From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs
 Andrea Milani,
 Zoran Knežević
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Contemporary surveys provide a huge number of detections of small solar system bodies, mostly asteroids. Typically, the reported astrometry is not enough to compute an orbit and/or perform an identification with an already discovered object. The classical methods for preliminary orbit determination fail in such cases: a new approach is necessary. When the observations are not enough to compute an orbit we represent the data with an attributable (two angles and their time derivatives). The undetermined variables range and range rate span an admissible region of solar system orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by an optimal triangulation. The attributable results from a fit and has an uncertainty represented by a covariance matrix, thus the predictions of future observations can be described by a quasiproduct structure (admissible region times confidence ellipsoid), which can be approximated by a triangulation with each node surrounded by a confidence ellipsoid. The problem of identifying two independent short arcs of observations has been solved. For each VA in the admissible region of the first arc we consider prediction at the time of the second arc and the corresponding covariance matrix, and we compare them with the attributable of the second arc with its own covariance. By using the penalty (increase in the sum of squares, as in the algorithms for identification) we select the VAs which can fit together both arcs and compute a preliminary orbit. Even two attributables may not be enough to compute an orbit with a convergent differential corrections algorithm. The preliminary orbits are used as first guess for constrained differential corrections, providing solutions along the Line Of Variations (LOV) which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a least squares orbit, with uncertainty described by the covariance matrix.
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 Title
 From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs
 Journal

Celestial Mechanics and Dynamical Astronomy
Volume 92, Issue 13 , pp 118
 Cover Date
 20050401
 DOI
 10.1007/s1056900533147
 Print ISSN
 09232958
 Online ISSN
 15729478
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 asteroid recovery
 ephemerides
 orbit determination
 Industry Sectors
 Authors

 Andrea Milani ^{(1)}
 Zoran Knežević ^{(2)}
 Author Affiliations

 1. Department of Mathematics, University of Pisa, via Buonarroti 2, 56127, Pisa, Italy
 2. Astronomical Observatory, Volgina 7, Belgrade 74, 11160, Serbia and Montenegro