  We use detailed simulations of the Gaia observations of synthetic planetary
systems and develop and utilize independent software codes in double-blind mode
to analyze the data, including statistical tools for planet detection and
different algorithms for single and multiple Keplerian orbit fitting that use
no a priori knowledge of the true orbital parameters of the systems. 1) Planets
with astrometric signatures $\alpha\simeq 3$ times the single-measurement error
$\sigma_\psi$ and period $P\leq 5$ yr can be detected reliably, with a very
small number of false positives. 2) At twice the detection limit, uncertainties
in orbital parameters and masses are typically $15%-20%$. 3) Over 70% of
two-planet systems with well-separated periods in the range $0.2\leq P\leq 9$
yr, $2\leq\alpha/\sigma_\psi\leq 50$, and eccentricity $e\leq 0.6$ are
correctly identified. 4) Favorable orbital configurations have orbital elements
measured to better than 10% accuracy $> 90%$ of the time, and the value of the
mutual inclination angle determined with uncertainties $\leq 10^{\degr}$. 5)
Finally, uncertainties obtained from the fitting procedures are a good estimate
of the actual errors. Extrapolating from the present-day statistical properties
of the exoplanet sample, the results imply that a Gaia with $\sigma_\psi$ = 8
$\mu$as, in its unbiased and complete magnitude-limited census of planetary
systems, will measure several thousand giant planets out to 3-4 AUs from stars
within 200 pc, and will characterize hundreds of multiple-planet systems,
including meaningful coplanarity tests. Finally, we put Gaia into context,
identifying several areas of planetary-system science in which Gaia can be
expected to have a relevant impact, when combined with data coming from other
ongoing and future planet search programs.
