Astron. Astrophys. 327, 404-415 (1997)

Finding "absolute" parallaxes directly

Heinrich Eichhorn

Osservatorio Astronomico di Torino, Pino Torinese, Italy1

Received 3 January 1996 / Accepted 17 June 1996

Abstract

We develop the formalism for estimating parallaxes, proper motions and positions from long-focus astrometric observations as well as additional extraneous reference material whenever this is available and relax the constraints on the star parameters (basically their sums and correlations with the coordinates on the frames), thus generating (albeit correlated) quasi-observations whose inclusion would make the solutions determinate even if there were no extraneous reference material. The result are data on the same system to which the reference material is referred, so that there is no need to perform the "reduction from relative to absolute" as an afterthought.

Key words: astrometry methods: analytical; data analysis

Contents

• 1. Introduction
• 2. Establishing C and its covariance matrix
• 3. Formulating the condition equations
  • 3.1. The coordinate measurements on the frames
  • 3.2. The extraneous reference materials
  • 3.3. The relaxed constraints
• 4. The normal equations
• 5. The simultaneous reduction of measurements in both coordinates
• 6. Star- and frame variances
• Acknowledgements
• Appendix A
  • Appendix A: notation
• References

© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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