Asteroid Close Encounters Characterization using Diffferential Algebra: the Case of Apophis
AbstractA method for the nonlinear propagation of uncertainties in Celestial Mechanics based
on differential algebra is presented. The arbitrary order Taylor expansion of the flow of ordinary
differential equations with respect to the initial condition delivered by differential algebra is exploited
to implement an accurate and computationally efficient Monte Carlo algorithm, in which
thousands of pointwise integrations are substituted by polynomial evaluations. The algorithm
is applied to study the close encounter of asteroid Apophis with our planet in 2029. To this
aim, we first compute the high order Taylor expansion of Apophis' close encounter distance from
the Earth by means of map inversion and composition; then we run the proposed Monte Carlo
algorithm to perform the statistical analysis.
R. Armellin, P. Di Lizia, F. Bernelli-Zazzera, M. Berz,
Celestial Mechanics and Dynamical Astronomy, 107,4 (2010) 451-470
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