Accuracy of Estimation of the Probability of Asteroid Collision with the Earth Based on Linear Stochastic Modeling of Parametric Uncertainty

This paper investigates the accuracy of probabilistic estimates of asteroid impacts with the Earth obtained by mapping over time the initial orbital uncertainty modeled by linear stochastic methods based on observational material. The accuracy of the estimated probabilities is established in comparison with the probabilities obtained using nonlinear stochastic methods. The example of test asteroids shows how linear methods can be inadequate under certain observational circumstances when applied for probabilistic assessment if the nonlinearity is extremely strong. The discrepancy between linear and nonlinear probability estimates sometimes reaches one or two orders of magnitude. In addition, nonlinear probability estimates may be zero even with very significant linear estimates; in other words, in the real absence of the risk of an asteroid colliding with the Earth, linear estimates will falsely indicate the danger of a catastrophe.