Lifetimes of small bodies in planetocentric (or heliocentric) orbits

Stray bodies orbiting a planet or the Sun are removed by collisions with larger objects or by expulsion from the system. However, their rate of removal generally cannot be described by the simple exponential law used to describe radioactive decay, because their effective half-life lengthens with time. Previous studies of planetesimals, comets, asteroids, meteorites, and impact ejecta from planets or satellites have fit the number of survivors S vs elapsed time t using exponential, logarithmic, and power laws, but no entirely satisfactory functional form has been found yet. Herein we model the removal rates of impact ejecta from various moons of Jupiter, Saturn, and Neptune. We find that most situations are fit best by stretched exponential decay, of the form S(t)=S(0)exp(−[t/t0]β). Here t0 is the time when the initial population has declined by a factor of e≈2.72, while the dimensionless exponent β lies between 0 and 1 (often near 1/3). The e-folding time S[dS/dt]−1 itself grows as the [1−β] power of t. This behavior is suggestive of a diffusion-like process.