Celestial Mechanics and Dynamical Astronomy

, Volume 103, Issue 4, pp 301–326

Multiple solutions in preliminary orbit determination from three observations

Original Article

DOI: 10.1007/s10569-009-9201-x

Cite this article as:
Gronchi, G.F. Celest Mech Dyn Astr (2009) 103: 301. doi:10.1007/s10569-009-9201-x


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.


Orbit determination Two-body problem Charlier’s limiting curve Multiple solutions in Laplace’s method 

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

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