Orbit determination with the two-body integrals. II

G. F. Gronchi (1) , D. Farnocchia (1) , L. Dimare (1)

1 Dipartimento di Matematica

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 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 et al. (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.

Mots clés: Orbit determination; Kepler problem; Polynomial equations; Laplace-Lenz vector; Linkage; Attributables

G. F. Gronchi, D. Farnocchia, L. Dimare. Orbit determination with the two-body integrals. II. Celestial Mechanics and Dynamical Astronomy, 2011, 110 (3), pp.257-270. ⟨10.1007/s10569-011-9357-z⟩. ⟨hal-00653185⟩