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Anna Nobili (University of Pisa & INFN) for the GG/GGG collaboration FPS-06 , LNF March 21-23 2006

“Galileo Galilei ( GG )” small satellite test of the Equivalence Principle and relevance of the results obtained with the GGG experiment. Anna Nobili (University of Pisa & INFN) for the GG/GGG collaboration FPS-06 , LNF March 21-23 2006.

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Anna Nobili (University of Pisa & INFN) for the GG/GGG collaboration FPS-06 , LNF March 21-23 2006

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  1. “Galileo Galilei (GG)” small satellite test of the Equivalence Principle and relevance of the results obtained with the GGG experiment Anna Nobili (University of Pisa & INFN) for the GG/GGG collaboration FPS-06, LNF March 21-23 2006

  2. GENERAL RELATIVITY NEEDS TESTS of the EQUIVALENCE PRINCIPLE Gravity is the weakest force of all but the dominant force at large scale. General Relativity (GR) is the best theory of gravity and has been put to stringent tests since the start of the space age. … Yet, the continued inability to merge gravity withquantum mechanics suggests that the pure tensor gravity of GR needs modification or augmentation. The most promising scenario for the quantization of gravity and the unification of all natural interactions is superstring theory. However, it naturally predicts the existence of long range scalar fields (in addition to the pure tensor field of GR) which are composition dependentand therefore violate the Equivalence Principle (EP)

  3. THE OBSERVABLE to be MEASURED for TESTING the EQUIVALENCE PRINCIPLE The most direct experimental consequence of the Equivalence Principle is the Universlaity of Free Fall (UFF): in the gravitational field of a source mass all bodies fall with the same acceleration regardless of their mass and composition The observable to be measured is the differential acceleration of different composition test masses in the gravitational field of a source body (i.e. Earth, Sun..): a/a=0 if UFF, hence the Equivalence Principle and GR hold (Eötvös parameter)

  4. The link between composition dependent effects expressed by the Eötvös parameter , and PPN (Parametrized Post Newtonian) deviations from GR expressed by the Eddington parameter  , is given by (PRD 2002): …and since  tests already give (since 1972..) while the best  tests (Cassini, 2003) give: EQUIVALENCE PRINCIPLE TESTS ARE by far the MOST POWERFUL TESTS of GENERAL RELATIVITY the superior probing power of UFF (hence EP) tests is beyond question !!! In simple terms, this expresses the fact that EP is the founding “principle” of GR: “hypothesis” of complete physical equivalence (Einstein 1907)

  5. EQUIVALENCE PRINCIPLE TESTS: WHAT’s ON The best ground tests (with slowly rotating torsion balance) provide:   9.310-13 Proposed and ongoing experiments for EP testing :   10-17 , 10-18 GG (I) 250 kg; STEP (USA) 1000 kg- LEO   10-14 , 10-15 GREaT (I-USA) -balloon, SCOPE (F) 200 kg -LEO   10-12 Torsion balances (USA)

  6. GG: configuration for EQUATORIAL ORBIT 1m 1m s/c configuration for equatoriial (VEGA launch; operantion from ASI ground station in Malindi)

  7. Because of classical tidal effects the test masses must be concentric (cylinders..) GG: the SPACE EXPERIMENT DRIVING CONCEPTS (I) The system must spin in order to up-convert the frequency of an EP violation from the orbital frequency to a higher, far away, frequency • By preserving the cylindrical symmetry of the experiment we have: 1) s/c is passive stabilized by spin around the symmetry axis  no active control of whole s/c required 3) no motor needed once the s/c has been spun to nominal spin rate (2 Hz) 4) accelerometer sensitive in 2-D rather than 1-D  gain by factor SQRT(2) By exploiting cylindrical symmetry we gain in sensitivity and reduce the mass of the satellite (+ its complexity and cost).

  8. GG: the SPACE EXPERIMENT DRIVING CONCEPTS (II) Fast rotation of whole spacecraft around symmetry axis for high frequency modulation (2 Hz) Large test masses to reduce thermal noise (with 10 kg test mass at room temperature the ratio T/m is the same as in STEP) High level of symmetry But people were scared to set large macroscopic test masses in rapid rotation !!!!! Small total satellite mass (250 kg) - determined in Phase A Studies with industry

  9. GG DIFFERENTIAL ACCELEROMETR Test masses of different composition (for EP testing) For CMR in the plane of sensitivity ( to symmetry/spin axis): test bodies coupled by suspensions (beam balance concept)& coupled by read-out (1 single capacitance read out in between cylinders)

  10. GG ACCELEROMETERS: SECTION ALONG THE SPIN AXIS GG inner & outer accelerometer (the outer one has equal composition test cylinders for systematic checks) Accelerometers co-centered at center of mass of spacecraft for best symmetry and best checking of systematics…

  11. GG ACCELEROMETERS CUTAWAY Design symmetry is extremely importnat in small force gravitational experiments….. Note the azimuthal symmetry of the accelerometers around the cylinders’ axis –which is also the spin axis- as well as the top/down symmetry. The rest of the spacecraft around the accelerometers preserves both these symmetries too.

  12. GGG vs GG design Local gravity in the lab forces the GGG design to break symmetry top/down….

  13. GGG in INFN lab GGG lab 2005 (March) 1m

  14. RESULTS from TILT MEASUREMENTS Automated Control of Low Frequency Terrain Tilts-0.9Hz spin rate Low frequency terrain tilts are strongly reduced: the control loop works very well. Work in progress to reduce thermal variation effects on the zero of the tilt sensor.

  15. DIFFERENTIAL MOTION of ROTATING TEST CYLINDERSfrom Rotating Capacitance Bridges: improvements since 2002 GGG operation in INFN lab started in 2004: • Gained by 2 orders of magnitude in residual noise • Long term stable continuous operation without instability demonstrated

  16. AUTOCENTERING of GGG TEST CYLINDERS vs SPIN FREQUENCY Experimental evidence of autocentering of the test cylinders in supercritical rotation: relative displacements of the test cylinders in the rotating frame (X in red, Y in blu) decrease as spin frequency increases and crosses the resonance zones (shown by dashed lines) ….. See next slide….

  17. AUTOCENTERING of GGG TEST CYLINDERS in the ROTATING PLANE Experimental evidence of autocentering of the test cylinders in supercritical rotation: in the horizontal plane of the rotating frame the centers of mass of the test cylinders approach each other as the spin frequency increases (along red arrow) from below the first resonance (L), to between the two resonances (M), to above both resonances (H). The equilibrium position reached is always the same (determined by physical laws..), thus allowing us to set the electric zero of the read out

  18. Q MEASUREMENTS @ NATURAL FREQUENCIES Q measured from free oscillations of full GGG system at its natural frequencies –see blu lines- with system not spinning: 0.0553 Hz (18 sec) 0.891 Hz (1.1 sec) 1.416 Hz (0.7 sec) Q MEASUREMENTS @ NATURAL FREQUENCIES (I) Q of GGG apparatus at frequencies other than the natural ones (e.g. at 0.16 Hz) can be measured (during supercritical rotation at that frequency) from the growth of whirl motion….

  19. Rotordynamics theory states that in supercritical rotation (defined by spin frequency > natural frequency) whirl motions arise at each natural frequency whose growth is determined by the Q of the full system at the SPIN frequency of the system (not at the natural frequency …..) Q in SUPERCRITYICAL ROTATION Integration time available until whirl of period Tw grows by factor k High Q means slow whirl growth, and Q at higher frequencies is larger …. ok In supercritical rotation thermal noise also depends on Q at the spin frequency (not at the –low- natural one) and this is a crucial advantage..

  20. Q MEASUREMENT from GROWTH of WHIRL MOTION (data of fixed electronics) Spin period 6.25 sec (0.16 Hz), whirl period 13 sec (O.0765 Hz), whirl control off

  21. Q MEASUREMENT from GROWTH of WHIRL MOTION (data of rotating electronics) Spin period 6.25 sec (0.16 Hz), whirl period 13 sec (O.0765 Hz), whirl control off Measurements of whirl growth made with 2 different read-outs give the same value of Q at 0.16 Hz: this is the relevant Q for operation at that spin rate

  22. ETA in GGG: In the field of the Earth from space (GG orbit) with natural differential period of TMs

  23. The sensitivity to differential accelerations between the test masses (sensitivity to EP tests), is inversely proportional to the square of their natural differential period: The GREAT ADVANTAGE of WEIGHTLESSNESS The natural differential period is inversely proportional to the stiffness of their coupling: In space, thanks to weightlessness, the stiffness of coupling can be weaker than on Earth by many orders of magnitude… From GG Phase A Study (ASI 1998; 2000), as compared to GGG, we see that the factor gained in absence of weight is:

  24. ETA in GG: In the lab, with this apparatus, we can improve x @ orbGG by a factor 50 In space we gain: 1500 (weaker suspensions in absence of weight, longer differential period - quadratic improvement) 10 (no motor , no motor noise…) 10 (no terrain tilts – the whole satellite spins together and spin energy is so large that disturbing torques are ineffective…) (FFEPs for drag compensation developed for SCOPE and LISA-PF anyway) If we shall be able to gain the required factor 50 in the sensitivity of the GGG experiment, the other factors are expected in space and the GG goal of an EP test to 10-17 can rely on solid experimental grounds

  25. GG SIMULATIONS During Phase A and Advanced Phase A Studies From GG Proposal to ESA, Jan 2000, p.16 http://eotvos.dm.unipi.it/nobili/ESA_F2&F3/gg.pdf Realistic simulation of GG space experiment (errors according to requirements; see reference for details) showing the relative displacements of the test masses after whirl and drag control, with an applied “EP violation” signal to 10-17. The applied EP signal could be recovered by separating it from residual whirl and drag, though they were both larger (see reference online to understand how…)

  26. Satellite: —spin axis stabilized; ADVANCED DRAG COMPENSATION by FEEP thrusters (ASI) — FEEP thrusters: 150 N thrust authority; built in Pisa, already funded by ESA for SCOPE and LISA-PF to be availbale 2008-2009 GG MISSION PROGRAMMATICS Payload: —differential accelerometer similar to GGG, incorporating all what has been learned in the lab (INFN) —PGB enclosing accelerometr (noise attenuation + test mass driving drag-free control (ISRO-Indian Space Resrch Organization) Launch: —VEGA (qualification launch…multiple launch since GG is MICRO) Operation: —MALINDI GG included in ASI National Space Plan recently approved – VEGA launch foreseen Data archiving and analysis: —University of Pisa

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