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

  • Alessandra Celletti
  • Gabriella Pinzari
Conference paper


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.


Orbital determination Gauss method Laplace method Mossotti method 


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  1. Celletti, A., Pinzari, G.: Four classical methods for determining planetary elliptic elements: a comparison. Celest. Mech. Dyn. Astr. 93(1), 1–52 (2005)CrossRefADSMathSciNetzbMATHGoogle Scholar
  2. Gallavotti, G.: Meccanica Elementare. P. Boringhieri (ed.), Torino, 2nd edn. pp. 498–516 (1980)Google Scholar
  3. Gauss, C.F.: Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections; Dover Publication. New York (1963)zbMATHGoogle Scholar
  4. Herrick, S. Jr.: On the Laplacian and Gaussian orbit methods. Astr. Soc. Pac. 49(287), 17–23 (1937)CrossRefADSGoogle Scholar
  5. Laplace, P.S.: Memoires de l’Académie Royale des Sciences de Paris. Coll. Works 10, 93–146 (1780)Google Scholar
  6. Milani, A., Gronchi, G.F., De’Michieli Vitturi, M., Knezevic, Z.: Orbit determination with very short arcs. I admissible regions. Celest. Mech. Dyn. Astr. 90(1–2), 57–85 (2004)CrossRefADSMathSciNetGoogle Scholar
  7. Milani, A., Gronchi, G.F., Knezevic, Z., Sansaturio, M.E., Arratia, O.: Orbit determination with very short arcs. Icarus 179(2), 350–374 (2005)CrossRefADSGoogle Scholar
  8. Milani, A., Knezevic, Z.: From astrometry to celestial mechanics: orbit determination with very short arcs. Celest. Mech. Dyn. Astr. 92(1–3), 1–18 (2005)CrossRefADSMathSciNetzbMATHGoogle Scholar
  9. Moulton, F.R.: Memoir on the theory of determining orbits. Astrono. J. iss. 661-662-663, 28, 103–124 (1914)CrossRefADSGoogle Scholar
  10. 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)Google Scholar
  11. Plummer, H.C.: An introductory treatise on dynamical astronomy. Cambridge University Press, Cambridge; Dover Publication, New York (1960)Google Scholar
  12. Poincare, H.: Sur la détermination des orbites par la méthode de Laplace. Bull. Astr. 23, 161–187 (1906)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Alessandra Celletti
    • 1
  • Gabriella Pinzari
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly
  2. 2.Dipartimento di MatematicaUniversità “Roma Tre”RomaItaly

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