Absolute measurements of trigonometric parallaxes with astrometric satellites

The concept of absolute trigonometric parallax measurements is formulated in strict mathematical terms, in connection with the widely discussed plans for a future astrometric space mission. The parallaxes determined for a large number of stars spread all over the sky are absolute if the expected error (accidental or systematic) of the zero–point, as well as other large–scale distortions are orders of magnitude smaller than the average random error for a given star. It is shown by a very general mathematical consideration that the Hipparcos strategy of one–dimensional angular measurements and revolving mode of scanning the sky provides absolute determinations of parallaxes, as far as accidental errors are concerned. As demonstrated by means of a spherical harmonics technique, an even higher absoluteness of parallaxes would be achieved in a future astrometric mission with a larger basic angle between the two viewing directions than that of Hipparcos (58◦), and a larger revolving scanning angle between the Sun direction and the spin axis of the satellite.