Investigation of the dynamical history of the long-period comet population is rather complicated. First of all, one should limit the sample to those comets with relatively good quality orbits - Marsden's orbital classes (Marsden et al. 1978) seem to be a convenient but probably a little bit outdated tool for this. Next, it is necessary to calculate the original cometary orbits for the whole sample accepted. The dynamical model and the computational procedure should be chosen carefully to obtain as accurate orbits as possible. In our paper we omit two important perturbing forces: non-gravitational effects and the perturbations from small Solar System bodies (mainly large asteroids, but in some cases large natural satellites should probably also be included - we include here only the Moon). Including nongravitational forces into the dynamical model of the motion of long-period comets is possible, but obtaining a reliable set of nongravitational parameters in case of those comets is very difficult, if at all possible. For a discussion on this subject see for example the review by Yeomans (1994). On the other hand, the advances in asteroid mass determination in recent years make it possible to include into the model their gravitational pull on comets and we plan to do so in the near future. We think, that for the majority of comets, their original orbits remain almost the same, but exceptions are possible.
Having a set of original orbit elements of all "good quality'' comets
one can investigate their past motion. For all comets which return to
the Planetary System, the limiting date is the previous perihelion - at
present we cannot say anything reliable about the planetary positions
several million years ago so, planetary perturbations cannot be included
at the previous return of such a comet and their motion cannot be traced
further in the past. The motion of all other comets can be followed for
a long time, provided we can model all perturbing forces with
sufficient accuracy. If the aphelion distance of a comet does not exceed
say
AU and for a time interval of a few cometary orbital
periods it seems to be sufficient to include Galactic Disk tidal forces
and stellar perturbations due to close approaches to the Sun. Galactic
perturbations can be easily included using the Heisler & Tremaine (1986)
approximation, but calculating the influence of all stars visiting the
neighbourhood of the Sun in the studied interval of time (say ten million
years) is difficult due to incompleteness and inaccuracies in stellar
data. We plan to include in our model all stars for which the data on
spatial position and velocity will be available.
For those comets, whose aphelion distances are quite large, and especially for originally hyperbolic comets, a more sophisticated dynamical model of the influence of the Galaxy should be adopted, including the motion of the Sun in the galactic frame. The problem of stellar perturbations remains very important here, but it seems that it can be solved only in a statistical manner through some kind of simulation. This population of comets is under study in a different project.
The widely used terms: dynamically "new'' and "old'' comets should be used with care, taking into account the past motion of those comets. One should not call "new'' a comet for which we can almost be sure that it penetrated the vicinity of the Sun at least once in the past. We know that original orbits are not free from errors, and due to this, some previous aphelia or perihelia are wrong. However, the whole population of previous long-period cometary orbits seems to be quite consistent with our theories of their origin and evolution.
Acknowledgements
The author wishes to thank Halina Pretka-Ziomek for valuable discussions during preparation of this paper and Tadeusz Jopek for his help in improving the first version of this manuscript. Special thanks should be given to Dr. Brian Marsden who, as a referee, formulated many important suggestions and comments which allowed us to greatly improve the final version of this paper.
Copyright ESO 2001