The orbits and physical parameters of three detached, double-lined A-F eclipsing binaries have been derived combining $H_{\rm P}, V_{\rm T}, B_{\rm T}$ photometry from the Hipparcos/Tycho mission with 8500-8750 Å ground-based spectroscopy, mimicking the photometric+spectroscopic observations that should be obtained by GAIA, the approved Cornerstone 6 mission by ESA. This study has two main objectives, namely ( a) to derive reasonable orbits for a number of new eclipsing binaries and ( b) to evaluate the expected performances by GAIA on eclipsing binaries and the accuracy achievable on the determination of fundamental stellar parameters like masses and radii. It is shown that a 1% precision in the basic stellar parameters can be achieved by GAIA on well observed detached eclipsing binaries provided that the spectroscopic observations are performed at high enough resolution. Other types of eclipsing binaries (including semi-detached and contact types) and different spectral types will be investigated in subseguent papers in this series.
