Size, density, and structure of comet Shoemaker - Levy 9 inferred from the physics of tidal breakup

Detailed consideration of possible fragmentation mechanisms shows that Comet Shoemaker - Levy 9 (SL9) had negligible effective strength, even in comparison with tide and selfgravity, by the time it attained perijove in 1992. This reduces the tidal physics to a computable basis: we model the elongation of this "rubble-pile," and the onset of the instability which created a chain of gravitationally bound clumps, using an N-body code with self-gravity and simple collisions. Gravitational clumping depends only on the density ρ_c of the progenitor (for a given orbit), and chain length then scales linearly with initial diameter d_c. We thus constrain from chain morphology that ρ_c ≈ 0.6 g cm^-3 and from chain length that d_c ≈ 1.5 km. Our numerical results accurately match analytical derivations for the threshold of tidal breakup, and lead to general relations for erosion and disruption of strengthless or regolith-covered bodies. For a given random encounter, we show that a rubble-pile comet, or one mantled in deep regolith, is half as likely to be destroyed by tides as it is to impact an outer planet. Because of their similar density ratio, the same holds true for rubble-pile asteroids encountering terrestrial planets. Split comets such as SL9 near Saturn are unlikely: the required periapses intersect the planet.