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We use Monte Carlo methods to simulate impacts of ecliptic comets on the synchronously rotating satellites of giant planets. We reconfirm the long-standing prediction that the cratering rate should be much higher on the leading hemispheres than on the trailing hemisphere; indeed we find that previously published analytical formulations modestly underestimate the degree of apex-antapex asymmetry to be expected. We then compare our results to new mapping of impact craters on Ganymede, Callisto, and Triton. Ganymede reveals a pronounced apex-antapex asymmetry that is nonetheless much less than predicted. All of Triton's confirmed impact craters are clustered toward the apex of motion, far exceeding the predicted asymmetry. No asymmetry is observed on Callisto. In each case at least one of our basic assumptions must be wrong. Likely candidates include the following: (i) the surfaces of all but the most sparsely cratered satellites are saturated or nearly saturated with impact craters; (ii) these satellites have rotated nonsynchronously over geological time; (iii) most of the craters are made not by heliocentric (Sun-orbiting) comets and asteroids but rather by planetocentric (planet-orbiting) debris of indeterminate origin; or (iv) pathological endogenic resurfacing has created illusions of structure. Callisto's surface is readily classified as nearly saturated. Ganymede's bright terrains, although less heavily cratered than those of Callisto, can also be explained by crater densities approaching saturation on a world where endogenic processes were active. The leading alternative is nonsynchronous rotation, an explanation supported by the distribution of catenae (crater chains produced by impact of tidally disrupted comets). Triton's craters can be explained by planetocentric debris or by capricious resurfacing, but both hypotheses are inherently improbable. |
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