## 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 (), and a larger revolving scanning angle between the Sun direction and the spin axis of the satellite.
This article contains no SIMBAD objects. ## Contents- 1. Introduction
- 2. Basic parameters
- 3. Spherical orthogonal functions
- 4. Normal equations
- 5. Condition number
- 6. Simulations and results
- 7. Conclusions
- Acknowledgements
- References
© European Southern Observatory (ESO) 1998 Online publication: November 3, 1998 |