numerical errors are larger in this second method.

-   The equations of motion are integrated backwards and forward in time for a period of, at least, $180$ minutes. In this first integration we ignore the perturbation forces.

-   The tidal forces and the zonal contribution to the perturbation are evaluated at the positions given by the zeroth-order keplerian approximation (the ideal hyperbolic orbit).

-   A new integration of the equations of motion is carried out with the perturbing forces evaluated in the previous step. This would be our first order approximation.

-   Subsequently, we evaluate the perturbation forces with the positions obtained in the $n$th-order approximation to obtain the position and velocities of the spacecraft in the $(n+1)$th-order approximation.

-   The algorithm stops when the differences among the $n$th-order and the $n+1$th-order approximation is below a given threshold.

We must also emphasize that computation was carried out with double precision to keep the accuracy of the model data throughout the evaluation of the predictions of the model. In the next section we will discuss the results obtained with the methods summarized here.

Evaluation of the residual acceleration at the perijove {#sec:3}
=======================================================

In this section we will discuss the analysis 