Cratering rates on synchronously rotating satellites

Kevin Zahnle and Paul Schenk

Impact cratering of synchronously-rotating satellites is expected to occur faster on the leading hemisphere than on the trailing hemisphere. This occurs because the satellite’s orbital velocity around the planet is generally large compared to the space velocities of comets and asteroids. The relationship between comets and moons is broadly akin to that between flies and windshields. As it is with cars, the predicted asymmetry is large, with cratering rates at the apex of motion (the center of the leading hemisphere) typically 30-80 times greater than at the antapex. However, the expected asymmetry is at best poorly expressed on actual satellites, with the alarming exception of Triton, where the observed asymmetry is apparently too great. The failure to observe the seemingly inevitable suggests that some of these satellites have led, and may still be leading, interesting lives.

This study used a suite of Monte Carlo simulations to better determine how cratering rates vary across the surfaces of synchronous satellites. The method generates orbits randomly from ancestral distributions that arguably are isotropic, or nearly so; assign to each orbit an impact probability and to each a possible impact site and appropriate crater diameter; while also allowing practical treatment of many effects that would be dauntingly difficult to treat analytically. An empirical fit to the suite of numerical experiments is that the cratering rate

,

where refers to the circular orbital velocity of the satellite and refers to the characteristic encounter velocity of the ecliptic comet with the planet; the angle b is the angular distance measured from the apex of motion; and the parameter g is the power law exponent describing the assumed cumulative size distribution of the impactors, , where d is diameter. The expression works well for 1<g<4; real solar system populations typically have 1.5<g<3.

As noted above, the predicted cratering asymmetries are not seen in fact. Most synchronous satellites are effectively saturated with impact craters, for which no signature of a leading/trailing cratering asymmetry is to be expected. The three interesting exceptions are Ganymede and Europa, moons of Jupiter, and Triton, chief moon of Neptune. Europa has few impact craters and no obvious leading/trailing asymmetry. But this is not surprising, because Europa’s icy shell is decoupled from the interior by a liquid water ocean: it would be relatively easy for the shell to rotate nonsynchronously. Ganymede is a more interesting case. Careful analysis reveals that Ganymede does preserve a fourfold asymmetry between fore and aft. This is much less than the 60-fold asymmetry expected but in the right direction; a possible interpretation is that Ganymede once rotated nonsynchronously but does so no longer. This in turn implicates a once thicker liquid water ocean for Ganymede, a conclusion in harmony with other clues that Ganymede was once much more like Europa than it is now.

Finally, there is Triton. Triton revolves in a retrograde orbit around Neptune. It appears to be a captured comet that melted as its orbit tidally evolved from a highly eccentric ellipse to a circle. Triton has very few craters. Its surface is obviously geologically young, probably no older than Europa’s. Essentially all of its impact craters are on its leading hemisphere. In particular, a lack of craters near b=90° appears to be real, as this region (facing Neptune) was the part of Triton seen best by the Voyager 2 spacecraft. This cratering pattern is too asymmetric to be accounted for by comets or other objects that orbit the sun. Required rather are objects in prograde orbit around Neptune. Such objects would strike Triton mostly head-on, and the resulting craters would be mostly confined to the leading hemisphere. The origin of the implied swarm of prograde, Neptune-orbiting debris is an open question. The alternative explanation is that Triton has been capriciously resurfaced so as to look to us, from the one viewpoint of the Voyager 2, as if it had run face-first into a swarm of debris.