Planets Across Space and Time (PAST). I. Characterizing the Memberships
  of Galactic Components and Stellar Ages: Revisiting the Kinematic Methods and
  Applying to Planet Host Stars
  Over 4,000 exoplanets have been identified and thousands of candidates are to
be confirmed. The relations between the characteristics of these planetary
systems and the kinematics, Galactic components, and ages of their host stars
have yet to be well explored. Aiming to addressing these questions, we conduct
a research project, dubbed as PAST (Planets Across Space and Time). To do this,
one of the key steps is to accurately characterize the planet host stars. In
this paper, the Paper I of the PAST series, we revisit the kinematic method for
classification of Galactic components and extend the applicable range of
velocity ellipsoid from about 100 pc to 1, 500 pc from the sun in order to
cover most known planet hosts. Furthermore, we revisit the Age-Velocity
dispersion Relation (AVR), which allows us to derive kinematic age with a
typical uncertainty of 10-20% for an ensemble of stars. Applying the above
revised methods, we present a catalog of kinematic properties (i.e. Galactic
positions, velocities, the relative membership probabilities among the thin
disk, thick disk, Hercules stream, and the halo) as well as other basic stellar
parameters for 2,174 host stars of 2,872 planets by combining data from Gaia,
LAMOST, APOGEE, RAVE, and the NASA exoplanet archive. The revised kinematic
method and AVR as well as the stellar catalog of kinematic properties and ages
lay foundation for future studies on exoplanets from two dimensions of space
and time in the Galactic context.
