Gravitational keyhole

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A gravitational keyhole is a tiny region of space where a planet's gravity would alter the orbit of a passing asteroid such that the asteroid would collide with that planet on a given future orbital pass. The word "keyhole" contrasts the large uncertainty of trajectory calculations (between the time of the observations of the asteroid and the first encounter with the planet) with the relatively narrow bundle(s) of critical trajectories. The term was coined by P. W. Chodas in 1999. It gained some public interest when it became clear, in January 2005, that the asteroid 99942 Apophis would miss the Earth in 2029 but may go through one or another keyhole leading to impacts in 2036 or 2037. Further research has since been done, however, which revealed the probability of Apophis passing through the keyhole was extremely low.^[1]

Keyholes for the nearer or further future are named by the numbers of orbital periods of the planet and the asteroid, respectively, between the two encounters (for example “7:6 resonance keyhole”). There are even more but smaller secondary keyholes, with trajectories including a less close intermediate encounter ("bank shots"). Secondary gravitational keyholes are searched for by importance sampling: virtual asteroid trajectories (or rather their ‘initial’ values at the time of the first encounter) are sampled according to their likelihood given the observations of the asteroid. Very few of these virtual asteroids are virtual impactors.