Multiple solutions in preliminary orbit determination from three observations |
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| Authors: | Giovanni Federico Gronchi |
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| Institution: | (1) Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, Pisa, Italy |
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| Abstract: | 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. |
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| Keywords: | Orbit determination Two-body problem Charlier’ s limiting curve Multiple solutions in Laplace’ s method |
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