Four Classical Methods for Determining Planetary Elliptic Elements: A Comparison |
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| Authors: | Alessandra Celletti Gabriella Pinzari |
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| Institution: | (1) Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy;(2) Dipartimento di Matematica, Università “Roma Tre”, Largo S. L. Murialdo 1, I-00146 Roma, Italy |
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| Abstract: | The discovery of the asteroid Ceres by Piazzi in 1801 motivated the development of a mathematical technique proposed by Gauss,
(Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, 1963) which allows to recover the orbit
of a celestial body starting from a minimum of three observations. Here we compare the method proposed by Gauss (Theory of
the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, New York, 1963) with the techniques (based on three
observations) developed by Laplace (Collected Works 10, 93–146, 1780) and by Mossotti (Memoria Postuma, 1866). We also consider
another method developed by Mossotti (Nuova analisi del problema di determinare le orbite dei corpi celesti, 1816–1818), based
on four observations. We provide a theoretical and numerical comparison among the different procedures. As an application,
we consider the computation of the orbit of the asteroid Juno. |
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| Keywords: | Gauss’ method Laplace’ s method Mossotti’ s method orbit determination |
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