1 Introduction

It is generally accepted that long-period comets (e.g. comets with periods greater than the traditional lower limit of 200 years) originate from the Oort cloud, from which their stable orbits have been perturbed into the inner Solar System by the cumulative effects of the galactic tidal field and the passage of nearby stars or giant molecular clouds. Such comets possess nearly parabolic incoming orbits described by positive reciprocals of semimajor axes, e.g.: $(1/a)_{\rm ori} > 0$.

However, in the sample of about three hundred long-period comets with well determined orbits there are about 10% which have hyperbolic incoming orbits ( $(1/a)_{\rm ori} < 0$). The problem of the negative tail of the distribution of original binding energies (proportional to $(1/a)_{\rm ori}$) has been discussed in detail in literature by many authors. First, the quality of astrometric data, the method of data selection (including the problem of weighting the individual measurements), and the applied method of integration may all strongly affect the orbit computation of each individual "hyperbolic'' comet (even comets with orbits ascribed as 1A - highest quality class). Second, since all the negative excess energies are small, corresponding to roughly -10^-4 AU^-1 in inverse semimajor axis, Marsden et al. (1973) speculate that neglecting the non-gravitational effects tends to produce original orbit which appear to be more hyperbolic than they really are. In particular, it is possible that most "hyperbolic'' comets with small perihelion distances originate from the Oort's cloud of comets. The latter suggestion is strongly supported by the fact that perihelion distances of two comets with a greatest negative excess of $(1/a)_{\rm ori}$ are smaller than 0.9 AU. On the other hand, Yabushita (1991) found that the maximum excess velocity at great distance due to non-symmetric outgassing from cometary nuclei is equal to 0.18 kms^-1. Thus, he argues that for at least 15 comets the calculated original orbits are "highly hyperbolic'' and are not "compatible with elliptical orbits modified by the non-gravitational accelerations''. More recently, Bolatto et al. (1995) concluded that the non-gravitational perturbation in a near-parabolic comet's energy per orbital revolution is generally smaller than about 10^-4 AU^-1. However these two papers neglect the influence of variations of osculating orbital elements on $(1/a)_{\rm ori}$ when the non-gravitational effects are implied from observational data. Present calculations show that hyperbolic original orbits are produced by hyperbolic osculating orbits resulting from positional data in the case of pure gravitational motions.

There are several generally accepted reasons that extrasolar comets exist. An important question is whether such comets could be observed if they actually were observed. The modern theories (e.g. Clube & Napier 1984; Duncan et al. 1987) for the formation of comets in the interstellar environment predict many more extrasolar comets than bound comets. However, the estimates of the expected rate for detection of extrasolar comets are uncertain. McGlynn & Chapman (1989) show that the rate of hyperbolic comets passing with perihelion q<2 AU is 0.6 per year which implies that a total of about six extrasolar comets should have been detected over the last 150 years. More recently, Sen & Rana (1993) argued that the density of stars in the solar neighbourhood was overestimated by McGlynn and Chapman. Using a value of 0.014 $M_{\odot}$ pc^-3Sen & Rana found that the expected number of detectable interstellar comets per century is less than one. Hughes (1991) gives an even smaller number of expected comets on hyperbolic orbits. He argues that hyperbolic comets occur at a rate of 0.00225 yr^-1, which yields one such comet on average every 450 yrs. It seems clear that at most only a few known "hyperbolic'' comets could really have interstellar origins. Nevertheless, using modern techniques for comet searches, the detection rate of extrasolar comets will increase dramatically in the future. Presently it is possible to weed out false members from the sample of "hyperbolic'' comets.

In this paper the non-gravitational motions of individual "hyperbolic'' comets from the Catalogue of Cometary Orbits (Marsden & Williams 1997; hereafter MW Catalogue) are examined. The aim of the present study is to prove that incoming orbits of "hyperbolic'' comets for which it was possible to determine the non-gravitational effects are almost all elliptical. Next, we show that using objective statistical criteria for the remaining "hyperbolic'' comets, excess energies derived for pure gravitational motion are systematically smaller than those given in the MW Catalogue. The new method of $(1/a)_{\rm ori}$uncertainty estimates are also used.