of $5.2$ Astronomical Units from the Sun, the tidal effect is less important than in the case of Earth flybys [@Anderson2008]. As Io is the closest satellite it also gives the larger tides, despite it is not as massive as Ganymede or Callisto.

![The difference among the distance of the Juno spacecraft to the center of Jupiter in the ideal hyperbolic approximation and the prediction of the orbital model (including only the effect of the tidal forces). This difference is measured in km and time in minutes since the perijove.[]{data-label="fig3"}](Figure3.eps){width="\columnwidth"}

In Fig. \[fig3\] we have plotted the results for the orbital model incorporating only the effect of the tides from Io, Europa, Ganymede, Callisto and the Sun. We show that there is a reduction, in the correct direction according to Fig. \[fig1\], for the prediction of the radial coordinate of the spacecraft. However, this is not sufficient to provide a good fit of the discrepancies.

Results for the complete orbital model
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Our interest is now to implement the whole orbital model as defined in Sec. \[sec:2\]. In the first place, we have plotted the difference among the radial coordinate in the zeroth-order keplerian approximation and the data compared with 