Orbit Fitting and Uncertainties for Kuiper Belt Objects

We present a procedure for determination of positions and orbital elements,and associated uncertainties, of outer Solar System planets. The orbit-fittingprocedure is greatly streamlined compared to traditional methods becauseacceleration can be treated as a perturbation to the inertial motion of thebody. These techniques are immediately applicable to Kuiper Belt Objects, forwhich recovery observations are costly. Our methods produce positionalestimates and uncertainty ellipses even in the face of the substantialdegeneracies of short-arc orbit fits; the sole a priori assumption is that theorbit should be bound or nearly so. We use these orbit-fitting techniques toderive a strategy for determining Kuiper Belt orbits with a minimal number ofobservations.