Gravitational keyhole

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 the asteroid passing through the keyhole was extremely insignificant.

Keyholes for the nearer or farther 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.

Due to observational inaccuracies, bias in the frame of reference stars, and largely unknown non-gravitational forces on the asteroid, mainly the Yarkovsky effect, its position at the predicted time of encounter is uncertain in three dimensions. Typically, the region of probable positions is formed like a hair, thin and elongated, because visual observations yield 2-dimensional positions at the sky but no distances. If the region is not too extended, less than about one percent of the orbital radius, it may be represented as a 3-dimensional uncertainty ellipsoid and the orbits (ignoring the interaction) approximated as straight lines.

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