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March 31 2006, Birmingham GR tests and micro-arcsecond light bending parameters by global and differential Gaia mesurements Maria Teresa Crosta Astronomical Observatory of Turin INAF - OATo

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March 31 2006, Birmingham Summary 1. PPN γ measurement through global astrometry 2. PPN γ and detection of the quadrupole effect due to a planet with differential astrometric measurements 3. Conclusions & perspectives

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March 31 2006, Birmingham Why? - arcsecond accuracy Relativistic models of Light propagation Tests of General Relativity (and alternative theories) Relativistic Astrometry

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March 31 2006, Birmingham Gaia relativity tests within the Solar System Light deflection Global astrometry PPN parameter amount of curvature by unit rest mass] Small field astrometry: Eddington-like experiments Local relativistic effects => new parameters + Precession of the perihelion Orbit fitting of asteroids PPN parameter [amount of non- linearity in the superposition law of gravitational fields] new tests to be set from the relativistic modelling

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March 31 2006, Birmingham The physical link The physical link a remnant of a long range scalar field would violate GR (the assumptions in the equivalence principle, lack of universality of the constants of microphysics etc..) The exact amount of the violations depends on the particular scalar-tensor theory adopted=>quantization of gravity for GR =1, alternative theories, called scalar-tensor predict small deviations from GR values: Current best estimate : GPB expected precision Cassini-Earth Sun conjunction (B. Bertotti, L.Iess & P.Tortora, Nature, 425, 2003)

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March 31 2006, Birmingham The adopted metric is the PPN expression for the Schwarzschild metric in isotropic coordinate (in geometrized units) 1.Light deflection: the PPN global experiment with Gaia Geodesics for light rays: k v k µ ; = 0 Relativistic astrometry models: the RAMOD project Bucciarelli B, Crosta MT, de Felice F, Lattanzi MG, and Vecchiato A (ESA SP 576 - p 259 )

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March 31 2006, Birmingham The mathematical problem 1 observation 1 condition equation Known BUT ….............. Unknown

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March 31 2006, Birmingham The mathematical problem 1 observation 1 condition equation · · b=Ax Over-determined system of equations to be solved with least- squares method A T b=A T Ax

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March 31 2006, Birmingham Gaia expected precision Vecchiato A et al. A&A, 399, 2003 No other foreseen measurements of can challenge Gaia in the next decade!

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March 31 2006, Birmingham First experiment: quadrupolar light deflection Simulation of light deflection experiments of the stars behind Jupiter: the observable is the relative displacement due to Jupiter’s presence with respect to the zero-deflection position without Jupiter New estimate of by comparison of small fields Detection of the Quadrupole Efficiency Factor due to the planet : = 0 no multipole light effect, =1 validation of GR prediction 2. The GAREX project GAia Relativistic Experiments Investigation of observational strategies to test General Relativity with Gaia. astro-ph/0512359

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March 31 2006, Birmingham Light deflection produced by an oblate body PPN formalism, locally perturbed minkowskian geometry Observer view. The position of the star is displaced both in the radial (- n) and orthoradial (m) directions. The spin axis of the planet lies somewhere out of plane the deflection angle is a vector

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March 31 2006, Birmingham Light deflection diplacements around Jupiter from the observer’s point of view: mid2013 monopole quadrupol e

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March 31 2006, Birmingham Cumulative effect (mid2012 -mid2018) monopolequadrupole

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March 31 2006, Birmingham Results of the Montecarlo runs

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March 31 2006, Birmingham Strategy for the actual experiments I. Evolution of the errors on and with the magnitude for various impact parameters & for various epochs = Full Gaia field o=2013 =>crossing of the galactic plane

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March 31 2006, Birmingham II. Open cluster against the galactic plane crossed by Jupiter M18, Sagittarius V=12 V=13 …but in 2019 !

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March 31 2006, Birmingham Our simulations prove that the expected accuracy of Gaia in the determination of the PPN parameter is 10 -7 ! give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter In a close future Realistic simulations with the final error budget and initial condition of scanning law (real field, background noise + straylight profile etc...) Test models of the light deflection with a moving body => speed of gravity? Extension of the simulation to the case of Saturn Investigation on the indirect determination of the center of gravity/mass of the planet throughout the light displacement vector field around it. 3. Conclusion & Perspectives

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Aldo Dell'Oro INAF- Observatory of Turin Detailed analysis of the signal from asteroids by GAIA and their size estimation Besançon November 6-7, 2003.

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