Rare Event Sampling Improves Mercury Instability Statistics – Dorian Abbot (UChicago)

Due to the chaotic nature of planetary dynamics, there is a non-zero
probability that Mercury’s orbit will become unstable in the future.
Previous efforts have estimated the probability of this happening
between 3 and 5 billion years in the future using a large number of
direct numerical simulations with an N-body code, but were not able to
obtain accurate estimates before 3 billion years in the future because
Mercury instability events are too rare. We use a new rare-event
sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate
that the probability of a Mercury instability event in the next 2
billion years is approximately 10^−4 in the REBOUND N- body code. We
show that QDMC provides unbiased probability estimates at a
computational cost of up to 100 times less than direct numerical
simulation. QDMC is easy to implement and could be applied to many
problems in planetary dynamics in which it is necessary to estimate
the probability of a rare event.