A fast method for estimation of the impact probability of near-Earth objects

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Abstract
We propose a new fast method for estimation of the impact probability of near-Earth objects (NEOs), based on the assumption that the errors in coordinates and velocities have a normal distribution at all times. In this method, a unique coordinate system associated with the nominal orbit of an asteroid is used. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. This system allows one to take into account the distribution of virtual asteroids mainly along the nominal asteroid orbit. The probability is calculated as a six-dimensional integral of the probability density functions of coordinates and velocity errors. This method has a limitation on usage due to this assumption. Close approaches to massive bodies can break the normal distribution of virtual asteroids and disturb the impact probability value. The impact probabilities for eight asteroids have been calculated by the proposed method. A comparison of these values with probabilities obtained by the Monte Carlo method shows good agreement for seven of them. For 2007 VK184, which has three close approaches to major planets, the impact probability obtained by the new method differs by about five times, but the proposed method takes several orders of magnitude fewer computation time than the Monte Carlo one. Also, we have demonstrated the advantage of using a curvilinear coordinate system in comparison with a Cartesian one.