istituto di fisica dello spazio interplanetario a gradiometric measurement of g xciv congresso...

Istituto di Fisica dello Spazio Interplanetario

A gradiometric measurement of G

XCIV Congresso Nazionale SIFGenova, 22-27 Settembre 2008

V. Iafolla, E. Fiorenza, C. Lefevre, S. Nozzoli,R. Peron, M. Persichini, A. Reale, F. SantoliIstituto di Fisica dello Spazio Interplanetario (IFSI/INAF), Roma, Italy


Gundlach, J. H. and Merkowitz, S.M. Phys. Rev. Lett. 85, 2869-2872 (2000)

Current knowledge of G

with a relative uncertainty:

Current experimental results for G are characterized by very small errors, but with big discrepancies among the various results:

Gu

nd

lach

et

al.

Last “best” measurement:

However, the values obtained in the various experiments differ one from the other by more than 600 ppm

2131110)000092.0674215.6( sKgmG

ppmG

G14


Gu

nd

lach

et

al.

The currently recommended value of G by CODATA is:

with a relative uncertainty:

The discrepancies in the results for G of the various experiments are a proof of the presence of significant systematic errors in the experiments, as well as of the difficulty in carrying out the experiment. This also stresses the importance of the use of different techniques in measuring G.

The difficulties of the measurement of G are related with the smallness of the gravitational effects, to the presence of spurious effects (vibrational, thermal, electromagnetic), as well as to the implementation of the required metrological precision.


2131110)00067.067428.6( sKgmG

ppmG

G100


Torsion balances

2r

MmGF

The test bodies are attached at the opposite ends of a horizontal beam which is suspended with a wire from its midpoint. Any force acting differently on the test masses and perpendicular to the plane formed by the beam and the wire, gives rise to a non zero net torque which will twist the wire by an angle proportional to the differential force itself.



Why measuring G ? (the locally measured gravitational constant GL)

G represents a fundamental constant of Nature both in Newton theory as well as in Einstein’s Geometrodynamics

G enters in several mathematical expressions with other fundamental constants (G is a conversion factor …)

One very important problem in modern physics is to know whether the quantities known as constants in Nature (G, c, h, e, …) can vary with time or not

Indeed, nonstandard theories of gravity predicts both a spatial and a time dependency of G

…

No more to say about the importance of G measurements



• A characteristic of such gradiometer is the detection of the off–diagonal components of the gravity gradient tensor

• At the same time the gradiometer rejects the linear acceleration due to the vibrational noise, the so–called Common Mode Rejection (CMR)

One–axis gravity gradiometer

Al 5056

X

Y

Z

ZX

A preliminary experimental work has been performed in order to measure the gravitational (constant) G using a one axis gravity gradiometer


• The test mass is connected to an external reference frame by means of two torsional arms

• The torsion axis is also the symmetry axis of the test mass

• The oscillator is sensitive to the rotations of the horizontal plane

• The torque produced by the gravity gradient is balanced by the torsional spring of the oscillator


Al 5056

X

Y

Z

ZX


One–axis gravity gradiometerMI

HzI

f 12

1

20

0

M gravitational torque signal deflection

torsion elastic constant I moment of inertia of the test mass coefficient of dissipation1.00

I

Q

The oscillator works in the region where its transfer function is flat, below the resonance frequency f0:

20

I

MM

Al 5056

X

Y

Z

ZX



fb

ICZT

Q

T

m

kM on

ntr

obt

2

22 24)(

The pick-up system The signal is detected by means of a capacitive transducer in a bridge configuration

The bridge is driven by a voltage with high frequency fp trough a transformer

The output signal at frequency fr = 10 KHz produced by the unbalancing of the bridge is detected as a modulation of the bias voltage

Total torque noise of the oscillator


Common mode rejection: CMR• Usually, the rejection is quite difficult with different instruments: we need two

equal transfer functions

• The rejection is very important because of the vertical seismic noise

• Indeed, the limit in the accuracy of measurement is given by the value of the seismic noise on the oscillator around the frequency of the gravitational signal to be detected

• Of course, the seismic noise that does apply a torque on the system is not rejected

Al 5056

X

Y

Z

ZX


• In order to obtain the CMR we need to take the difference of the two measurements (time span of about 8 days)

• With the one–axis gradiometer the rejection is automatic and the CMR is valid both for the mechanical signal and the thermal one

Common mode rejection: CMRA way to obtain CMR is to take two equal accelerometers (with the same transfer function) with their sensitive axis almost parallel to the horizontal plane

Two equal accelerometers


System parameters: experimental measurements…

The main parameters to be measured in the laboratory are:

1. The system resonance frequency

2. The mechanical quality factor

3. The system transfer function (ambient conditions)

4. The electrical parameters

5. The transducer factor (calibration)

6. The seismic noise at the frequencies of interest of the gravitational signal


System parameters: experimental measurements …

• The measurement has been performed under vacuum conditions in order to have a higher Q(=3), but low enough in order to excite the system with an electric signal

• The experimental value for the frequency is 1.01 Hz

Q=3Q=3

Amplitude Phase

Hzf 01.10

Transfer function and resonance frequency


• At ambient pressure the oscillator is an overdamped system because of the gas between the capacitor plates

• We are interested to measure gravitational signals around 101 Hz, therefore a smaller Q is possible

• Again, the system has been excited with an electric signal

Q=0.1 Q=0.1

Amplitude Phase

System parameters: experimental measurements …

Transfer function in ambient conditions


System parameters: experimental measurements…

V

mN

V

M

41058.1M

ΔV

Calibration procedure for the transducer factor

The response of the system is linear


Measurement of the gravitational effect• The rotor is made by suspending a system

of two masses on a wire

• The one–axis gradiometer detector is placed inside a metallic box in order to provide electric isolation of the system

• The sources are two cylinder filled with fused Pb: 29 kg each mass

• The frequency of the gravitational signal is twice the rotation frequency of the rotor: in this way noise effects induced by the rotation of the system are avoided

An electric motor produces the desired rotation

Source masses:

D = 18 cm

H= 11.5 cm

The experimental apparatus


Measurement of the gravitational effect

In order to maximize the gravitational effect, the two centers-of-mass of the gradiometer (in black) were placed as close as possible to the two sources (in red)

Blue = gravitational signal

Red = noise of the rotor

Spectrum of the signalSignal

The experimental apparatus



2 4 6 8 10 12 14 16

0

1

2

3

4

5

6

7

x 10-9

Time [s]

Mom

entu

m N

*m

10-3

10-2

10-1

100

101

10-12

10-11

10-10

10-9

10-8

Frequency [Hz]

Mom

entu

m N

*m

Numerical evaluations with a finite elements method

221110*)22.8( KgmNG

Experimental results

Comparison of the experimental results with the theoretical (numerical) predictions

Metrological errors:

• Masses

• Distances



10-5

10-4

10-3

10-2

10-1

100

10-14

10-12

10-10

10-8

10-6

10-4

freq(Hz)

acce

lera

tion(

g/sq

rt(H

z))

Electronic noise

Rotor noise

Rotor + signal noise

Accuracy of the measurement

32 1010 N

S

At IFSI laboratory

5 hours integration time

HzgS 710

HzgN 10105

HzgN 11101

410N

S

At Gran Sasso laboratory: lower differential noise


Recent results

New design for the gradiometer

istituto di fisica dello spazio interplanetario a gradiometric measurement of g xciv congresso...

Documents

gravitational constant

time dependency of g

oscillator slide

fundamental constants

axis gravity gradiometer

recommended value of

santoli istituto

ppm slide