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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Abstract

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 orbit determination, two--body problem Area01 - Scienze matematiche e informatiche > MAT/07 - Fisica matematica Dipartimenti (until 2012) > DIPARTIMENTO DI MATEMATICA "L. TONELLI" Dott. Giovanni Federico Gronchi 11 Oct 2010 20 Dec 2010 11:44 http://eprints.adm.unipi.it/id/eprint/747

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