Asteroid Initial Orbit Computation Using Bayesian Probabilities

Details Asteroid Initial Orbit Computation Using Bayesian Probabilities Asteroid Initial Orbit Computation Using Bayesian Probabilities

Sep 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999dps....31.1201v&link_type=abstract

American Astronomical Society, DPS meeting #31, #12.01

Statistics

Computation

Scientific paper

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 OX4 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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