Combination of polhode external torque effects creates new modeling complication

33. Clever solutions
Deliberately misaligned satellite at end to increase measurable effect of anomalies and model them
Incorporate classical effects from patch potentials on a per-orbit basis
Analytically model polhode effects to correct for error signal

34. SQUID Magnetic Gyro Readout
Super –conducting Quantum Interference Device
Provides gyro spin axis orientation readout by measuring magnetic field from spinning sphere
.1 milliarcsecond precision over arcseconds
Noise: 190 marc-s/Hz
DC Trapped Flux < 10^-6 gauss
AC Shielding > 10^12
Requirements to avoid interference with gyroscope measurement precision

35. SQUID Diagram

36. Telescope: Image Detection
36 cm reflector
3.8m focal length
Detect orientation to guidestar
.1 milliarcsecond accuracy required
Diffraction limit size only 1.4 arcseconds: PROBLEM
Solution: split axes and measure intensity to orient
Sn = (S+ - wS-)/(S+ + wS-)

37. Telescope Schematic View

38. Telescope and Housing

39. Guidestar Want a fixed point to maintain “static” angular orientation
Would want to use a quasar, but too far to track with optical telescope
Solution: use a closer, more visible star that can be motion-tracked to quasars separately
Also radio-visible which helped correlate motion
Star chosen: IM Pegasi (HR 8703)

40. Star Images
Image: Stanford

41. Gyro and Telescope Mounting

42. Dewar and Thrusters
Essentially a giant thermos to maintain specific temp
Doubles as propulsion system by venting helium
Image credit: Stanford

43. Nine Degrees of Freedom
Required 9 DOF to maintain drift-free alignment with guidestar, essential to measure gyroscope axial rotation
3 translational + 3 rotational for the spacecraft + 3 interior translational for gyroscopes
Highest precision satellite control system at launch

44. Data Collection Anomalies
Single bit errors (SBE) or single bit upsets (SBU)
Charged particle interactions from Earth’s magnetic field or solar weather cause memory errors
Image: GPB Post-Flight Analysis - Final Report

45. Operation Summary Liftoff April 20, 2004 10AM 4 month initialization
Collecting data started Aug 24, 2004 for 50 weeks
Data Analysis begins October 2005, continues over time allotted due to systematic error source effects
NASA Funding ends 2008
Funding from Saudi Arabia until 2010
Final findings announced May 4, 2011
Raw data not yet released

46. Final Unmodeled Results (raw data)
Graph: Everitt et al 2011

47. Modeled Data
Graph: Stanford 2009

48. Final Experimental Data
Gravity Probe B — Final Experimental Results
Gyroscope
rN-S (Geodetic Measurement)
rW-E (Frame-Dragging Measurement)
Individual Gyroscope Results
Gyroscope #1
-6,588.6±31.7 mas/yr
-41.3±24.6 mas/yr
Gyroscope #2
-6,707.0±64.1 mas/ yr
-16.1±29.7 mas/yr
Gyroscope #3
-6,610.5±43.2 mas/yr
-25.0±12.1 mas/yr
Gyroscope #4
-6,588.7±33.2 mas/yr
-49.3±11.4 mas/yr
Weighted-Average Results for All Four Gyroscopes
All Gyroscopes
-6,601.8±18.3 mas/yr
-37.2±7.2 mas/yr
Schiff-Einstein Predicted Theoretical Values
Theoretical Gyroscope
-6,606.1 mas/yr
-39.2 mas/yr
Credit: Stanford 2011 “GP-B Status Update”

50. Significance Second space gravity measurement Politics: Funding
Most precise check of GR to date
Politics: Funding
Spinoffs

51. First Space Gravity Measurement
Gravity Probe A: Calculated redshift by measuring elapsed time of identical hydrogen MASER clocks
Confirmed Einstein redshifit prediction to 1.4 parts in 10^4

52. Politics
Ran out of NASA funding in 2008 and were supported by King Abdulaziz City for Science and Technology (KACST)

53. Quick Facts
Spacecraft Length 6.43 meters (21 feet) Diameter 2.64 meters (8.65 feet) Weight 3,100 kg (3 tons) Power Total Power: 606 Watts (Spacecraft: 293 W, Payload: 313 W) Batteries (2) 35 Amp Hour Dewar Size 2.74 meters (9 feet) tall, 2.64 meters (8.65 feet) diameter Contents 2,441 liters (645 gallons) superfluid 1.8 Kelvin (-271.4°C) Telescope Composition Homogeneous fused quartz Length centimeters (14 inches) Aperture centimeter (5.5-inch) Focal length 3.81 meters (12.5 feet) Mirror diameter 14.2 centimeters (5.6 inches) Guide Star HR 8703 (IM Pegasi) Gyroscopes (4) Shape Spherical (Sphericity < 40 atom layers from perfect) Size 3.81 centimeter (1.5-inch) diameter Composition Homogeneous fused quartz (Purity within 2 parts per million) Coating Niobium (uniform layer 1,270 nanometers thick) Spin Rate Between 5,000 – 10,000 RPM Drift Rate Less than degrees/hour Launch Vehicle Manufacturer & Type Boeing Delta II, Model Length 38.6 meters (126.2 feet) Diameter 3 meters (10 feet) Weight 231,821 kg (511,077 lbs or tons) Stages 2 Fuel 9 strap-on solid rocket motors; kerosene and liquid O2 in 1st stage; hydrazine and N-tetroxide in 2nd
Mission Launch Date April 20, 2004 Site Vandenberg Air Force Base, Lompoc, CA Duration months, following days of checkout and start-up after launch Orbit Characteristics Polar orbit at 640 kilometers (400 miles), passing over each pole every min. Semi-major axis km (4,366.8 miles) Eccentricity Apogee altitude km (409.6 miles) Perigee altitude km (397.4 miles Inclination ° Perigee Arg. 71.3° Right Asc. of asc. node ° Measurements Geodetic Effect 6,614.4 milliarcseconds or 6.6 arcseconds (1.83x10-3 degrees) Frame Dragging 40.9 milliarcseconds (1.14x10-5 degrees) Required Accuracy Better than 0.5 milliarcseconds (1.39x10-7 degrees) Program Duration 43 years from original conception; 40 years of NASA funding Cost $750 million dollars

54. Sources
Everitt et. al. 2011, “Gravity Probe B: Final Results of a Space Experiment to Test General Relativity” Physical Review Letters, June p.106
Keiser, Mac. “Gravity Probe B: Data Analysis Challenges, Insights, and Results” April 15, 2007
Turneaure, John. “The Gravity Probe B Science Instrument”
Will, Clifford M. “Finally, Results from Gravity Probe B.” Physics Viewpoint, May
Everitt, Francis. “Gravity Probe B: The Engineering of a Physics Experiment in Space” May
Everitt, Francis. “Testing Einstein in Space: The Gravity Probe B Mission” 18 May 2006
“Frame Dragging” Wikipedia:
“Geodetic Effect” Wikipedia:
“GP-B Mission Overview” Standford.
“The Gravity Probe B Experiment: Post-Flight Analysis – Final Report” NASA, Stanford, Lockheed Martin. March 2007
Muhlfelder, Barry. “Gravity Probe B Overview: HEPL-AA Seminar” June 17, 2009
Jonah. “The Geodetic Effect: Measuring the Curvature of Spacetime” The Physics Mill: December 27,