On Mercury’s past rotation, in light of its large craters

We have simulated in-orbit variations of the impact flux and spatial distributions of >100 km diameter (D) crater production for Mercury in its current 3:2 and hypothetical 2:1 and 1:1 spin–orbit resonances. Results show that impact fluxes and D > 100 km cratering are non-uniform for these rotational states when Mercury's orbit is significantly eccentric. Variations in the impact flux and D > 100 km cratering depend on the orbital elements of Mercury and its impactors. The observed spatial distribution of large Mercurian craters is difficult to generate by cratering in Mercury's current 3:2 spin–orbit resonance, but can be produced by cratering in a former 1:1 (as previously proposed by Wieczorek et al., 2012) or 2:1 spin–orbit resonance. We have calculated capture probabilities at spin–orbit resonances for a rigid Mercury. If Mercury's initial rotation was prograde, we find that a higher order spin–orbit resonance is the most likely first capture for feasible (low) values of Mercury's past triaxiality. In light of Mercury's crater record, we examined the possibility that impacts have initiated transitions in past spin–orbit resonances. Although the number of craters whose generating impact would have destabilized a spin–orbit resonance is sensitive to the crater scaling procedure, any initial rotational state of Mercury has likely been destabilized by impacts. An initial and permanent 3:2 spin–orbit resonance capture seems untenable. Mercury's tidal torque decelerates Mercury's rotation for the most likely range of Mercury's orbital eccentricity. Only one or two craters are candidate relics of an impact-event that facilitates an instantaneous transition from a former synchronous rotation to the 3:2 spin–orbit resonance, and only for a small crater scaling factor. We propose a rotational evolution trajectory for Mercury with visits to spin–orbit resonances of decreasing order including a substantial period in the 2:1 spin–orbit resonance, which can account for the observed spatial distribution of large craters.