  Observational data from the ESA astrometric mission Gaia determining the
positions of celestial objects within an accuracy of few microarcseconds will
be soon fully available. Other satellite-based space missions are currently
planned to significantly improve such precision in the next years. The data
reduction process needs high-precision general relativistic models, allowing
one to solve the inverse ray-tracing problem in the gravitational field of the
Solar System up to the requested level of accuracy and leading then to the
estimate of astrometric parameters. Besides a satisfactory description of the
background field due to the planets (which should include their multipolar
structure), one should consider also other effects which may induce
modifications to the light propagation. For instance, the interaction of the
light signal with the superposed gravitational field of a gravitational wave
emitted by a distant source would cause a shift in the apparent positions of
the stars. We compute here the main astrometric observables needed for data
reduction of satellite-based missions in the presence of a passing plane
gravitational wave. We also take into account the effect of the mass quadrupole
moment of the planets, improving previous results obtained for Gaia.
