Analyzing a planet that crosses a small comet’s fragment chain

Abstract This article studies a planet whose orbit intersects the orbit of a small comet’s fragment chain. A simple, general, multi-generational model of comet fragmentation and fragment separation is developed, yielding the fragment distribution for each generation of the comet’s fragment chain. The fragment chain is used in analysis of the planet’s chain crossing and fragment capture. Simulating the chain crossing and fragment capture, the probability distributions for the chain crossing and fragment capture are calculated. The average probability for the planet crossing the fragment chain of a small, long period comet is 0.43 × 10− 3 per perihelion passage. The average probability for the planet crossing the fragment chain of a small, short period comet is 1.01 × 10− 3 per perihelion passage. For both, the average probability of fragment capture in chain crossing is 5.84 × 10− 2 per crossing. The probabilities calculated for the planet crossing a fragment chain and capturing fragments are higher than the planet-comet collision probability of the order of 10− 9 per perihelion passage for both the short period and long period comets, thus making chain crossing and fragment capture more probable planetary events.