Linking Scarce Asteroid Astrometry At Discovery And Over Apparitions

Mathematics – Probability

Scientific paper

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Scientific paper

Currently about 10% of all asteroid astrometry reported to the Minor Planet Center (MPC) belong to single-night observation sets. Similarly, roughly 10-15% of the asteroids that have received a designation by the MPC have been observed only during one apparition. Due to the scarce astrometry, which leads to large ephemeris uncertainties, most of the underlying asteroids have essentially been lost. However, by linking a few of these scarce data sets, the underlying object can be recovered. Due to challenges such as short observational time spans, a small amount of observed positions, astrometric uncertainties, long linking intervals, parallax, and --- particularly in the future --- massive amounts of data, the linking task is highly non-trivial. We have developed novel linking methods capable of dealing with the challenges posed both by the short-term linking of single-night astrometry and by the long-term linking of single-apparition astrometry. The methods are based on statistical inversion of asteroid astrometry for the probability-density functions of the orbital elements. Through the use of dimensionality-reduction techniques and efficient data structures the methods scale as Ο(n log n), where n is the number of included observation sets. The methods are thus suitable for future large-scale surveys which anticipate a substantial increase in the astrometric data rate. We will present the methods and the key techniques used, with an emphasis on the new long-term linking method. We will also show results obtained for both simulated and real astrometry. The focus will be on the results obtained when searching for linkages among the tens of thousands of real observation sets spanning less than two days.

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