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S.I. Ipatov (Inst. Appl. Math., Moscow; NASA/GSFC), J.S. Mather (NASA/GSFC)
We investigated the evolution for periods of at least 5-10 Myr of 2500 Jupiter-crossing objects (JCOs) under the gravitational influence of all planets, except for Mercury and Pluto (without dissipative factors). In the first series we considered N=2000 orbits near the orbits of 30 real Jupiter-family comets with period <10 yr, and in the second series we took 500 orbits close to the orbit of Comet 10P Tempel 2. We calculated the probabilities of collisions of objects with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr and then summarized the results for all time intervals and all bodies, obtaining the total probability P\Sigma of collisions with a planet and the total time interval T\Sigma during which perihelion distance of bodies was less than a semimajor axis of the planet. The values of P = 106 P\Sigma /N and T = T\Sigma /1000 yr are presented in Table together with the ratio r of the total time interval when orbits were of Apollo type (at e<0.999) to that of Amor type.
\begin{array}{lccccccc}
& Venus & Venus & Earth & Earth & Mars & Mars & - \\ N & T & P & T & P & T & P & r \\ 2000 & 9.3 & 6.62 & 14.0 & 6.65 & 24.7 & 2.03 & 1.32 \\ 500 & 24.9 & 16.3 & 44.0 & 24.5 & 96.2 & 5.92 & 1.49
\end{array}
The probability of collisions with the Earth for 3 former JCOs, each of which moved for more than 1 Myr in Earth-crossing orbits, (usually more than 80% of such collisions with the terrestrial planets were from orbits with aphelion distance <4.2 AU) was 1.5 times greater than that for 1997 other JCOs. About 1 of 300 JCOs collided with the Sun. The total time during which former 2000 JCOs were in Apollo-type and Amor-type orbits was 28.7 and 21.75 Myr, respectively, but 12.7 and 11.4 Myr of the above times were due to three objects. One former JCO spent some time in orbits with aphelia deep inside Jupiter's orbit, and then it moved for tens of Myr in the trans-Neptunian region, partly in low eccentricity and partly in high eccentricity orbits. We acknowledge support of this work by NASA grant NAG5-10776, INTAS~(00-240) and RFBR~(01-02-17540).
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Bulletin of the American Astronomical Society, 34
© 2002. The American Astronomical Soceity.