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E. Asphaug (UCSC), L. Dones (SwRI), P.M. Schenk (LPI)
Levison et al. (1999) estimate the present impact rate RI 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} RI = 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} RT = 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 RJ/\rho1/3, where RJ is the radius of Jupiter, and \rho is comet density in g/cm3. ECs are gravitationally focused by Jupiter, implying uniform distribution of perijove distances; hence
\begin{equation} RT/RI = 1.37/\rho1/3 - 1. \label{eq:ratio} \end{equation}
Substituting from (1) and (2) gives \rho = 0.07~g/cm3, 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/cm3, 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.