Orbit Determination with Topocentric Correction: Algorithms for the Next Generation Surveys

Given a set of astrometric observations assumed to belong to the same object, the problem of orbit determination is to compute the orbit with all the necessary tools to assess its uncertainty and reliability. Under the conditions of the next generation surveys, with much larger number density of observed objects, new algorithms, or at least substantial revisions of the classical ones, are needed. The problem has three main steps, preliminary orbit, least squares orbit, and quality control. The classical theory of preliminary orbit algorithms was incomplete, in that the consequences of the topocentric correction had not been fully studied. We show that it is possible to rigorously account for the topocentric correction, possibly with an increase in the number of alternate preliminary orbit solutions, without impairing the overall orbit determination

[1]  Giacomo Tommei,et al.  Multiple solutions for asteroid orbits: Computational procedure and applications , 2005 .

[2]  Andrea Milani,et al.  The Asteroid Identification Problem: I. Recovery of Lost Asteroids☆ , 1999 .

[3]  S. Chesley,et al.  The Asteroid Identification Problem IV: Attributions , 2001 .

[4]  Larry Denneau,et al.  Efficient intra- and inter-night linking of asteroid detections using kd-trees , 2007, astro-ph/0703475.

[5]  Andrea Milani,et al.  From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs , 2005 .

[6]  A. Milani,et al.  Orbit Determination with Very Short Arcs. II Identifications , 2005 .

[7]  New Definition of Discovery for Solar System Objects , 2007 .

[8]  G. Bernstein,et al.  Orbit Fitting and Uncertainties for Kuiper Belt Objects , 2000 .

[9]  C. Gauss.  Theory of the Motion of the Heavenly Bodies Moving About the Sun in Conic Sections , 1957 .

[10]  Second Note on Multiple Solutions in the Determination of Orbits from Three Observations , 1911 .

[11]  Andrea Milani.  Virtual asteroids and virtual impactors , 2004, Proceedings of the International Astronomical Union.

[12]  T. Teichmann,et al.  Fundamentals of celestial mechanics , 1963 .

[13]  M. Carpino,et al.  Error statistics of asteroid optical astrometric observations , 2003 .

[14]  Larry Denneau,et al.  Unbiased orbit determination for the next generation asteroid/comet surveys , 2005 .

[15]  Steven R. Chesley,et al.  The Asteroid Identification Problem: III. Proposing Identifications , 2000 .

[16]  B. G. Marsden,et al.  Initial orbit determination - The pragmatist's point of view , 1985 .

[17]  A. Celletti,et al.  Four Classical Methods for Determining Planetary Elliptic Elements: A Comparison , 2005 .

[18]  Giovanni B. Valsecchi,et al.  Low solar elongation searches for NEO: a deep sky test and its implications for survey strategies , 2006, Proceedings of the International Astronomical Union.

[19]  H. Plummer,et al.  An Introductory Treatise on Dynamical Astronomy , 1919 .

[20]  A. Milani,et al.  Orbit determination with very short arcs. I admissible regions , 2004 .

[21]  A. Celletti,et al.  Dependence on the observational time intervals and domain of convergence of orbital determination methods , 2006 .

[22]  Robert Jedicke,et al.  The next decade of Solar System discovery with Pan-STARRS , 2006, Proceedings of the International Astronomical Union.

[23]  Trails of solar system minor bodies on WFC/ACS images , 2004, astro-ph/0407164.

[24]  On Multiple Solutions in the Determination of Orbits from three Observations , 1910 .

[25]  J. Kubica,et al.  LSST: Comprehensive NEO detection, characterization, and orbits , 2006, Proceedings of the International Astronomical Union.

[26]  Dario Bini,et al.  Numerical computation of polynomial zeros by means of Aberth's method , 1996, Numerical Algorithms.