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L.H. Wasserman (Lowell Obs.)
Orbital elements for KBOs are published by the Minor Planet Center once an object has been observed twice in a single apparition. Such orbits are typically derived from an observational arc that may only be one month long and can be as short as a day or two. Such a relatively short arc requires that at least some assumptions be made to obtain the elements -- typically that the orbit is circular or that the object was observed at perihelion or aphelion (the Väisälä assumption). Later observations will refine the elements and improve the accuracy of the orbital elements. But, some objects are never followed up, and are effectively lost -- their orbits are never improved. The MPC publishes orbits without any indication of the uncertainties in the elements. As a result, orbital elements for all KBOs have been included in published graphs and statistics as though they had zero error, even though some of the objects may have large but unknown errors in their elements.
We have investigated how our knowledge of KBO orbital elements: the semi-major axis, the eccentricity, and the inclination; as well as a derived quantity: the heliocentric distance at the time of discovery, improve with increasing observational arc using a monte--carlo method. KBO ``observations'' are generated using random KBO--like orbits. Orbital elements from these ``observations'' (with added noise) are calculated using both the ``traditional'' Väisälä method and the formalism of Bernstein and Khushalani (2000). The derived elements can then be compared with the known input elements to see how well the starting orbital parameters are recovered. Results derived from 400 ``test particles'' with orbital arcs of 2 hours, 30 days, 60 days, and 1 year will be presented. As a sanity check, we have also performed the same test on real KBO observations and find similar results.
\noindent This work is supported by NASA grants NAG5-8990 and NAG5-11058.
\noindent Reference:
\noindent Bernstein, G. and Khushalani, B. 2000, AJ, 120, 3323.
The author(s) of this abstract have provided an email address for comments about the abstract: lhw@lowell.edu