**AAS 199th meeting, Washington, DC, January 2002**

*Session 28. Solar System: Dynamics and Collisions*

Oral, Monday, January 7, 2002, 10:00-11:30am, Jefferson East
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## [28.03] Characteristic Times for Collisions of Minor Bodies With Terrestrial Planets

*S.I. Ipatov (IAM, Moscow), L.M. Ozernoy (GMU)*

Previous analytical calculations of characteristic times,
T, for collisions of Earth-crossing objects (ECOs) and
comets with the Earth were mainly based on Öpik's
formulas. However, this approach becomes very inaccurate
whenever the periods of a minor body and the planet are
close to each other. While taking into account this
situation, we also abandon the limitations of other
approaches, which consider bodies moving in their orbots
with an invariable velocity. When a minor body moving in an
orbit with semimajor axis a collides with a planet at a
distance r from the Sun, then T is larger by a factor of
k = \sqrt{2a/r -1} compared to the approximation of a
constant velocity. The obtained values of T (in Myr) and
k (in parenthesis) are presented in the following table.

\begin{array}{lccccc}

& Atens & Apollos & Amors & ECOs & JFCs \\ Venus & 106~
(1.2) & 186~ (1.7) & & 154~ (1.5) & 2900~ (2.5) \\

Earth &15~ (0.9) & 164~ (1.4) & 211~ (2.0) & 67~ (1.1)
&2200~ (2.3)\\

Mars &475~ (0.4) & 4250~ (0.9) &5810~ (1.1)&4710~ (1.0)
&17000~ (1.8)

\end{array}

Note that relatively small values of T for Atens and all
ECOs colliding with the Earth are due to just several Atens
with small inclinations i, which were discovered during
last two years. If for the Aten object having 0.1^{\}circ
one takes i=1^{\}circ, then for collisions with Earth one
gets 28 Myr for Atens and T=97 Myr for ECOs.

For Jupiter-family comets (JFCs) colliding with the
terrestrial planets, k\ge2. For three Halley-type
comets with periods between 71 and 76 yr, we obtained
T=350 Gyr and k=6 (collision with Earth) and T=3500
Gyr and k=5 (collision with Mars). We have performed a
series of runs of orbital evolution of resonant asteroids
and JFCs and computed values of T for those runs. The
results demonstrate that the effect of non-constant velocity
must be taken into account, especially when semimajor axes
of a minor body and a planet differ considerably.

We acknowledge support of this work by NASA grant
NAG5-10776, the RFP ``Astronomy", RFBR~(01-02-17540), and
INTAS~(00-240).

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