  We show that the errors in the Hipparcos parallaxes towards the Pleiades and
the Hyades open clusters are spatially correlated over angular scales of 2 to 3
deg, with an amplitude of up to 2 mas. This correlation is stronger than
expected based on the analysis of the Hipparcos catalog. We predict the
parallaxes of individual cluster members, pi_pm, from their Hipparcos proper
motions, assuming that all cluster members have the same space velocity. We
compare pi_pm with their Hipparcos parallaxes, pi_Hip, and find that there are
significant spatial correlations in pi_Hip. We derive a distance modulus to the
Pleiades of 5.58 +- 0.18 mag using the radial-velocity gradient method. This
value, agrees very well with the distance modulus of 5.60 +- 0.04 mag
determined using the main-sequence fitting technique, compared with the value
of 5.33 +- 0.06 inferred from the average of the Hipparcos parallaxes of the
Pleiades members. We show that the difference between the main-sequence fitting
distance and the Hipparcos parallax distance can arise from spatially
correlated errors in the Hipparcos parallaxes of individual Pleiades members.
Although the Hipparcos parallax errors towards the Hyades are spatially
correlated in a manner similar to those of the Pleiades, the center of the
Hyades is located on a node of this spatial structure. Therefore, the parallax
errors cancel out when the average distance is estimated, leading to a mean
Hyades distance modulus that agrees with the pre-Hipparcos value. We speculate
that these spatial correlations are also responsible for the discrepant
distances that are inferred using the mean Hipparcos parallaxes to some open
clusters. Finally, we note that our conclusions are based on a purely geometric
method and do not rely on any models of stellar isochrones.
