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\centerline{\bf MIGRATION OF CELESTIAL BODIES IN THE SOLAR SYSTEM}
\centerline{
{\bf Ipatov S.I.} {\it (Institute of Applied Mathematics, Miusskaya sq. 4,
125047 Moscow, Russia.}}
\centerline{\it Fax: 7(095)972-0737. E-mail: ipatov@applmat.msk.su)}
\medskip
\begin{sloppypar}
   We investigated several cases of migration of celestial bodies
in the forming and present Solar System.
       The results of numerical
integration of the equations of motion for the plane three-body problem (the
Sun and two bodies) showed [6]
that for initially circular heliocentric orbits and
the chaotic variations in orbital elements at $\mu_1 \leq 10^{-5}$
the maximum eccentricity $e_{max}$
usually doesn't exceed $7-8 \times \mu_1^{1/3}$, where $\mu_1$
is a ratio of the larger body mass to the Sun mass.
For initially eccentric orbits and a large time interval,
the values of $e_{max}$ may depend mostly on initial orbits
but not on $\mu_1$. We showed [1] that in the case of close
encounters, using the spheres' method (two
two-bodies problems) and
choosing the radius of the sphere in an appropriate way,
we can obtain almost the same values of $e_{max}$ as those
obtained by numerical integration.
For the case of three identical bodies circling the Sun,
the maximum eccentricity can be several
tens of times larger than that for two such bodies [7].
The obtained results showed that some bodies of the beyond-Neptune
belt can migrate
to the orbit of Neptune under the gravitational influence of other bodies of
this belt.
\end{sloppypar}
       Our investigations of migration of bodies during the accumulation
of planets were based mainly on the results of computer simulation of the
evolution of disks that originally consisted of hundreds of gravitating bodies
moving around the Sun [2, 5].
In some models the initial disks included also almost-formed planets.
The mutual gravitational influence of bodies
was taken into account by the spheres' method. We also analytically studied
the dependencies of the time of disk evolution and the average eccentricity
as a function of the number of bodies constituting the disk [3, 7].
The obtained results showed that each terrestrial planet incorporated
planetesimals from the feeding zones of all these planets.
The total mass of bodies ejected from the zones of giant planets into
hyperbolic orbits may have been ten times as large as the mass of bodies
that entered into the planets. The embryos of unformed planets
with masses equal to several Earth masses in the zone of Jupiter
and Saturn would be necessary to explain present eccentricities as well
as present axial rotations of these planets.
The embryos of Uranus and Neptune with  initial  masses  equal  to
several Earth masses may have originated near the orbit of  Saturn
and then may have migrated to the present distances from  the  Sun
moving all time in nearly circular orbits. The mass  of  solid bodies,
which entered into Jupiter's envelope  and  nucleus,  may  be
larger than that in any other planet and may  exceed  the  Earth's
mass by several tens' times.
A large amount of water could be delivered to
Earth during the accumulation of Uranus and Neptune.

We investigated the present migration of bodies to the Earth from
the asteroid and trans-Neptune belts [8]. Computer simulations of the
evolution of disks that originally consisted of planets and hundreds of
bodies located in various regions of the Solar System were carried out.
We obtained that some bodies, which migrated to the Earth from these regions,
replenished the family of bodies, which orbits
entirely lie inside the Earth's orbit (and some orbits lie inside the orbit of
Venus). Most of asteroids of the Amor group should have come from the asteroid
belt. Together with the 3:1 gap, the 5:2 Kirkwood gap may play noticeable role
in the replenishment of Apollo and Amor groups [4].
For most of bodies that collided the Earth, the time interval between the
moment when they obtained
the orbit intersecting the Earth's orbit and a collision with the Earth does 
not
exceed 10 Myr.

This work  was  supported  by  Russian  Fund  of  Fundamental
Investigations under Grant 93-02-17035.
{\bf References}: [1] Ipatov S.I. (1981) {\it Sov. Astron.}
{\bf 25 (58)}, 617-622. [2] Ipatov S.I. (1987) {\it Earth, Moon, and Planets.} 
{\bf 39}, 101-128. [3] Ipatov S.I. (1988) {\it Sov. Astron.}
{\bf 32 (65)}, 560-566. [4] Ipatov S.I. (1992) {\it Sol. Syst. Res.} {\bf 26},
520-541. [5] Ipatov S.I. (1993) {\it Sol. Syst. Res.} {\bf 27},
65-79. [6] Ipatov S.I. (1994) {\it Sol. Syst. Res.} {\bf 28}, {\it N} 6.
[7] Ipatov S.I. (1995) {\it Sol. Syst. Res.} {\bf 29}, {\it N} 1.
[8] Ipatov S.I. (1995) {\it Sol. Syst. Res.} {\bf 29}, {\it N} 4 ({\it in
press}).

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