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3 Statistics of the original orbits

The most famous statistics of the original orbit set was presented by Oort in his fundamental paper on the existence of the cloud of comets surrounding the Solar System (Oort 1950). Those statistics consisted of only 19 orbits, and a high concentration of the reciprocal original semimajor axes of those comets towards a small, positive value was the main argument for the existence of the cometary cloud. Oort repeated this work lately, in a paper published as a chapter in the book on the physics of comets, edited by W. F. Huebner (Oort 1990). He accumulated data for 66 comets, restricted to those with a perihelion distance greater than 1.5 AU to be sure that he excluded any comets that may be influenced by non-gravitational effects. In our set (last updated in September 1999) we have almost doubled this number and we present a comparison of those three distributions in Table 2.

It has been well known since the publication of the Oort (1950) paper that dynamically "new'' comets, entering the planetary region for the first time, should have the smallest 1/a values. A widely-used definition of dynamically "new'' comets, (e.g. Oort & Schmid 1951; Kresák 1977, 1994; Marsden et al. 1978; Oort 1990; Levison 1996) states that their $1/a<1\times 10^{-4}$ AU-1, which is equivalent to $a >10\,000$ AU. Table 3 shows the division of the whole set of 327 original orbits into dynamically "new'' and "old'' comets according to the above definition, with additional division with respect to the orbit quality class (Marsden et al. 1978). The statistics for the restricted (q>1.5 AU) sample is also shown separately.


Table 3: Dynamically "new'' and "old'' comets among 327 original orbits, according to the classical definition.
  class 1 class 2 classes 1 + 2
q [AU] >1.5 $\leq$1.5 >1.5 $\leq$1.5 >1.5 $\leq$1.5
"new'' 60 31 6 16 66 47
"old'' 56 48 23 87 79 135
all 116 79 29 103 145 182
Total 195 132 327

However, treating all comets with $a >10\,000$ AU as new is an obvious oversimplification. Some of those comets may have passed near the Sun during earlier returns. One of the perturbing agents acting on those comets, namely the galactic disk tide, causes periodic changes of the perihelion distances with periods of order of 104-105years. Depending on the semimajor axis and geometrical configuration with respect to the galactic plane, the perihelion distance can be significantly changed even during one orbital period, so we decided to follow backward the motion of those comets to their previous perihelion passage.

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