**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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## [8.02] Orbit Determination with Very Short Arcs: Preliminary Orbits and Identifications

*A. Milani, G.F. Gronchi, Z. Knezevic, M.E. Sansaturio (Department of Mathematics, University of Pisa)*

When the observation of a new asteroid are not enough to
compute an orbit we can represent them with an attributable
(two angles and their time derivatives). The undetermined
range and range rate span an *admissible region* of
solar system orbits, which can be represented by a set of
*Virtual Asteroids* (VAs) selected by an optimal
triangulation (see the presentation by G. Gronchi).

The four coordinates of the attributable are the result of a
fit and have a covariance matrix. Thus the predictions of
future observations have a quasi-product structure
(admissible region times confidence ellipsoid), approximated
by a triangulation with a confidence ellipsoid for each
node.

If we have >2 observations we can also estimate the
geodetic curvature and the acceleration of the observed path
on the celestial sphere. If both are significantly measured
they constrain the range and the range rate and may allow to
reduce the size of the admissible region.

To compute a a preliminary orbit starting from two
attributables, for each VA (selected in the admissible
region of the first arc) we consider the prediction at the
time of the second and its covariance matrix, and we compare
them with the attributable of the second arc with its
covariance. By using the identification penalty (as in the
algorithms for orbit identification) we can select as a
preliminary orbit the VAs which fits together both arcs in
the 8-dimensional space.

Two attributables may not be enough to compute an orbit with
convergent differential corrections. The preliminary orbit
is used in a constrained differential correction, providing
solutions along the *Line Of Variations*, to be used as
second generation VAs to predict the observations at the
time of a third arc. In general the identification with a
third arc ensures a well determined orbit.

The author(s) of this abstract have provided an email address
for comments about the abstract:
milani@dm.unipi.it

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Bulletin of the American Astronomical Society, **36** #2

© 2004. The American Astronomical Soceity.