Multiple solutions in preliminary orbit determination from three observations

Details Multiple solutions in preliminary orbit determination from three observations Multiple solutions in preliminary orbit determination from three observations

Apr 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cemda.103..301g&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 103, Issue 4, pp.301-326

Astronomy and Astrophysics

Astronomy

5

Orbit Determination, Two-Body Problem, Charlier'S Limiting Curve, Multiple Solutions In Laplace'S Method

Scientific paper

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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