**31st Annual Meeting of the DPS, October 1999**

*Session 12. Near Earth Asteroids Posters*

Poster Group I, Monday-Wednesday, October 11, 1999, , Kursaal Center
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## [12.01] Asteroid Initial Orbit Computation Using Bayesian Probabilities

*J. Virtanen, K. Muinonen (Univ. Helsinki)*

We consider initial orbit computation for near-Earth and
main-belt asteroids in the case of small numbers of
observations and short observational arcs. The a posteriori
probability density of the orbital elements can then be
highly complicated, and the covariance matrix of the linear
approximation fails to describe the true orbital
uncertainties. The recent results for asteroid 1998 OX_{4}
indicate that the straightforward application of linear
approximation has its risks and that the validity of the
approximation should always be checked beforehand. Instead,
we examine the phase space of the orbital elements
systematically and compute the rigorous, non-Gaussian a
posteriori probability density of the orbital elements. In
order to distinguish between realistic and unrealistic orbit
solutions, we incorporate (optionally) the three-dimensional
distribution of the semimajor axes, eccentricities, and
inclinations of all numbered asteroids as the a priori
probability density of the Bayesian technique. By using a
new Monte Carlo method, we study the a posteriori
probability density of several asteroids in the two-body
approximation. We can also account for planetary
perturbations with the many-body version of the method. For
each asteroid, we further compute the probability density of
the minimum orbital intersection distance to assess the
possibility of a close Earth-approach in the future. Our new
method allows us to check whether some of the
single-apparition main-belt asteroids can, in fact, be
near-Earth asteroids. Finally, our method can prove useful
in the linkage of two sets of (two or more) astrometric
observations. Application of the two-body method to asteroid
(719) Albert resulted in a set of possible orbits that allow
comparison to existing observations of asteroids.

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