**31st Annual Meeting of the DPS, October 1999**

*Session 6. Celestial Mechanics of Planets and Comets*

Contributed Oral Parallel Session, Monday, October 11, 1999, 10:30am-12:00noon, Sala Pietro d'Abano
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## [6.08] Near-Misses and Collisions With Comets

*E. Asphaug (UCSC), L. Dones (SwRI), P.M. Schenk (LPI)*

Levison et al. (1999) estimate the present impact rate R_{I}
on Jupiter due to ecliptic comets (ECs) with diameters
>2~km at 1/1300 years. Assuming this comet population has
declined as 1/time since the origin, the averaged impact
rate over the last 4 Gyr is higher by \log{[4.56/(4.56 -
4)]} = 2.1. Thus, over 4 Gyr,

\begin{equation} R_{I} = 1.6 \times 10^{-3}/{\rm year}.
\label{eq: ri} \end{equation}

From Voyager observations of crater chains on Callisto,
Schenk et al. (1996) estimated the rate of tidal disruption
of comets by Jupiter, averaged over 4 Gyr, as

\begin{equation} R_{T} = 3.7 \times 10^{-3}/{\rm year}.
\label{eq: rt} \end{equation}

Asphaug and Benz (1996) predict threshold catastrophic tidal
disruption of a comet near Jupiter for perijove distance q
< 1.37 R_{J}/\rho^{1/3}, where R_{J} is the radius of
Jupiter, and \rho is comet density in g/cm^{3}. ECs are
gravitationally focused by Jupiter, implying uniform
distribution of perijove distances; hence

\begin{equation} R_{T}/R_{I} = 1.37/\rho^{1/3} - 1.
\label{eq:ratio} \end{equation}

Substituting from (1) and (2) gives \rho = 0.07~g/cm^{3},
significantly lower than the density for Shoemaker-Levy 9
derived by Asphaug and Benz (1996). The consideration of
comet strength makes this density an upper limit.

Alternatively, if we use the higher present-day impact rate
(1/330 years) of Levison and Duncan (1997), we find \rho =
0.64~g/cm^{3}, in good agreement with Asphaug and Benz.

These issues are tied to the cratering versus catenae record
on the Galilean moons, which adds a third independent
element for constraint, to be presented.

Asphaug, E. and Benz, W. (1996). {\em Icarus} **121**,
225--248.

Levison, H.F. and Duncan, M.J. (1997). {\em Icarus} **
127**, 13--32.

Levison, H.F., Duncan, M.J., Zahnle, K., and Dones, L.
(1999). Submitted to {\em Icarus}.

Schenk, P.M., Asphaug, E., McKinnon, W.B., Melosh, H.J., and
Weissman, P.R. (1996). {\em Icarus} **121**, 249--274.

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