## 1. IntroductionIn a previous paper (Dravins et al. 1999, hereafter
Paper I) three methods were described by which stellar radial
velocities can be determined astrometrically, i.e. from geometric
measurements independent of spectroscopy. Such The third method is based on the changing angular extent of a star
cluster as it approaches or recedes from the Sun: the relative rate of
apparent contraction equals the relative change in distance. Since the
distance is known from trigonometric parallaxes, the radial velocities
follow. Only this method can provide sub-km s An overview of the method is presented in Sect. 2, followed by the precise mathematical formulation in Sect. 3. Details of the practical implementation are given in Appendix A. The validity of the method is studied in Sect. 4 by means of Monte Carlo simulations, and in Sect. 5 we apply the method to the Hyades cluster as observed by Hipparcos. It is concluded that the method can indeed yield accurate results under realistic assumptions, although special procedures are needed to correctly estimate the internal velocity dispersion of the cluster and the accuracies of the estimated parameters. In a subsequent paper (Paper III: Madsen et al., in preparation) the method is systematically applied to Hipparcos observations of nearby open star clusters. A by-product of the moving-cluster method is that the distance estimates to the individual cluster stars may be significantly improved compared with the original parallax measurements. As discussed in Paper I (Sect. 6.3), these `kinematically improved parallaxes' can be understood as resulting from a combination of trigonometric and kinematic distance information, where kinematic distances follow from the observed proper motions and the derived cluster velocity. © European Southern Observatory (ESO) 2000 Online publication: April 17, 2000 |