Orbit determination with the twobody integrals. II
Abstract
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 et al. (Celest. Mech. Dyn. Astron. 107(3):299318, 2010), where the angular momentum and the energy integrals were used. The use of a suitable component of the LaplaceLenz 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.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 July 2011
 DOI:
 10.1007/s105690119357z
 arXiv:
 arXiv:1101.4569
 Bibcode:
 2011CeMDA.110..257G
 Keywords:

 Orbit determination;
 Kepler problem;
 Polynomial equations;
 LaplaceLenz vector;
 Linkage;
 Attributables;
 Mathematical Physics;
 Physics  Classical Physics
 EPrint:
 15 pages, 4 figures