Testing the distance scale of the Gaia TGAS catalogue by kinematic
  method
  We have studied the simultaneous and separate solutions of the basic
kinematic equations obtained using the stellar velocities calculated on the
basis of data from the Gaia TGAS and RAVE5 catalogues. By comparing the values
of Omega_0' found by separately analyzing only the line-of-sight velocities of
stars and only their proper motions, we have determined the distance scale
correction factor p to be close to unity, 0.97+/-0.04. Based on the proper
motions of stars from the Gaia TGAS catalogue with relative trigonometric
parallax errors less than 10% (they are at a mean distance of 226 pc), we have
found the components of the group velocity vector for the sample stars relative
to the Sun (U,V,W)o=(9.28,20.35,7.36)+/-(0.05,0.07,0.05) km s^{-1}, the angular
velocity of Galactic rotation Omega0=27.24+/-0.30 km s^{-1} kpc^{-1}, and its
first derivative Omega_0'=-3.77+/-0.06 km s^{-1} kpc^{-2}; here, the circular
rotation velocity of the Sun around the Galactic center is V_0=218+/-6 km
s^{-1} kpc (for the adopted distance R_0=8.0+/-0.2 kpc), while the Oort
constants are A=15.07+/-0.25 km s^{-1} kpc^{-1} and B=-12.17+/-0.39 km s^{-1}
kpc^{-1}, p=0.98+/-0.08. The kinematics of Gaia TGAS stars with parallax errors
more than 10% has been studied by invoking the distances from a paper by
Astraatmadja and Bailer-Jones that were corrected for the Lutz-Kelker bias. We
show that the second derivative of the angular velocity of Galactic rotation
Omega_0"=0.864+/-0.021 km s^{-1} kpc^{-3} is well determined from stars at a
mean distance of 537 pc. On the whole, we have found that the distances of
stars from the Gaia TGAS catalogue calculated using their trigonometric
parallaxes do not require any additional correction factor.
