def add_virtual_columns_cartesian_velocities_to_pmvr(self, x="x", y="y", z="z", vx="vx", vy="vy", vz="vz", vr="vr", pm_long="pm_long", pm_lat="pm_lat", distance=None):
    """Concert velocities from a cartesian system to proper motions and radial velocities

    TODO: errors

    :param x: name of x column (input)
    :param y:         y
    :param z:         z
    :param vx:       vx
    :param vy:       vy
    :param vz:       vz
    :param vr: name of the column for the radial velocity in the r direction (output)
    :param pm_long: name of the column for the proper motion component in the longitude direction  (output)
    :param pm_lat: name of the column for the proper motion component in the latitude direction, positive points to the north pole (output)
    :param distance: Expression for distance, if not given defaults to sqrt(x**2+y**2+z**2), but if this column already exists, passing this expression may lead to a better performance
    :return:
    """
    if distance is None:
        distance = "sqrt({x}**2+{y}**2+{z}**2)".format(**locals())
    k = 4.74057
    self.add_variable("k", k, overwrite=False)
    self.add_virtual_column(vr, "({x}*{vx}+{y}*{vy}+{z}*{vz})/{distance}".format(**locals()))
    self.add_virtual_column(pm_long, "-({vx}*{y}-{x}*{vy})/sqrt({x}**2+{y}**2)/{distance}/k".format(**locals()))
    self.add_virtual_column(pm_lat, "-({z}*({x}*{vx}+{y}*{vy}) - ({x}**2+{y}**2)*{vz})/( ({x}**2+{y}**2+{z}**2) * sqrt({x}**2+{y}**2) )/k".format(**locals()))
Concert velocities from a cartesian system to proper motions and radial velocities

    TODO: errors

    :param x: name of x column (input)
    :param y:         y
    :param z:         z
    :param vx:       vx
    :param vy:       vy
    :param vz:       vz
    :param vr: name of the column for the radial velocity in the r direction (output)
    :param pm_long: name of the column for the proper motion component in the longitude direction  (output)
    :param pm_lat: name of the column for the proper motion component in the latitude direction, positive points to the north pole (output)
    :param distance: Expression for distance, if not given defaults to sqrt(x**2+y**2+z**2), but if this column already exists, passing this expression may lead to a better performance
    :return: