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Gravity Probe B – Testing General Relativity with Orbiting Gyroscopes

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Gravity Probe B – Testing General Relativity with Orbiting Gyroscopes GP-B T0082 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 GP-B T0083 GGI Workshop 2006 1 Outline • Gravity Probe B – Description of the experimental concept – Difficult requirements and key enabling technologies. – Status of post-flight data analysis • STEP Mission Update GP-B T0083 GGI Workshop 2006 2 Testing GR with Orbiting Gyroscopes “If, at first, the idea is not absurd, then there is no hope for it.” - Albert Einstein 3GM GI ⎡3R ⎤ Leonard Schiff’s =Ω R() × v + ()ω⋅R −ω relativistic c2 2 R 3 c2 R 3⎣⎢ R 2 ⎦⎥ precessions: Geodetic, ΩG Frame Dragging, ΩFD ds Spin axis orientation: = Ω×s dt GP-B T0083 shop 2006GGI Work 3 How Big is a 0.1 Milli-Arc-Second? 0.1 marc-sec = Angular width of Lincoln’s eye in New York seen from Paris! 0.1 marc-sec GP-B T0083 GGI Workshop 2006 4 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. GP-B T0083 GGI Workshop 2006 5 Why a Space-based Experiment? 6614 Electrostatic vacuum 1010 Geodetic effect gyro on Earth 103 uncompensated <0.002% accuracy (10-1 deg/hr) 109 102 Spacecraft gyros 8 10 marc-s / yr -3 Frame dragging (3x10 deg/hr) 41 <0.3% accuracy 10 Best laser gyro 107 (10-3 deg/hr) 6 10 1 Electrostatic vacuum gyro 0.5 GP-B requirement on Earth (torque marc-s / yr Single gyro expectation modeling) (10-5 deg/hr) 105 0.21 0.1 0.12 4 Gyro expectation (3x10-10 deg/√hr) 104 Cold Atom Gyro -6 (3x10 deg/√hr) 0.01 Expected GP-B 103 (Kasevich 2006) performance on orbit Operation in 1g environment degrades mechanical gyro performance Laser gyroscopes and other technologies fidelity too low for GP-B GP-B T0083 GGI Workshop 2006 6 The “simplest experiment” “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) 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 GP-B T0083 GGI Workshop 2006 7 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! GP-B T0083 GGI Workshop 2006 8 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 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 T0083 GGI Workshop 2006 9 GP-B Launch - 20 April 2004 Launch! Release from launch vehicle Fairing Installation GP-B T0083 GGI Workshop 2006 10 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. GP-B T0083 GGI Workshop 2006 11 “Perfect” Mass Balance Needed! ω Mass Balance Requirements: r s o yr G n pi s s xi On Earth (ƒ = 1 g) δr < 5.8 x 10-18 δ r CG a r (ridiculous – 10 -4 of a proton!) Standard satellite (ƒ ~ 10-8 g) δr f r < 5.8 x 10-10 (unlikely – 0.1 of H atom diameter) External forces acting GP-B drag-free (ƒ ~ 10-12 g δr through center of force, r < 5.8 X 10-6 different than CM cross- track average) (straightforward – 100 nm) Drag-free eliminates δr Demonstrated GP-B rotor: < 3 x 10-7 mass-unbalance torque r and key to Requirement Ω < Ω δ r 2 rωs understanding of other 0 < Ω ~ 0.1 marc-s/yr 0 support torques rf5 (1.54 x 10-17 rad/s) Drift-rate: Ω =τ Iωs Torque: τδ= mf r Moment of Inertia: I = (25)mr 2 GP-B T0083 GGI Workshop 2006 12 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! GP-B T0083 GGI Workshop 2006 13 Flight Proportional Thruster Design • Cold gas (no FEEP!) proportional thruster; 16 units on space vehicle. • Operates under choked flow conditions • Pressure feedback makes thrust independent of temperature Thrust 3.5mm ia Thrust: 0 – 10 mN Propellant: Helium Dewar Boiloff ISP: 130 sec Supply: 5 to 17.5 torr Mdot: 6-7 mg·s−1 Noise: 25 µN·Hz−1/2 Location of thrusters on Space Vehicle GP-B T0083 GGI Workshop 2006 14 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. 1 G U Ms2 G R G G ()rR− G r 1 G u ms2 GP-B T0083 GGI Workshop 2006 15 Drag Free Control for a Perfect Orbit Prime and Backup Drag Free operations, GP-B Gyro3 (VT=142273900) Demonstrated performance 20 better than 10-11 g residual Xs v Normal gyro Ysv acceleration on drag free 0 Zsv gyroscope in measurement Gyro suspension band Gyro3 pos (nm) -20 0 1000 2000 3000 4000 5000 6000 Position (nm) (12.9mHz ± 0.2mHz) 0.1 Rejection ~ 10,000x N) Xs v Accelerometer μ Prime N) Ysv μ mode mode 0 Zsv Suspension Inertial space – Frequency domain Suspension ON OFF Gyro3 CE ( effort ( Gyro control -0.1 Drag-free control effort and residual gyroscope acceleration (2004/239-333) -7 0 1000 2000 3000 4000 5000 106000 Polhode 5 Gravity Gyro CE inertial frequency SV CE inertial Xs v Gradient Ysv -8 Roll rate 10 thrust 0 Zsv (mN) Thruster SV Thrust -9 -5 10 Force SV trans force (mN) 0 1000 2000 3000 4000 5000 6000 seconds -10 10 Drag free modes in operation Control Effort (g) Residual gyro Acceleration (g) acceleration -11 5x10-12 g in band 10 ~1.5x10-8 (m/s2)/√Hz 0.02mHz – 80 mHz -12 10 -4 -3 -2 -1 0 10 10 10 10 10 Frequency (Hz) GP-B T0083 GGI Workshop 2006 16 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? The Solution: 2mc −7 London Moment Readout. A M Ls=−ωω =−1.14 × 10 s() Gauss e spinning superconductor develops a magnetic “pointer” aligned with its spin axis. Magnetic field sensed by a SQUID, SQUID electronics in Niobium carrier a quantum limited, DC coupled magnetic sensor. Performance: measurement better Requirement than 200 marc-s/√Hz GP-B T0083 GGI Workshop 2006 17 Science Instrument Assembly Stanford-developed silicate Star bonding technique to join Guide star block and telescope. tracking telescope IM Pegasi (HR 8703) Gyros 1 & 2 1 2 3 4 Quartz Mounting block flange Gyros 3 & 4 GP-B T0083 GGI Workshop 2006 18 Star Tracking Telescope Detector Package • Field of View: ±60 arc-sec. • Measurement noise: ~ 34 marc-s/√Hz • All-quartz construction. • Cryogenic temperatures make a very stable mechanical system. Physical length 0.33 m At focal plane: Focal length 3.81 m Image diameter 50 μm Aperture 0.14 m 0.1 marc-s = 0.18 nm Telescope in Probe Image divider Integrated Telescope GP-B T0083 GGI Workshop 2006 19 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 Enables the readout system to function to its stringent requirements Expanded lead bag GP-B T0083 GGI Workshop 2006 20 Cryogenic Dewar and Probe Probe during assembly Gyro- • 2524 liter superfluid helium (1.82K dewar) scopes • Porous plug phase separator.
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