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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Formation and migration of trans--Neptunian objects
S. I. Ipatov 1;2
1 Institute of Applied Mathematics, Moscow, Russia
2 NASA/GSFC, Greenbelt, USA
We support the Eneev's idea [1] that the largest (with diameter d?100 km)
trans­Neptunian objects (TNOs) moving now in not very eccentric orbits could
be formed directly by the compression of rarefied dust condensations (with a?30
AU) of the protoplanetary cloud (we do not support Eneev's opinion that planets
were formed directly from large condensations) but not by the accretion of smaller
(for example, 1­km) planetesimals, because such accretion could take place only
at a large total mass of TNOs (several tens of Earth masses) and very small
eccentricities (ё 0:001), which probably could not exist during the time needed
for such accretion. Probably, some planetesimals with d ё 100--1000 km in the
feeding zone of the giant planets and even large main--belt asteroids also could be
formed directly by such compression. Some smaller objects (TNOs, planetesimals,
and asteroids) could be debris of larger objects, and other such objects could be
formed directly by compression of condensations. A small portion of planetesimals
from the feeding zone of the giant planets that entered into the trans--Neptunian
region could remain in eccentric orbits beyond Neptune and became so called
``scattered objects''. These objects could supply most of bodies that collided the
Earth at the end of its bombardment 4 Gyr ago. The total amount of water
delivered to the Earth during the formation of the giant planets was about the
mass of water in the Earth's oceans.
The motion of TNOs to Jupiter's orbit was investigated by several authors.
We considered the evolution for intervals T S – 5 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 (a ъ 3:1 AU, e ъ 0:53, i ъ 12 ffi ). 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
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the total time interval T \Sigma during which perihelion distance q of bodies was less
than a semimajor axis of the planet. The values of P r = 10 6 P = 10 6 P \Sigma =N and
T = T \Sigma =N are presented in the Table together with the ratio r of the total time
interval when orbits were of Apollo type (at a ? 1 AU, q = a(1 \Gamma e) ! 1:017 AU,
e ! 0:999) to that of Amor type (1:017 ! q ! 1:33 AU); r 2 is the same as r but
for Apollo objects with e ! 0:9. For observed near--Earth objects r is close to 1.
Table: Values of T (in kyr), T c = T=P (in Myr), P r , r, r 2 for the terrestrial
planets (Venus = V, Earth = E, Mars = M)
V V E E E M M \Gamma \Gamma
N T P r T P r T c T P r r r 2
JCOs 2000 9:3 6:62 14 6:65 2110 24:7 2:03 1:32 1:15
10P 500 24:9 16:3 44 24:5 1800 96:2 5:92 1:49 1:34
For integrations we used the Bulirsh--Stoer method (BULSTO) and a sym­
plectic method. The probabilities of collisions of former JCOs with planets were
close for these methods, but bodies got resonant orbits more often in the case of
BULSTO. The obtained values of T and P r are larger than those in [2], because
in our last runs we considered much larger (than in [2]) number of JCOs and
obtained several former JCOs that moved in orbits with aphelia inside Jupiter's
orbit (mainly with Q ! 4:7 AU) during more than 1 Myr. The probability of col­
lisions with the Earth for 3 former JCOs from such orbits was 1.5 times greater
than that for the other 1997 JCOs. About 1 of 300 JCOs collided with the Sun.
The analysis of the results of the orbital evolution of JCOs and TNOs showed
that, in principle, as it was suggested earlier by T. M. Eneev, the trans--Neptunian
belt can provide up to 100% of Earth--crossing objects, but, of course, some of
them came from the main asteroid belt. The ratio of the total mass of icy plan­
etesimals that migrated from the feeding zone of the giant planets and collided
with the planet to the mass of this planet was greater (by a factor of 3 in our
runs) for Mars than that for Earth and Venus.
This work was supported by Russian Foundation for Basic Research (01­02­
17540), INTAS (00­240), NASA (NAG5­10776), and NRC (0158730).
References
1. Eneev T. M. About possible structure of outer (trans--Neptunian) regions of
the Solar system. Pis'ma v astron. zhurnal, 1980, 6, 295--300 (in Russian).
2. Ipatov S. I. Comet Hazard to the Earth, Advances in Space Research, 2001,
28, 1107--1116.
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