How selection and weighting of astrometric observations influence the impact probability. Asteroid (99942) Apophis case

The aim is to show that in case of low probability of asteroid collision with Earth, the appropriate selection and weighing of the data are crucial for the impact investigation, and to analyze the impact possibilities using extensive numerical simulations. By means of the Monte Carlo special method a large number of clone'' orbits have been generated. A full range of orbital elements in the 6-dimensional parameter space, e.g. in the entire confidence region allowed by the observational material has been examined. On the basis of 1000 astrometric observations of (99942) Apophis, the best solution for the geocentric encounter distance of 6.065\pm 0.081 R_{Earth} were derived for the close encounter with the Earth on April 13, 2029. The present uncertainties allow for the special configurations (keyholes’') during these encounter which may lead to the very close encounters in the future approaches of Apophis. Two groups of keyholes are connected with the close encounter with the Earth in 2036 (within the minimal distance of 5.7736-5.7763 R_{Earth} on April 13, 2029) and 2037 (within the minimal distance of 6.3359-6.3488 R_{Earth}). The nominal orbits for our most accurate models run almost exactly in the middle between these two impact keyhole groups. A very small keyhole for the impact in 2076 has been found between these groups at the minimal distance of 5.97347 R_{Earth} (close to the nominal orbit).