Comparison between Different Models of Galactic Tidal Effects on Cometary Orbits

Different models of the action of the galactic tide are compared. Each model is a substitute for direct numerical integrations allowing a drastic decrease of the computation time. The models are built using two different techniques, (i) averaging of the fast variable (the mean anomaly) over one cometary period and (ii) fixing the comet in its aphelion direction. Moreover, we consider two different formalisms (Lagrangian and Hamiltonian) and also two different sets of variables. As expected, we find that the model results are independent of the formalism and the set of variables considered, and are highly accurate, whereas mathematical technique leads to poor results. In order to further reduce the computation time, mappings are built from the development of the solution of the models. We show that for these mappings, the set of variables giving the most accurate results is strongly dependent on the cometary eccentricity, e, and semimajor axis, a.