  The orbital evolution of more than 22000 Jupiter-crossing objects under the
gravitational influence of planets was investigated. We found that the mean
collision probabilities of Jupiter-crossing objects (from initial orbits close
to the orbit of a comet) with the terrestrial planets can differ by more than
two orders of magnitude for different comets. For initial orbital elements
close to those of some comets (e.g. 2P and 10P), about 0.1% of objects got
Earth-crossing orbits with semi-major axes a<2 AU and moved in such orbits for
more than a Myr (up to tens or even hundreds of Myrs). Results of our runs
testify in favor of at least one of these conclusions: 1) the portion of 1-km
former trans-Neptunian objects (TNOs) among near-Earth objects (NEOs) can
exceed several tens of percents, 2) the number of TNOs migrating inside solar
system could be smaller by a factor of several than it was earlier considered,
3) most of 1-km former TNOs that had got NEO orbits disintegrated into
mini-comets and dust during a smaller part of their dynamical lifetimes if
these lifetimes are not small.
