Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cemda.107..451a&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 107, Issue 4, pp.451-470
Astronomy and Astrophysics
Astronomy
1
Uncertainties Propagation, Monte Carlo Simulation, Apophis Close Encounter, Differential Algebra
Scientific paper
A 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.
Armellin Roberto
Bernelli-Zazzera Franco
Berz M.
di Lizia Pierluigi
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