Analysis of galaxy kinematics based on Cepheids from the Gaia DR2
  Catalogue
  To construct the rotation curve of the Galaxy, classical Cepheids with proper
motions, parallaxes and line-of-sight velocities from the Gaia DR2 Catalog are
used in large part. The working sample formed from literature data contains
about 800 Cepheids with estimates of their age. We determined that the linear
rotation velocity of the Galaxy at a solar distance is $V_0=240\pm3$~km
s$^{-1}$. In this case, the distance from the Sun to the axis of rotation of
the Galaxy is found to be $R_0=8.27\pm0.10$~kpc. A spectral analysis of radial
and residual tangential velocities of Cepheids younger than 120 Myr showed
close estimates of the parameters of the spiral density wave obtained from data
both at present time and in the past. So, the value of the wavelength
$\lambda_{R,\theta}$ is in the range of [2.4--3.0] kpc, the pitch angle
$i_{R,\theta}$ is in the range of [$-13^\circ$,$-10^\circ$] for a four-arm
pattern model, the amplitudes of the radial and tangential perturbations are
$f_R\sim12$~km s$^{-1}$ and $f_\theta\sim9$~km s$^{-1}$, respectively.
Velocities of Cepheids older than 120 Myr are currently giving a wavelength
$\lambda_{R,\theta}\sim5$~kpc. This value differs significantly from one that
we obtained from the samples of young Cepheids. An analysis of positions and
velocities of old Cepheids, calculated by integrating their orbits backward in
time, made it possible to determine significantly more reliable values of the
parameters of the spiral density wave: wavelength $\lambda_{R,\theta}=2.7$~kpc,
amplitudes of radial and tangential perturbations are $f_R=7.9$~km s$^{-1}$ and
$f_\theta=5$~km s$^{-1}$, respectively.
