On an efficient and accurate method to integrate restricted three-body orbits

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Abstract

view Abstract Citations (30) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On an Efficient and Accurate Method to Integrate Restricted Three-Body Orbits Murison, Marc A. Abstract This work is a quantitative analysis of the advantages of the Bulirsch-Stoer (1966) method, demonstrating that this method is certainly worth considering when working with small N dynamical systems. The results, qualitatively suspected by many users, are quantitatively confirmed as follows: (1) the Bulirsch-Stoer extrapolation method is very fast and moderately accurate; (2) regularization of the equations of motion stabilizes the error behavior of the method and is, of course, essential during close approaches; and (3) when applicable, a manifold-correction algorithm reduces numerical errors to the limits of machine accuracy. In addition, for the specific case of the restricted three-body problem, even a small eccentricity for the orbit of the primaries drastically affects the accuracy of integrations, whether regularized or not; the circular restricted problem integrates much more accurately. Publication: The Astronomical Journal Pub Date: May 1989 DOI: 10.1086/115089 Bibcode: 1989AJ.....97.1496M Keywords: Orbital Mechanics; Three Body Problem; Equations Of Motion; Error Analysis; Astrodynamics; CELESTIAL MECHANICS full text sources ADS |

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