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.
Due to observational inaccuracies, inaccuracies in the frame of reference stars, bias in the weighting of major observatories over smaller ones, 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.
Now imagine a plane comoving with the planet and perpendicular to the incoming velocity of the asteroid (unperturbed by the interaction).
According to Ernst Öpik's theory of close encounters, the set of points in the b-plane leading to a given resonance ratio forms a circle.
For a rapidly rotating planet such as the Earth, calculation of trajectories passing close to it, less than a dozen radii, should include the oblateness of the planet—its gravitational field is not spherically symmetric.
For a large asteroid (or comet) passing close to the Roche limit, its size, which is inferred from its magnitude, affects not only the Roche limit but also the trajectory because the center of gravitational force on the body deviates from its center of mass resulting in a higher-order tidal force shifting the keyhole.