“Galileo Galilei (GG)” A test of the Equivalence Principle

Suresh Doravari (University of Pisa & INFN)

for the GG/GGG collaboration

http://eotvos.dm.unipi.it/nobili/

The motivation:

GENERAL RELATIVITY NEEDS TESTS of the EQUIVALENCE PRINCIPLEGENERAL RELATIVITY NEEDS TESTS of the EQUIVALENCE PRINCIPLE

However, superstring theory 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) (see for eg. PRL, 89, 081601)

The difficulties we encounter in merging gravity with quantum mechanics suggest that the pure tensor structure of GR needs modification or augmentation.

The most promising scenario for the quantization of gravity and the unification of all natural interactions is the superstring theory.

The Observable Consequence:

Universality of Free Fall

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 or composition

The Eötvös parameter:

A measure of the violation of the Universality of free

fall. = 0 if the Equivalence Principle holds.

The quantity to be measured is the relative acceleration of test masses of different composition in the gravitational field of a source body (i.e. Earth, Sun..):

a/a=0

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

Configuration for equatorial orbit (VEGA launch; operantion from ASI ground station in Malindi)

1m

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

1. The satellite chassis and the test masses are concentric cylinders -- avoids the classical tidal effects

2. The experiment is housed in a Pico-Gravity Box -- vibration isolated and drag-free

3. The masses coupled by weak springs and constrained to move opposite to each other in the orbital plane – common mode rejection

4. Capacitance sensors measure relative displacements in 2-D and are sensitive only to the differential motion – a further attentuation of the common mode

GG: the SPACE EXPERIMENT DRIVING CONCEPTS (II)GG: the SPACE EXPERIMENT DRIVING CONCEPTS (II)

5. The satellite and the test masses are together set into rotation about the symmetry axis Spin

6. Passive stabilisation by supercritical rotation

7. . The spin modulates the EP violation signal at a frequency much higher than the orbital frequency -- separates out many systematic effects

8. Two identical experiments in one satellite: one with masses of same composition and another with different composition) -- provides a zero-check

GG inner & outer accelerometer (the outer one has same 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…..

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….

In supercritical rotation (defined by spin frequency > natural frequency)

whirl motion arises at each natural frequency

whose growth is determined by the Q of the system at the SPIN frequency

(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

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 FREQUENCIESQ MEASUREMENTS @ NATURAL FREQUENCIESQ 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….

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

GROWTH of WHIRL MOTIONGROWTH of WHIRL MOTION

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

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

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

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

1m

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 for drag-free control (ISRO-Indian Space Research 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