One of the problems of the numerical integrations of cometary orbits is that of their numerical stability. For those bodies which undergo close encounters with the giant planets the problem has a specific feature. Apart from the numerical instability of integrations in the mathematical sense, there is an additional source of instability due to the inaccuracy of initial data, i.e. the orbital elements. An example of this case is presented in this paper by the numerical integration of the motion of comet P/Shajn-Schaldach over an interval of 368.4 years, within which six close encounters with Jupiter occurred. The inaccuracy of the starting orbital elements of this comet is modelled by changes in the last digit of each element of the central orbit, determined by the set of the best orbital elements. In the process of integration, eight model orbits experience differential perturbations with respect to the central orbit. The numerical instability, caused by the inaccuracy of starting orbital elements and represented by the dispersion of these orbits, tends to increase abruptly beyond each encounter with Jupiter. It is shown that, with the attainable accuracy of the osculating elements representing the observations, one or two approaches to within 1 AU from Jupiter can make the orbit entirely indeterminate.

All the known short-period comets have been followed by numerical integration over a time span of 821 years, from 1585 to 2406. A preliminary survey of the results of these integrations has shown some interesting features, which become recognizable thanks to the length of the time interval covered, not negligible if compared with the typical evolutionary time scale of comets moving in short-period orbits. Interesting phenomena that have been recognized include: (1) captures from, or ejections into, very elongated ellipses, with perihelia of the parking orbits close to the orbit of Jupiter and aphelia within or beyond the region of outer planets; (2) passages of comets from the control of Saturn to that of Jupiter; (3) orbital evolutions controlled mainly by Saturn; (4) librations of comets around low-order resonances; (5) repeated close approaches of comets to Jupiter, often with the comet being captured as a temporary satellite; (6) an almost perfect coincidence of two comet orbits just before a close approach to Jupiter, suggesting their genetic relationship.

In 1961 Kazimirchak-Polonskaya (1961a, 1961b) published comprehensive reviews of all investigations on the dynamics of cometary orbits as well as on close approaches of the short-period comets with Jupiter for the time span covering 1770–1960 and for the first time put forward the basic problems of cometary astronomy from the standpoint of celestial mechanics. Chebotarev (1971) pointed out that “these reviews, supplemented with extensive references, can serve as a valuable manual for all researchers of cometary motions”. In 1967 Kazimirchak-Polonskaya (1967a) developed the advanced problems in a definitive form. The corresponding member of the USSR Academy of Science M.F. Subbotin (at that time the Head of the Institute) characterized the above mentioned works as “the general plan for cometary studies in the important branch of cometary astronomy”.

A historical review of investigations on encounters of minor bodies with outer planets is presented. The dominating role of Jupiter in the capture of comets and in determining their secular evolution is emphasized. Participation in the above process of Saturn, Uranus and, especially, Neptune is investigated. In the present paper are considered five fictitious comets, penetrating into the depths of Neptune’s sphere of action, where they undergo large orbital transformations and capture by Neptune. Two near-circular orbits are transformed into elliptical ones, their perihelia being moved inside the planetary system; one hyperbolic orbit is transformed into a transplutonian one, another into a typical short-period orbit of the Neptune’s family with a perihelion accessible to terrestrial observers. One fictitious comet is captured by Neptune as a stable satellite.

The evolutionary paths connecting cometary reservoirs in the outer solar system and the population of periodic comets involve stellar and planetary perturbations. Close planetary encounters play a special role, making the dynamical evolution slow or fast depending on the orbital elements of the comet at various stages of the process. In this paper numerical work done in the last decades on this subject, using both real and fictitious objects, is reviewed.

The aging of comets is evidenced by a number of observable phenomena: production of gas, dust and meteor particles, splitting of cometary nuclei, nongravitational effects in the comet’s motion, sudden and progressive absolute brightness variations, and ultimate disappearance. Statistical data on comet losses, absolute magnitudes and orbits also bear signatures of their aging. The knowledge of potential active lifetimes of individual objects is a prerequisite of any realistic model of the long-term evolution of the whole comet complex. This paper reviews different sources of information on the aging process and summarizes implications for the mean lifetimes of comets, their dispersion and dependence on the orbital parameters. Two alternative end fates of comets - their total disintegration or change into an inactive asteroid-like object - are also discussed.

Planetary perturbations, dynamical energy and orbital evolution of the elements of three comets are calculated. This paper presents a part of the catalogue that will be issued in the next year.

The background to the problem of explaining the frequency distribution of cometary 1/a-values is briefly reviewed and it is emphasised that the explanation in terms of the Oort Cloud model relies on an ad hoc fitting function - the fading/disruption probability per revolution. Assuming an underlying steady-state Oort Cloud and the integral equation formalism developed by Oort and Yabushita to predict the 1/a-distribution for an arbitrary fading probability, we have been able to constrain the unknown fading function by comparison with observations. In agreement with previous work we find that the tendency for fading or disruption should be strong at small 1/a-values and weak at large 1/a-values. The mean fading probability per revolution, k(x), is found to lie within a factor roughly of order 2 about k(x) ≈ 0.3(1+(x/4 × 10−3)2)−3/2, where × is 1/a in units AU−1. A physical model for fading which might qualitatively account for this behaviour is tentatively proposed. This depends on the thermal shock experienced by a long-period comet nucleus around perihelion passage. It is emphasised that until a viable model for fading has been found, the validity of the steady-state primordial hypothesis remains unresolved.

The recent and current situation with regard to our analysis and understanding of the nongravitational effects in cometary motions is reviewed. Comets can be categorized according to the different physical situations that may exist in their nuclei. Further experimentation with theoretical models and empirical fits to observations is encouraged.

The phenomena of comet groups, i.e. sets of comets that exhibit similarity in their orbital elements, is investigated. A computer program based on the D-criterion of orbital similarity is used to search for comet pairs and groups. The reality of the groups is tested by making computer searches in random samples of comet orbits.

The data base for the study is 599 long-period comet orbits. The degree of orbital similarity within a comet group was first assumed to be identical to that encountered in meteor streams. The computer search at this level produced five comet pairs plus two groups with four and seven members, respectively. The latter two represented the eleven known members of the Kreutz group of sun-grazing comets. A comparison with searches in random samples showed that the two Kreutz groups were significant. There is a probability of 0.2 that the five comet pairs found in the real sample could be accidental formations.

In a second study the orbital similarity parameter Ds was varied and the number of comet groups found in the real and synthetic comet populations was compared at each level of Ds. Apart from the Kreutz group of comets, the number of groups detected in the real comet sample was for all levels of orbital similarity only slightly higher than the average found in the random samples. At the 2σ confidence level we conclude that comet groups exhibit similarity in their orbital elements, that is no greater than might be expected by chance.

Our investigation demonstrates that the asteroidal objects 1983 SA and 1983 XF can be considered as temporary visitors of the 4/3 and 2/1 resonance with Jupiter, respectively. Evidence is given that both objects are first rank candidates for a cometary origin. The case of 1983 SA is remarkable in so far as (279) Thule is up to now the only known asteroidal 4/3 librator.

This paper is concerned with the influence of non-gravitational forces on the orbital evolution of the short-period comets. This influence is variable for different comets and is especially noticeable for those comets which undergo approaches with Jupiter. When studying the dynamic evolution it is desirable to take into account the non-gravitational effects.

A factor depending on geomagnetic index was introduced in the B. Marsden’s formula for the nongravita-tional force. The orbit of the cornet Encke covering seven apparitions (1895-1914) obtained with this modified formula shows better residuals than that obtained with the non-modified one.

The history of the attempts to predict the motion of comet Halley is outlined and the importance of the so-called nongravitational forces acting upon this comet is emphasized. Recent orbital work of the International Halley Watch Astrometry Network is reviewed. Comet Halley’s transverse nongravitational parameter is positive and nearly constant with time suggesting that the comet is in direct rotation without precession of the spin pole. The nongravitational effects are consistent with the vaporization of water ice from the comet’s nucleus and long term integrations suggest that the comet has been in its present orbit for at least 16,000 years and probably much longer.

The present paper studies the structural features of the meteor streams associated with Comet Halley deduced from the observations of its meteor showers, as check points of orbital elements in a deeper history of the comet orbit. Libration of the argument of perihelion of the comet and the corresponding displacement of the nodes, as recognized in the distribution of condensations within the stream, allows to estimate the maximum lifetime of the comet in the inner Solar System at about 2 × 105 years.

The ICE spacecraft will pass through the tail of P/Giacobini-Zinner on September 11, 1985, to make in situ measurements of particles, fields, and waves that will contribute significantly to the knowledge of plasma tails and other aspects of the cometary/solar wind interaction. By obtaining data on the downstream side of G/Z, the ICE will complement the later upstream measurements obtained by the Comet Halley probes.

The criteria used to select a short period comet for possible future rendezvous space missions are stated and the selection process is outlined. For the time period 1900 - 2000, several candidate comets offer opportunities for spacecraft rendezvous. Two of the best candidates are periodic comets Kopff and Wild 2.