Info

For the integrations we used the Bulirsh-Stoer method (BULSTO) and a symplectic method. The calculated values of probability of collision of former JCOs with planets, were close to each other for both these methods, although bodies obtained resonant orbits more often in the case of BULSTO.

Besides JCOs, we considered asteroids with initial values of e and i equal to 0.15 and 10° respectively. For the asteroids initially located at the 3:1 resonance with Jupiter, we found that the ratio of the number of asteroids ejected into hyperbolic orbits to the number that collided with the Sun, was 5.6 for BULSTO, and 0.38 and 0.87 for a symplectic method using integration steps equal to 10 and 30 days respectively. So in some cases a symplectic method can give a large error. For the 5:2 resonance with Jupiter, r^ equaled 20 and 10 for BULSTO and symplectic methods respectively. In Table 1, for asteroids we present only results obtained by the BULSTO code at 7s=50 Myr (at Xs=10 Myr the values of P and T are smaller by a factor less than 1.2 and 1.01 for the 3:1 and 5:2 resonances respectively) and for TNOs we present results obtained by both codes.

Migration of matter from the Edgeworth-Kuiper, and main asteroid belts to the earth

The total time during which 2000 former JCOs were in Apollo-type and Amor-type orbits was 28.7 and 21.75 Myr respectively, although 12.7 and 11.4 Myr of the above times were due to three objects. We found that several former TNOs spent more than 1 Myr in orbits with aphelion distance Q<4.7 AU. The time interval during which a body had Q less than 3.2 and 3.7 AU exceeded 0.1 and 2.6 Myr respectively.

Most of the collisions of former JCOs with the Earth were from orbits with aphelia inside Jupiter's orbit. The probability of collision with the Earth, for 3 former JCOs which had spent more than 1 Myr in Earth-crossing orbits (mainly with Q<4.7 AU) was 1.5 times greater than that for the other 1997 JCOs. About 1 in 300 JCOs collided with the Sun. In [9] we considered a much smaller number of objects, which did not get aphelia inside Jupiter's orbit, and the values of Pr and T were smaller than those in Table 1. For the 2000 JCOs we have considered, the mean probability of collision with Venus is about the same as with Earth, but 3 times smaller for Mars. These values are mainly due to a few bodies that spent more than 1 Myr in orbits with aphelia deep inside Jupiter's orbit (for such bodies usually more than 80% of collisions with planets were from orbits with Q<4.2 AU). If we consider 1000 JCOs, for which most of the collisions with planets were from orbits with Q>4.2 AU, then the mean probability for Venus and Mars is less by a factor of 1.6 and 3 respectively, than that for Earth. Therefore, the ratio of the total mass of icy planetesimals that migrated from the feeding zone of the giant planets and collided with an inner planet, to the mass of the inner planet, was greater for Mars than that for Earth and Venus.

The mean time during which an object crossed Jupiter's orbit was 0.13 Myr for 2500 JCOs. An object had a period Pa<10 yr usually only for about 12% of this time, so our consideration of initial objects with only Pa<10 yr does not influence much on the obtained results. At N=2000 for 10<Pa<20, 20<Pa<50 and 50<Pa<200 yr, we got 23%, 22% and 16% respectively. One former JCO spent some time in orbits with aphelia deep inside Jupiter's orbit, and then it moved for tens of Myr into the trans-Neptunian region, partly in low eccentricity and partly in high eccentricity orbits. This result shows that some bodies can get from the MAB into the trans-Neptunian region, and that typical TNOs can become scattered objects (with high eccentricities) and vice versa.

Was this article helpful?

0 0

Post a comment