we will discuss some possible sources of error that could explain the discrepancy among the trajectory fitted by the Juno’s team and the orbital model proposed in this paper. And, in particular, the perturbing acceleration whose components in spherical coordinates are plotted in Figs. \[fig6\]-\[fig8\].

![The difference (in meters) between the radial coordinate for the second and the third iteration of the Picard’s method discussed in the text. Time is measured in minutes from the closes approach to Jupiter in the first Juno’s flyby.[]{data-label="fig9"}](Figure9.eps){width="\columnwidth"}

In Fig. \[fig9\] we have shown the difference among the second and the third iteration of the Picard’s method applied to the solution of the equations of motion Eq. (\[eqmotionr\])-(\[eqmotionv\]) that, for a period of fifty minutes around the perigee, is of the order of $10$ meters and, consequently, three orders of magnitude below the differences of the second iteration and the JPL’s fitting as shown in Fig. \[fig5\]. So, we can be confident that the convergence of the method is very fast for our problem and the results are reliable.

Another question is the accuracy of the ephemeris of the moons of Jupiter. Since the beginning of radar astronomy the precision of these measurements has 