35th Meeting of the AAS Division on Dynamical Astronomy, April 2004
Session 8 Techniques
Oral, Friday, April 23, 2004, 9:30am-12:55pm,

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[8.01] Orbit Determination with Very Short Arcs: Admissible Regions

G.F. Gronchi, A. Milani, M. de'Michieli Vitturi (Department of Mathematics, University of Pisa), Z. Knezevic (Astronomical Observatory of Belgrade)

Contemporary observational surveys provide a huge number of detections of small solar system bodies, in particular of asteroids. These have to be reduced in real time in order to optimize the observational strategy and to select the targets for the follow-up and for the subsequent determination of an orbit.

Typically, reported astrometry consists of few positions over a short time span, and this information is often not enough to compute a preliminary orbit and perform an identification. Classical methods for preliminary orbit determination based on three observations fail in such cases, and a new approach is necessary to cope with the problem.

We introduce the concept of attributable, which is a vector composed by two angles and two angular velocities at a given time.

It is then shown that the missing values (geocentric range and range rate), necessary for the computation of an orbit, can be constrained to a compact set that we call admissible region (AR). The latter is defined on the basis of requirements that the body belongs to the solar system, that it is not a satellite of the Earth, and that it is not a "shooting star" (very close and very small).

A mathematical description of the AR is given, together with the proof of its topological properties: it turns out that the AR cannot have more than two connected components.

A sampling of the AR can be performed by means of a Delaunay triangulation. A finite number of six-parameter sets of initial conditions are thus defined, with each node of triangulation representing a Virtual Asteroid for which it is possible to propagate the corresponding orbit and to predict ephemerides.

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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.