the ideal hyperbolic keplerian solution as a crude approximation to the real trajectory. As shown in Fig. \[fig1\] the difference seems small, in the distance scale of Jupiter’s radius, but it is critical in our analysis of the trajectories.

Tidal forces
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It is convenient to consider separately the effect of tidal forces to compare its impact on the trajectory perturbations with that of the zonal harmonics. We will see that in the vicinity of the perijove the tidal contribution is small in relation to the effect of the multipole terms in the gravitational model of Jupiter. To visualize the magnitude of the different tidal forces we have plotted in Fig. \[fig2\] the magnitude of the tidal forces exerted by any of the Galilean satellites and, also, by the Sun.

![Tidal acceleration exerted upon the Juno spacecraft by (from top to bottom): Io, Ganymede, Europa, Callisto and the Sun. The tidal force per unit mass is measured in km$/$s$^2$ and time is given in seconds from the perijove. []{data-label="fig2"}](Figure2.eps){width="\columnwidth"}

Notice that the distance to the planet and the spacecraft during the flyby seems the most important factor on the determination of the magnitude of these forces. At an average distance 