  The abundance and properties of planets orbiting binary stars - circumbinary
planets - are largely unknown because they are difficult to detect with
currently available techniques. Results from the Kepler satellite and other
studies indicate a minimum occurrence rate of circumbinary giant planets of ~10
%, yet only a handful are presently known. Here, we study the potential of
ESA's Gaia mission to discover and characterise extrasolar planets orbiting
nearby binary stars by detecting the binary's periodic astrometric motion
caused by the orbiting planet. We expect that Gaia will discover hundreds of
giant planets around binaries with FGK dwarf primaries within 200 pc of the
Sun, if we assume that the giant planet mass distribution and abundance are
similar around binaries and single stars. If on the other hand all circumbinary
gas giants have masses lower than two Jupiter masses, we expect only four
detections. Gaia is critically sensitive to the properties of giant
circumbinary planets and will therefore make the detailed study of their
population possible. Gaia's precision is such that the distribution in mutual
inclination between the binary and planetary orbital planes will be obtained.
It also possesses the capacity to establish the frequency of planets across the
H-R diagram, both as a function of mass and of stellar evolutionary state from
pre-main sequence to stellar remnants. Gaia's discoveries can reveal whether a
second epoch of planetary formation occurs after the red-giant phase.
