A Reality Check For the Tracking Fit

The least squares fit for the tracking polynomial was in very good agreement with the observations but there was some disagreement between the gravitational acceleration and the fit acceleration. An examination of the eigenvalues for the matrix, Σ, revealed that there were some directions which were insensitive to changes.

These directions were used to adjust the fit to bring the two accelerations into better agreement. At the distances involved a linear approximation could be made to relative acceleration of 2012 DA14 to the Earth and a new set of polynomial coefficients was computed. An average value for the direction of the Sun, e_S, was used. I in the expression is the 3D identity matrix.

The relative deviation between the two accelerations was much smaller and the time at which the error was a minimum was used to compute a position and velocity for 2012 DA14.

These values for position and velocity could be used to compute the path of the asteroid and get the details of the close approach.

Some accuracy for the fit was sacrificed to produce a better correspondence with reality.