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Determination of absolute parallaxes by means of a scanning astrometricsatellite such as Hipparcos or Gaia relies on the short-term stability of theso-called basic angle between the two viewing directions. Uncalibratedvariations of the basic angle may produce systematic errors in the computedparallaxes. We examine the coupling between a global parallax shift andspecific variations of the basic angle, namely those related to the satelliteattitude with respect to the Sun. The changes in observables produced by smallperturbations of the basic angle, attitude, and parallaxes are calculatedanalytically. We then look for a combination of perturbations that has no neteffect on the observables. In the approximation of infinitely small fields ofview, it is shown that certain perturbations of the basic angle areobservationally indistinguishable from a global shift of the parallaxes. Ifsuch perturbations exist, they cannot be calibrated from the astrometricobservations but will produce a global parallax bias. Numerical simulations ofthe astrometric solution, using both direct and iterative methods, confirm thistheoretical result. For a given amplitude of the basic angle perturbation, theparallax bias is smaller for a larger basic angle and a larger solar aspectangle. In both these respects Gaia has a more favourable geometry thanHipparcos. In the case of Gaia, internal metrology is used to monitor basicangle variations. Additionally, Gaia has the advantage of detecting numerousquasars, which can be used to verify the parallax zero point.

Impact of basic angle variations on the parallax zero point for a scanning astrometric satellite