4.3 MTP analysis with the precovery observations

By adding the precovery observations of 1939, the orbit determination becomes so accurate that the target plane uncertainty for the 2004 encounter is very much reduced. The semiaxes of the $\sigma =3$ ellipse are 240 and 1200 km; the semilinear boundary has a similar size, although its shape is distorted. This refers, however, to a portion of the MTP centered at the nominal miss distance of $4\,000$ km from the center of the Earth, that is well inside the Earth volume. Since the Earth surface is 2-dimensional, basically the same mathematical formalism described in Section 2.2 could be used to draw confidence boundaries of the impact point.