The linearized relative acceleration used to check the least squares fit of the 2012 DA14 observations was evaluated for a neighborhood centered on the Earth's position. One can derive the formula as follows,
GM is the gravitational constant for the Sun, XE the Earth's position relative to the Sun and X is the position relative to the Earth where one wants to evaluate the acceleration. Beyond 500 RE the error in the linear approximation is quite noticable. It might be better if one used the methods above to derive the linearized acceleration for a neighborhood about the position of the object at Xo.