Absolute measurements of trigonometric parallaxes with astrometric satellites

Abstract

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(deg) ), and a larger revolving scanning angle between the Sun direction and the spin axis of the satellite.