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''Galileo Galilei'' (GG) is a small mission currently under study by eight research institutions in Italy with approval and funding by the Italian national space agency ASI (Agenzia Spaziale Italiana). The mission concerns a small, low altitude, Earth satellite (less than or similar to 150 kg total mass and 520 km altitude) with two objectives. One is scientific, in the field of fundamental physics, and the other technological in the frame of spacecraft propulsion and drag compensation. The scientific goal is to test a fundamental principle of modern physics-the Equivalence Principle (EP) formulated by Einstein generalizing Galileo's and Newton's work-to 1 part in 10(16), four orders of magnitude better than the best ground results. The technological goal is a full, comprehensive test of FEEP (Field Emission Electric Propulsion) thrusters for accurate drag compensation. FEEPs have been invented, designed and developed by ESA (European Space Agency) in Europe and will most probably become an essential component of all space experiments which require measurement of small forces. The GG satellite is stabilized by single axis rotation at 5 Hz, it carries two concentric cylindrical test bodies (10 kg each) made of different materials and whose relative displacements are measured by capacitive sensors to detect an EP violation. Rotation in supercritical conditions and absence of weight are exploited for self-centering the test bodies and reducing the vibrational perturbations. The experiment is noncryogenic and temperature stability is ensured by passive insulation only. The very small mass, low Earth orbit, passive one axis stabilization, loose constraints for …