The discovery of Dark Energy and the fact that only about 5% of the
mass of the universe can be explained on the basis of the current laws
of physics have led to a serious impasse. Based on past history,
physics might indeed be on the verge of major discoveries; but the
challenge is enormous. The way to tackle it is twofold. On one side,
scientists try to perform large scale direct observations and
measurements -mostly from space. On the other, they multiply their
efforts to put to the most stringent tests ever the physical theories
underlying the current view of the physical world, from the very small
to the very large. On the extremely small scale very exciting results
are expected from one of the most impressive experiments in the
history of mankind: the Large Hadron Collider. On the very large
scale, the universe is dominated by gravity and the present impasse
undoubtedly calls for more powerful tests of General Relativity -the
best theory of gravity to date. Experiments testing the Weak
Equivalence Principle, on which General Relativity ultimately lies,
have the strongest probing power of them all; a breakthrough in
sensitivity by 4 orders of magnitude is possible with the "Galileo
Galilei" (GG) satellite experiment to fly in low Earth orbit. We
briefly report the results of the recent ASI Study of the GG mission
and the sensitivity of the GGG ("GG on the Ground") prototype under
development at the INFN laboratories in Pisa-San Piero a Grado.