New fast models of the Galactic tide

New models of the action of the Galactic tide on the motion of the Oort Cloud comets are investigated. The first one consists of the Hamiltonian form of the equations of motion which are averaged over the mean anomaly including the radial component of the tide. The second is a series of mappings which allows a noticeable reduction of the computer time. These models are checked in three different frames, and some of them turn out to be reliable for a wide range of initial conditions. In the last experiment we simulate the transport of 10(5) Oort Cloud comets to the inner Solar system under the Galactic tide impulse alone. For such a simulation, the best compromise between reliability and computer time is given by a mapping of order 3 which is more than 500 times faster than the usual numerical integrations and may be safely used when the comet semimajor axes a < 30 000 au. The present study highlights the qualitative effects of the radial component of the Galactic tide. The models built here will be used in a forthcoming paper for a more realistic study of the transport of long-period comets including planetary perturbations.