Abstract
The uncertainty of the close approach distance of a Potentially Hazardous Object (PHO), either an asteroid or a comet, can be represented on the Modified Target Plane (MTP), a modification of the one used by Opik. The MTP is orthogonal to the geocentric velocity at the plosest approach along the nominal orbit, solution of the least square fit to the observations. The confidence regions of this solution in the 6-D space of orbital elements (for an epoch close to the observations) are well approximated by a family of concentric ellipsoids, if the observed arc is not too short. In the linear approximation these ellipsoids are mapped on the MTP into concentric ellipses, which can be computed by solving for the state transition matrix.
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