Advertisement

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

  • Alessandra Celletti
  • Gabriella Pinzari
Original Article

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.

Keywords

Orbital determination Gauss method Laplace method Mossotti method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly
  2. 2.Dipartimento di MatematicaUniversità “Roma Tre”RomaItaly

Personalised recommendations