h's orbit, and the satellite's orbit with respect to the Earth, were essential for describing the location of the observer at each epoch of observation, and were supplied by an appropriate Earth ephemeris combined with accurate satellite ranging. Corrections due to special relativity (stellar aberration) made use of the corresponding satellite velocity. Modifications due to general relativistic light bending were significant (4 milliarc-sec at 90° to the ecliptic) and corrected for deterministically assuming γ=1 in the PPN formalism. Residuals were examined to establish limits on any deviations from this general relativistic value, and no significant discrepancies were found.
The Hipparcos reference frame
The satellite observations essentially yielded highly accurate relative positions of stars with respect to each other, throughout the measurement period (1989–93). In the absence of direct observations of extragalactic sources (apart from marginal observations of quasar 3C273) the resulting rigid reference frame was transformed to an inertial frame of reference linked to extragalactic sources. This allows surveys at different wavelengths to be directly correlated with the Hipparcos stars, and ensures that the catalogue proper motions are, as far as possible, kinematically non-rotating. The determination of the relevant three solid-body rotation angles, and the three time-dependent rotation rates, was conducted and completed in advance of the catalogue publication. This resulted in an accurate but indirect link to an inertial, extragalactic, reference frame.
A variety of methods to establish this reference frame link before catalogue publication were included and appropriately weighted: interferometric observations of radio stars by VLBI networks, MERLIN and VLA; observations of quasars relative to Hipparcos stars using CCDs, photographic plates, and the Hubble Space Telescope; photographic programmes to determine stellar proper motions with respect to extragalactic objects (Bonn, Kiev, Lick, Potsdam, Yale/San Juan); and comparison of Earth rotation parameters obtained by VLBI and by ground-based optical observations of Hipparcos stars. Although very different in terms of instruments, observational methods and objects involved, the various techniques generally agreed to within 10 milliarc-sec in the orientation and 1 milliarc-sec/yr in the rotation of the system. From appropriate weighting, the coordinate axes defined by the published catalogue are believed to be aligned with the extragalactic radio frame to within ±0.6 milliarc-sec at the epoch J1991.25, and non-rotating with respect to distant extragalactic objects to within ±0.25 milliarc-sec/yr.
The Hipparcos and Tycho Catalogues were then constructed such that the Hipparcos reference frame coincides, to within observational uncertainties, with the International Celestial Reference System (the ICRS), and representing the best estimates at the time of the catalogue completion (in 1996). The resulting Hipparcos reference frame is thus the materialisation of the ICRS in the optical. It extends and improves the J2000 (FK5) system, retaining approximately the global orientation of that system but without its regional errors.
Double and multiple stars
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Whilst of enormous astronomical importance, double stars and multiple stars provided considerable complications to the observations (due to the finite size and profile of the detector's sensitive field of view) and to the data analysis. The data processing classified the astrometric solutions as follows:
- single-star solutions: 100,038 entries, of which 6,763 were flagged as suspected double
- component solutions (Annex C): 13,211 entries, comprising 24,588 components in 12,195 solutions
- acceleration solutions (Annex G): 2,622 solutions
- orbital solutions (Annex O): 235 entries
- variability-induced movers (Annex V): 288 entries
- stochastic solutions (Annex X): 1,561 entries
- no valid astrometric solution: 263 entries (of which 218 were flagged as 