Trigonometric Parallax

Based on purely geometric principles, trigonometric parallax is one of the most direct methods for determination of stellar distances and hence for the luminosity calibration of standard candles. Technical advances over the past decades, in particular the space missions Hipparcos, the Hubble Space Telescope (HST), and Gaia in the optical regime, and very long baseline interferometry using phase referencing at radio frequencies, have vastly expanded the region around the Sun accessible with the method, as well as the number of objects measured. After a brief review of the historical development of the method, I discuss the principles underlying differential and global measurements of parallaxes and their different challenges. The use of the HST (FGS and WFC3 spatial scanning) for differential measurements and the global method employed by Gaia are described. In all statistical uses of trigonometric parallaxes, for example the calibration of PL relations, the issue of systematic errors is of paramount interest. This is especially true for Gaia, where the large samples of sources available for the luminosity calibration potentially allow the random errors to be beaten down by a large factor, making the systematic errors relatively more important. I discuss the origin of systematics in the Gaia parallaxes and the possibility to determine and correct the bias. The statistical meaning of trigonometric parallax and the future prospects of the method are outlined.