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Dependence on the observational time intervals and domain of convergence of orbital determination methods

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Abstract

In the framework of the orbital determination methods, we study some properties related to the algorithms developed by Gauss, Laplace and Mossotti. In particular, we investigate the dependence of such methods upon the size of the intervals between successive observations, encompassing also the case of two nearby observations performed within the same night. Moreover we study the convergence of Gauss algorithm by computing the maximal eigenvalue of the jacobian matrix associated to the Gauss map. Applications to asteroids and Kuiper belt objects are considered.

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References

  • Celletti A., Pinzari G. (2005) Four classical methods for determining planetary elliptic elements: a comparison. Celest. Mech. Dyn. Astr. 93(1): 1–52

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Gallavotti, G. Meccanica Elementare. P. Boringhieri (ed.), Torino, 2nd edn. pp. 498–516 (1980)

  • Gauss C.F. (1963) Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections. Dover Publication, New York

    MATH  Google Scholar 

  • Herrick S. Jr. (1937) On the Laplacian and Gaussian orbit methods. Astr. Soc. Pac. 49(287): 17–23

    Article  ADS  Google Scholar 

  • Laplace P.S. (1780) Memoires de l’Académie Royale des Sciences de Paris. Coll. Works 10, 93–146

    Google Scholar 

  • Milani A., Gronchi G.F., De’ Michieli Vitturi M., Knezevic Z. (2004) Orbit determination with very short arcs. I admissible regions. Celest. Mech. Dyn. Astr. 90(1–2): 57–85

    Article  MathSciNet  ADS  Google Scholar 

  • Milani A., Gronchi G.F., Knezevic Z., Sansaturio M.E., Arratia O. (2005) Orbit determination with very short arcs. Icarus 179(2): 350–374

    Article  ADS  Google Scholar 

  • Milani A., Knezevic Z. (2005) From astrometry to celestial mechanics: orbit determination with very short arcs. Celest. Mech. Dyn. Astr. 92(1–3): 1–18

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Moulton F.R. (1914) Memoir on the theory of determining orbits. Astrono. J. iss. 661-662-663, 28, 103–124

    Google Scholar 

  • Mossotti, O.F. Sopra la Determinazione delle Orbite dei Corpi Celesti per Mezzo di Tre Osservazioni, Scritti. Pisa, Domus Galileana, original version: Memoria Postuma (1942)

  • Plummer, H.C. An introductory treatise on dynamical astronomy. Cambridge University Press, Cambridge; Dover Publication, New York (1960)

  • Poincare H. (1906) Sur la détermination des orbites par la méthode de Laplace. Bull. Astr. 23, 161–187

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133, Roma, Italy

    Alessandra Celletti

  2. Dipartimento di Matematica, Università “Roma Tre”, Largo S. L. Murialdo 1, I-00146, Roma, Italy

    Gabriella Pinzari

Authors
  1. Alessandra Celletti
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  2. Gabriella Pinzari
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Correspondence to Gabriella Pinzari.

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Celletti, A., Pinzari, G. Dependence on the observational time intervals and domain of convergence of orbital determination methods. Celestial Mech Dyn Astr 95, 327–344 (2006). https://doi.org/10.1007/s10569-006-9022-0

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  • DOI: https://doi.org/10.1007/s10569-006-9022-0

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