**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.