  During the 2014-2015 campaign of mutual events, we recorded ground-based
photometric observations of eclipses of Amalthea (JV) and, for the first time,
Thebe (JXIV) by the Galilean moons. We focused on estimating whether the
positioning accuracy of the inner satellites determined with photometry is
sufficient for dynamical studies. We observed two eclipses of Amalthea and one
of Thebe with the 1 m telescope at Pic du Midi Observatory using an IR filter
and a mask placed over the planetary image to avoid blooming features. A third
observation of Amalthea was taken at Saint-Sulpice Observatory with a 60 cm
telescope using a methane filter (890 nm) and a deep absorption band to
decrease the contrast between the planet and the satellites. After background
removal, we computed a differential aperture photometry to obtain the light
flux, and followed with an astrometric reduction. We provide astrometric
results with an external precision of 53 mas for the eclipse of Thebe, and 20
mas for that of Amalthea. These observation accuracies largely override
standard astrometric measurements. The (O-C)s for the eclipse of Thebe are 75
mas on the X-axis and 120 mas on the Y-axis. The (O-C)s for the total eclipses
of Amalthea are 95 mas and 22 mas, along the orbit, for two of the three
events. Taking into account the ratio of (O-C) to precision of the astrometric
results, we show a significant discrepancy with the theory established by
Avdyushev and Ban'shikova in 2008, and the JPL JUP 310 ephemeris.
