This research aims at modeling the trajectory followed by the Galileo spacecraft during a variety of flybys about the Galilean moons. The chosen flybys have good Earth’s elevation angles and either low or high closest-approach altitudes, so that the comparison of the two can give relevant insight into the accuracy of the corresponding trajectories. By propagating the state of the spacecraft during these flybys, optimizing the nominal initial state of the spacecraft (obtained through the SPICE program) and the spherical harmonics of the moons, and estimating new harmonics, the minimum root mean square error between the resulting trajectory and the ephemerides by Jet Propulsion Laboratory (JPL) is found. The analysis of its components along the Local Orbital axes gives insight into the existing relation between them and the Earth's elevation and azimuth angles. In particular, a low-altitude flyby implies in general a higher error, but when two flybys have similar altitudes, then the Earth's elevation plays a relevant role and the flyby with the largest one is more likely to have a larger error too. The root mean square error of the fitted trajectories can vary from 15 cm to 7 m, so always less than the 9 m declared by National Aeronautics and Space Administration (NASA) as the maximum error of the moons ephemerides. Furthermore, the flybys about Ganymede and Callisto show a high error in the along-track and cross-track directions, since the radius of their sphere of influence is quite larger than that of the inner moons' ones, hence there is more time for the perturbations to influence the orbit. A by-product of this research is the estimate of the Galilean moons' gravity field, in particular the new values for their J2 and C2,2 coefficients led to the conclusion that Io is less hydrostatic, while Europa and Callisto are more hydrostatic than previously thought.