“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 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 with quantum
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 dependent and therefore violate the Equivalence
Principle (EP)
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)
EQUIVALENCE PRINCIPLE TESTS ARE by far the MOST POWERFUL TESTS of
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):
a

a
2.6 105    1
…and since  tests already give (since 1972..)
 Be Cu
 a 
12
7

10



1

10

a

 Be Cu
while the best  tests (Cassini, 2003) give:
  1 2.3 105
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 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
  10-14 , 10-15
  10-12
GG (I) 250 kg; STEP (USA) 1000 kg- LEO
GREaT (I-USA) -balloon, SCOPE (F) 200
kg -LEO
Torsion balances (USA)
GG: configuration for EQUATORIAL ORBIT
1m
s/c configuration for equatoriial (VEGA launch;
operantion from ASI ground station in Malindi)
GG: the SPACE EXPERIMENT DRIVING CONCEPTS (I)
• Because of classical tidal effects the test masses must be concentric (cylinders..)
• 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)
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 !!!!!
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)
GG ACCELEROMETERS: SECTION ALONG THE SPIN AXIS
GG inner & outer
accelerometer (the
outer one has equal
composition test
cylinders for systematic
checks)
Accelerometers cocentered at center of
mass of spacecraft for
best symmetry and best
checking of
systematics…
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.
GGG vs GG design
Local gravity in the lab forces the GGG
design to break symmetry top/down….
GGG
GGG
labin2005
INFN
(March)
lab
1m
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.
DIFFERENTIAL MOTION of ROTATING TEST CYLINDERS
from 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 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 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
QQMEASUREMENTS
MEASUREMENTS@@NATURAL
NATURALFREQUENCIES
FREQUENCIES(I)
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 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….
Q in SUPERCRITYICAL ROTATION
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 …..)
rw (t )  rw (0)e
Tkint

Qspin



Qspin
 t / Tw 
n k  Tw
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..
4 K BT d .m.
1
ath 

mQspin
Tint
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
WHIRL GROWTH - Tw=13 sec (0.077 Hz); Tspin=6.25 sec (0.16 Hz)
700,000
600,000
A= 137.41e
7E-05 t
Amplitude (microV)
500,000
400,000
300,000
200,000
100,000
0,000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
Time (sec)

t
 7 105 t
Qspin Tw

Q0.16 Hz  3430
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
ETA in GGG:
 Eotvos  aTMs / adriving
In the field of the Earth from space (GG orbit)
hGG
520 km ,  orbGG
x GGGbest
109 m
1/ 5700 s 1.75  104 Hz , aGG
with natural differential period of TMs
x @ orbGG
Tdiff  13.2 s
5  109 m
a @ orbGG  ( 2 / Tdiff )2  x@ orbGG
1.13  109 m / s 2
GGG  a @ orbGG / aGG  1.4  1010
8.4 m / s 2
The GREAT ADVANTAGE of WEIGHTLESSNESS
The sensitivity to differential accelerations between the test masses (sensitivity to
EP tests), is inversely proportional to the square of their natural differential
period:
2
a  ( 2 / Tdiff )  x
The natural differential period is inversely proportional to the stiffness of their
coupling:
Tdiff  1/ k
2
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:
 Tdiff _ space

 Tdiff _ GGG



2
 545 s 
 13 s 


2
1760
ETA in GG:
 Eotvos  aTMs / adriving
GGG  a @ orbGG / aGG 1.4  1010
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
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…)
GG 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