FIG. 2.
The results of our moon simulations, plotted against different predictors. The lettered plot symbols identify Io, Europa, Ganymede, Callisto, and Titan by their first letter, and Enceladus is represented with an N. (a) The Liouville theorem prediction is represented by the black line. “A” is the cross-section area, “Fg” is focusing factor, and subscripts “m” and “p” indicate moon and planet, respectively. (b) A useful empirical correlation was observed between the moon-planet collision ratio and a combination of the moon and planet parameters. The x axis is the gravitational focusing factor of the moon divided by that of the planet, times the planet's Hill sphere radius divided by the square of the moon's semimajor axis. The black line is a fit to the points, with a slope of 4.8×109 and intercept 1.3×10−6.