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Asteroid close encounters characterization using differential algebra: the case of Apophis

Asteroid close encounters characterization using differential algebra: the case of Apophis
Asteroid close encounters characterization using differential algebra: the case of Apophis
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.
uncertainties propagation, monte carlo simulation, apophis close encounter, differential algebra
0923-2958
451-470
Armellin, R.
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Di Lizia, P.
0f45735c-5c72-418f-945d-a5688f10c71e
Bernelli-Zazzera, F.
93fc01c1-dc9e-4758-8cab-8b946e089e3d
Berz, M.
95c4e8a8-e1d9-4ad7-91c6-2832b7a1dd02
Armellin, R.
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Di Lizia, P.
0f45735c-5c72-418f-945d-a5688f10c71e
Bernelli-Zazzera, F.
93fc01c1-dc9e-4758-8cab-8b946e089e3d
Berz, M.
95c4e8a8-e1d9-4ad7-91c6-2832b7a1dd02

Armellin, R., Di Lizia, P., Bernelli-Zazzera, F. and Berz, M. (2010) Asteroid close encounters characterization using differential algebra: the case of Apophis. Journal of Celestial Mechanics and Dynamical Astronomy, 107 (4), 451-470. (doi:10.1007/s10569-010-9283-5).

Record type: Article

Abstract

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.

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More information

e-pub ahead of print date: 13 June 2010
Published date: 1 August 2010
Keywords: uncertainties propagation, monte carlo simulation, apophis close encounter, differential algebra
Organisations: Aeronautics, Astronautics & Comp. Eng

Identifiers

Local EPrints ID: 358465
URI: https://eprints.soton.ac.uk/id/eprint/358465
ISSN: 0923-2958
PURE UUID: 0711bda2-e6e3-4960-bceb-cf3e5dcc8e88

Catalogue record

Date deposited: 07 Oct 2013 11:09
Last modified: 16 Jul 2019 21:21

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Contributors

Author: R. Armellin
Author: P. Di Lizia
Author: F. Bernelli-Zazzera
Author: M. Berz

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