Physics  P01 - Space-Time symmetries  P02 - Fundamental constants  P03 - Relativistic reference frames  P04 - Equivalence Principle  P05 - General Relativity  P06 - Astrometry, VLBI, Pulsar Timing  P07 - Atomic physics for clocks  P08 - Astronomy and GNSS  P09 - Quantum non-locality and decoherence

Misje kosmiczne związane z badaniami efektów relatywistycznych  Gravity Probe-B – badanie efektu Lense-Thirringa  LAGEOS I, II, III – różne efekty  GPS – różne efekty  LISA – zbadanie fal grawitacyjnych  STEP – test zasady równoważności  BepiColombo – perihelium Merkurego

Possible detection of the gravity field disturbance with help of gradiometer on the Galileo orbit and higher Janusz B. Zieliński 1, Robert R. Gałązka 2, Roberto Peron 3 1 / Space Research Centre, Polish Academy of Sciences, POLAND 2 / Institute of Physics, Polish Academy of Sciences, POLAND 3 / Instituto di Fisica dello Spazio Interplanetario, Istituto Nazionale di Astrofisica, ITALY Scientific and Fundamental Aspects of the Galileo Programme Toulouse,1-4 October 2007

Introductory remarks  Temporal variations of the gravity field exist in the local inertial space around the Earth  Gradiometry – the differential measurement of the gravitational acceleration  GNSS – the most precise tool for position measurements in space and time  Is it possible to combine Gradiometry + GNNS for the determination of c g ?

Gravity field of the Earth EIGEN-GRACE02S 150 × 150 from GRACE mission

Expression for the vertical component of the gradient T rr Eötvös unit of the gravity acceleration gradient 1 EU = m s -2 / m

Gradient T rr profiles along equator, model n,m = 250

Gradient T rr evolution with height from 200 km to 1000 km, model n,m = 250

Upward continuation procedure

Lense-Thirring precession 0.042”/y

Upward Continuation in ECIR (Earth Centered Inertial Reference Frame) - rate of change of the

with t = δT rr = T rr (t 2,r 1 ) ۞ UC –T rr (t 1,r 2 ) and c g =(r 2 – r 1 )/Δt or c g =

For GPS-Galileo case  For r 2 – r 1 ≈ 3000 km and c g =c  Δt ≈ 0.01 s  ≈ 0.15 a.s.  ≈ 18 m for Galileo orbit

Period of the signal ≈ 12 hours and the amplitude 1*10 -4 EU. It means that from the bottom to the peak of the signal we have about 6 hours. With the linear approximation we can tell that for 1 s we get the 0.5*10 -8 EU change of the gradient. As we are interested in the ±0.001 s accuracy in the determination of the signal arrival time it means that equivalent accuracy in the measurement should be ± 0.5* EU.

GOCE Mission (ESA) Circular orbit, mean altitude ≈ 250 km, i = 96.50, launch spring 2008

 To accurately measure the Earth's gravity field, the GOCE (Gravity field and steady- state Ocean Circulation Explorer) satellite is equipped with a core instrument called the Electrostatic Gradiometer, which consists of three pairs of identical ultra- sensitive accelerometers, mounted on three mutually orthogonal 'gradiometer arms'.

GOCE gradiometer Length of Baseline for an accelerometer pair: 0.5 mAccelerometer noise: < 3 mEU = 3 * s -2

Experimental activity at IFSI-INAF Experimental Gravitation Since many years the Experimental Gravitation group (head V. Iafolla) is active in the field of gravitation physics with a number of projects:  Gravimetry  Support to satellite missions  Geophysics  Fundamental physics

ISA (Italian Spring Accelerometer) High sensitivity three axes accelerometer

ISA accelerometer BepiColomboGEOSTAR

STEP accelerometer sensitivity g ~ to m s -2

Expected development in gradiometry  GOCE EU  IFSI EU  Paik EU  STEP EU

If we have the accurate theoretical model of the curve that should be fitted by measurements then only one term of the zero order has to be determined. The accuracy of this term is roughly described as M 0 = ± σ 0 /√n where σ 0 is the standard deviation of the measurement and n is the number of measurements.

Supposing that the measurement is done with the frequency 1 Hz, during 24 hours we have measurements and during 12 days more than one million. With the individual measurement error ±10 -8 EU and 12 days measurement interval we can get close to the desired accuracy ±

Conclusions  It seems that concept for the determi na- tion of the velocity of the gravitational signal, using the rotating Earth as the signal generator, and GNNS plus gradio - metry as detector, is realistic, but of course not easy. It should provide the motivation for the development of the gradiometry technology and could widen the spectrum of scientific applications of GNSS.

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