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.
Multiple solutions in preliminary orbit determination from three observations
GRONCHI, GIOVANNI FEDERICO
2009-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
