Tests of fundamental physics with the Gaia mission through the dynamics of minor planets

Abstract

With a launch planned in March 2013, the ESA Gaia mission will scan the whole sky several times during its operational five years. It will provide highly accurate astrometric observations of celestial bodies (at the sub-milli-arcsecond level) not exclusively beyond the Solar System, since about 250 000 asteroids will be observed. Gaia will thus give us the opportunity of performing various valuable tests of fundamental physics by assessing global parameters from the dynamics of minor planets; in this paper, we evaluated its performance from realistic simulated data and a variance analysis carried out from the observation residuals on a data model linearized with respect to the initial position and velocity of each asteroid and the set of global parameters. Currently, the most relevant fits turn out to be for the PPN parameter $\ensuremath{\beta}$ (${\ensuremath{\sigma}}_{\ensuremath{\beta}}\ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$), the temporal variation of the gravitational constant $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{G}/G$ (${\ensuremath{\sigma}}_{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{G}/G}\ensuremath{\sim}3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{y}{\mathrm{r}}^{\ensuremath{-}1}$), the Nordtvedt parameter $\ensuremath{\eta}$ (${\ensuremath{\sigma}}_{\ensuremath{\eta}}\ensuremath{\sim}2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$) and the $Gm$ of Jupiter (${\ensuremath{\sigma}}_{G{m}_{j}}\ensuremath{\sim}\phantom{\rule{0ex}{0ex}}2.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }\text{ }{\mathrm{au}}^{3}\text{ }{\mathrm{d}}^{\ensuremath{-}2}$), which show a low level of correlation. The underestimated astrometric precision used in the simulations and the possibility to combine Gaia data with future accurate ground-based observations foreshadow more accurate determinations.