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
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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)
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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..)
if UFF, hence the Equivalence Principle and GR
hold (Eötvös parameter)
???a/a0
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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)
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EQUIVALENCE PRINCIPLE TESTS WHATs 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)
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GG configuration for EQUATORIAL ORBIT
1m
1m
s/c configuration for equatoriial (VEGA launch
operantion from ASI ground station in Malindi)
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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).
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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
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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)
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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
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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.
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GGG vs GG design
Local gravity in the lab forces the GGG design to
break symmetry top/down.
13
GGG lab 2005 (March)
GGG in INFN lab
1m
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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.
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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

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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.
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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
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Q MEASUREMENTS _at_ NATURAL FREQUENCIES (I)
Q MEASUREMENTS _at_ 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 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.
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Q in SUPERCRITYICAL ROTATION
Rotordynamics theory states that in supercritical
rotation (defined by spin frequency gt 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 ..)
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..
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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
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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
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ETA in GGG

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

In the lab, with this apparatus, we can improve
?x _at_ ?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
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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_F2F3/g
g.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)
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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 launchmultiple
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