caa a22 4500 445863498 CHVBK 20180317145450.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10569-011-9357-z doi (NATIONALLICENCE)springer-10.1007/s10569-011-9357-z Orbit determination with the two-body integrals. II [Elektronische Daten] [G. Gronchi, D. Farnocchia, L. Dimare] The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or by radar observations. We write polynomial equations for this problem, which can be solved using the powerful tools of computational Algebra. An algorithm to decide if the linkage of two short arcs is successful, i.e. if they belong to the same observed body, is proposed and tested numerically. This paper continues the research started in Gronchi etal. (Celest. Mech. Dyn. Astron. 107(3):299-318, 2010), where the angular momentum and the energy integrals were used. The use of a suitable component of the Laplace-Lenz vector in place of the energy turns out to be convenient, in fact the degree of the resulting system is reduced to less than half. Springer Science+Business Media B.V., 2011 Orbit determination nationallicence Kepler problem nationallicence Polynomial equations nationallicence Laplace-Lenz vector nationallicence Linkage nationallicence Attributables nationallicence Gronchi G. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, Pisa, Italy aut Farnocchia D. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, Pisa, Italy aut Dimare L. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, Pisa, Italy aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/3(2011-07-01), 257-270 0923-2958 110:3<257 2011 110 10569 https://doi.org/10.1007/s10569-011-9357-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-011-9357-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gronchi G. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, Pisa, Italy aut NATIONALLICENCE 700 1- Farnocchia D. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, Pisa, Italy aut NATIONALLICENCE 700 1- Dimare L. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, Pisa, Italy aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/3(2011-07-01), 257-270 0923-2958 110:3<257 2011 110 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445863498 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer