4.2 MTP analysis with the 1992-93 observations

Using all 58 observations up to March 1993, the least squares fit residuals have an RMS of 0.62 arc seconds, but the orbit determination is of course much improved: the conditioning number of the covariance matrix is $7\times 10^5$, with a largest eigenvalue $\sigma_1^2=2.9\times 10^{-9}$. Thus the confidence ellipsoid is roughly comparable to that of 1997 XF₁₁ as discussed in Section 3.1. Propagation of the nominal orbit results in a much deeper close approach in 2004, at a nominal distance of $0.001\,55$ AU, taking place on September 29. The $\sigma =3$ linear confidence ellipse on the MTP is now much smaller, with semiaxes of 190 km and 0.01 AU. The long axis is still much longer than the nominal miss distance, and the angle between the long axis and the center of the Earth direction is slightly increased to $0.^\circ 9$: now the linear confidence boundary includes a good portion of the Earth cross section, and this is confirmed by the semilinear boundary.

By the same procedure used in Section 3.3, we have superimposed on the MTP of the solution including only the early observations also the semilinear confidence boundary of the solution with all the 1992-93 observations. Again the semilinear confidence boundary with more data is almost entirely contained in the semilinear confidence boundary with less data. This condition is not fulfilled by the linear approximations: the linear ellipse with more data is entirely outside the linear ellipse with less data described in the previous Subsection.