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Multiple Solutions in Preliminary Orbit Determination from Three Observations

Gronchi, Giovanni Federico (2009) Multiple Solutions in Preliminary Orbit Determination from Three Observations. Celestial Mechanics and Dynamical Astronomy, 103 (4). pp. 301-326. ISSN 1572-9478

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    SUMMARY Charlier's theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace's method of preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized theory works for both Laplace's and Gauss' methods. We also provide a geometric definition of a curve that generalizes Charlier's limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier's: they may change according to the value of a parameter that depends on the observations.

    Item Type: Article
    Uncontrolled Keywords: orbit determination, two--body problem
    Subjects: Area01 - Scienze matematiche e informatiche > MAT/07 - Fisica matematica
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI MATEMATICA "L. TONELLI"
    Depositing User: Dott. Giovanni Federico Gronchi
    Date Deposited: 11 Oct 2010
    Last Modified: 20 Dec 2010 11:44
    URI: http://eprints.adm.unipi.it/id/eprint/747

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