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L.H. Wasserman (Lowell Observatory)
The discovery arc of a KBO can be very short, perhaps only a few hours, and determined by only two observations. We are then faced with the problem of recovering the object in a later lunation, one, two, or perhaps, three months later. Predicting a future position based on a short arc is done using the method of Väisälä (1939) or a recent method derived by Bernstein and Kushalani (2000) (hence, BK). The Väisälä method only requires two observations, but in order to derive the six orbital elements, the method assumes that the object was discovered at perihelion. In addition, an assumed distance to the object must be provided. For a given object, there is a range of distances which give ``reasonable'' orbital elements for the object and hence, a range of predicted positions in the sky at some future time. Since the semi-major axis (a) and eccentricity ( e) are correlated, the range of orbital elements runs from small e, small a to large e, large a solutions. In contrast, for short-arc objects, the BK method yields a Väisälä-like orbit but always gives a solution with small eccentricity. The question then arises: Are we better off using a Väisälä solution taken from the middle of the range of solutions than the BK solution which might be biased to one side of the range of possible solutions?
We have investigated this question using Monte-Carlo generated KBO orbits. We find that it does not matter (at least up to two months after the intial observation) which method one uses for a prediction -- the scatter about the ''true'' position of the object is very similar for both methods. We also find that the Bernstein formalism gives a good approximation to the one-sigma sky-plane error, provided that one's estimate of the astrometric errors (which are input to the Bernstein method) are correct.
This work is supported by NASA grants NAG5-11058 and NAG5-8990.
References:
Bernstein, G. and Khushalani, B. 2000, AJ,
120, 3323
Väisälä, Y. 1939, Inforno Astron.-Opt. Inst. Turku Univ., No. 1
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Bulletin of the American Astronomical Society, 34, #3< br> © 2002. The American Astronomical Soceity.