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The light curves of mutual eclipses and occultations between the natural satellites of a planet allow us to obtain high-precision position and relative motion from differential photometry, enough to detect weak orbital disturbing forces, such as tidal forces. The observations are made during the equinoxes of the planet.We studied 25 light curves observed in Brazil during the 2009 campaign of the Galilean satellites’ mutual phenomena. A narrow-band filter centred at 890 nm was used, strongly attenuating the Jupiter's scattered light. We fitted the occultation and eclipse light curves using semi-analytical models that take into account the gradual decrease of light over the shadow, the solar limb darkening and the solar phase angle. The Oren–Nayar reflexive model was used to map the inhomogeneous light scattering on the surface of the satellites. For the first time it is used in a work about mutual events. Here, we include the study that made us decide for this model.We measured the impact parameter, relative velocity and central instant with average precisions of 7.46 km (2.2 mas), 0.08 km s−1 (0.02 mas s−1) and 0.42 s (6.13 km), respectively. The fit precision of the normalized light-curve fluxes ranged between 0.4 and 4.4 per cent. [ABSTRACT FROM AUTHOR]