  Tests of the Weak Equivalence Principle can reveal a new, composition
dependent, force of nature or disprove many models of new physics. For the
first time such a test is successfully carried out in space by the MICROSCOPE
satellite. Early results show no violation sourced by the Earth for Pt and Ti
test masses with random errors (after 8.26d of integration time) of about 1
part in 1e14, and similar systematic errors.It improves by 10 times over the
best ground tests with rotating torsion balances despite 70 times less
sensitivity to differential accelerations, thanks to the much stronger driving
signal in orbit. The test is limited by thermal noise from internal damping in
the gold wires used for electrical grounding. This noise was shown to decrease
when the s/c was set to rotate faster than planned. The result will improve by
the end of the mission, as thermal noise decreases with more data. Not so
systematic errors. We investigate major non-gravitational effects and find that
the Pt-Pt sensor does not allow their separation from the signal. The early
test reports an upper limit of systematic errors in the Pt-Ti sensor which are
not detected in the Pt-Pt one, hence would not be distinguished from a
violation. Once all the integration time is used to reduce random noise there
will be no time left to check systematics. MICROSCOPE demonstrates the huge
potential of space for WEP tests of very high precision and indicates how to
reach it. To realize the potential, a new experiment needs the spacecraft to be
in rapid, stable rotation around the symmetry axis, needs high quality
state-of-the-art mechanical suspensions, and must allow systematic checks. The
design of the "Galileo Galilei" (GG) experiment, aiming to test the WEP to 1
part in 1e17 unites all the needed features, indicating that a quantum leap in
space is possible provided the new experiment heeds the lessons of MICROSCOPE.
