“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

GENERAL RELATIVITY NEEDS TESTS of the EQUIVALENCE PRINCIPLEGENERAL 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.

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 dependent and therefore violate the Equivalence Principle (EP)

… Yet, the continued inability to merge gravity with quantum mechanics suggests that the pure tensor gravity of GR needs modification or augmentation.

THE OBSERVABLE to be MEASURED for TESTING the EQUIVALENCE PRINCIPLE 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

if UFF, hence the Equivalence Principle and GR hold (Eötvös parameter)

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

EQUIVALENCE PRINCIPLE TESTS ARE by far the MOST POWERFUL TESTS of EQUIVALENCE PRINCIPLE TESTS ARE by far the MOST POWERFUL TESTS of GENERAL RELATIVITY GENERAL RELATIVITY

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):

52.6 10 1

a

a…and since tests already give (since 1972..)

12 710 1 10

Be CuBe Cu

a

a

while the best tests (Cassini, 2003) give:

51 2.3 10 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)

EQUIVALENCE PRINCIPLE TESTS: WHAT’s ONEQUIVALENCE PRINCIPLE TESTS: WHAT’s ON

The best ground tests (with slowly rotating torsion balance) provide:

Proposed and ongoing experiments for EP testing :

GG (I) 250 kg; STEP (USA) 1000 kg- LEO

GREaT (I-USA) -balloon, SCOPE (F) 200 kg -LEO

Torsion balances (USA)

9.310-13

10-17 , 10-18

10-14 , 10-15

10-12

GG: configuration for EQUATORIAL ORBITGG: configuration for EQUATORIAL ORBIT

s/c configuration for equatoriial (VEGA launch; operantion from ASI ground station in Malindi)

1m1m

• Because of classical tidal effects the test masses must be concentric (cylinders..)

GG: the SPACE EXPERIMENT DRIVING CONCEPTS (I)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).

GG: the SPACE EXPERIMENT DRIVING CONCEPTS (II) 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

Small total satellite mass (250 kg) - determined in Phase A Studies with industry

But people were scared to set large macroscopic test masses in rapid rotation !!!!!

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)

GG DIFFERENTIAL ACCELEROMETRGG DIFFERENTIAL ACCELEROMETR

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…

GG ACCELEROMETERS: SECTION ALONG THE SPIN AXISGG ACCELEROMETERS: SECTION ALONG THE SPIN AXIS

GG ACCELEROMETERS CUTAWAYGG ACCELEROMETERS CUTAWAY

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.

Design symmetry is extremely importnat in small force gravitational experiments…..

GGG vs GG designGGG vs GG design

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

GGG lab 2005 (March) GGG lab 2005 (March) GGG in INFN lab GGG in INFN lab

1m

RESULTS from TILT MEASUREMENTS RESULTS from TILT MEASUREMENTS Automated Control of Low Frequency Terrain Tilts-0.9Hz spin rate 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.

DIFFERENTIAL MOTION of ROTATING TEST CYLINDERSDIFFERENTIAL MOTION of ROTATING TEST CYLINDERSfrom Rotating Capacitance Bridges: improvements since 2002from Rotating Capacitance Bridges: improvements since 2002

GGG operation in INFN lab started in 2004:

1) Gained by 2 orders of magnitude in residual noise

2) Long term stable continuous operation without instability demonstrated

AUTOCENTERING of GGG TEST CYLINDERS vs SPIN FREQUENCYAUTOCENTERING 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….

AUTOCENTERING of GGG TEST CYLINDERS in the ROTATING PLANEAUTOCENTERING 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

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 MEASUREMENTS @ NATURAL FREQUENCIES (I)Q MEASUREMENTS @ NATURAL FREQUENCIES Q MEASUREMENTS @ NATURAL FREQUENCIES

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….

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 …..)

/( ) (0)

spin

wt TQ

w wr t r e

spinint

k wQ

T n k T

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..

Q in SUPERCRITYICAL ROTATION Q in SUPERCRITYICAL ROTATION

. .

int

4 1 B d m

thspin

K Ta

mQ T

Spin period 6.25 sec (0.16 Hz), whirl period 13 sec (O.0765 Hz), whirl control off

WHIRL GROWTH - Tw=13 sec (0.077 Hz); Tspin=6.25 sec (0.16 Hz)

A= 137.41e7E-05 t

0,000

100,000

200,000

300,000

400,000

500,000

600,000

700,000

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Time (sec)

Am

plit

ude

(mic

roV

)

57 10 spin w

tt

Q T

0.16 3430HzQ

Q MEASUREMENT from GROWTH of WHIRL MOTION (data of fixed electronics)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

Q MEASUREMENT from GROWTH of WHIRL MOTION (data of rotating Q MEASUREMENT from GROWTH of WHIRL MOTION (data of rotating electronics)electronics)

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

ETA in GGG: ETA in GGG:

In the field of the Earth from space (GG orbit)

910GGGbestx m

95 10@ orbGGx m

2 9 22 1 13 10@ @( / ) . /orbGG diff orbGGa T x m s

101 4 10@ / .GGG orbGG GGa a

/Eotvos TMs drivinga a

4 2520 1 5700 1 75 10 8 4, / . , . / GG orbGG GGh km s Hz a m s

13 2.diffT swith natural differential period of TMs

The GREAT ADVANTAGE of WEIGHTLESSNESSThe GREAT ADVANTAGE of WEIGHTLESSNESS

22( / )diffa T x

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 natural differential period is inversely proportional to the stiffness of their coupling:

2 1/diffT k

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:

2 2545

176013

_

_

diff space

diff GGG

T s

T s

ETA in GG: ETA in GG:

101 4 10@ / .GGG orbGG GGa a

In the lab, with this apparatus, we can improve x @ orbGG by a factor 50

/Eotvos TMs drivinga a

10 (no motor , no motor noise…)

In space we gain:

1500 (weaker suspensions in absence of weight, longer differential period - quadratic improvement)

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

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)

GG SIMULATIONS During Phase A and Advanced Phase A StudiesGG SIMULATIONS During Phase A and Advanced Phase A Studies

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…)

From GG Proposal to ESA, Jan 2000, p.16http://eotvos.dm.unipi.it/nobili/ESA_F2&F3/gg.pdf

GG MISSION PROGRAMMATICSGG MISSION PROGRAMMATICS

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

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

Data archiving and analysis:

—University of Pisa

GG included in ASI National Space Plan recently approved – VEGA launch foreseen