  Gedankenexperiments have consistently played a major role in the development
of quantum theory. A paradigmatic example is Wheeler's delayed-choice
experiment, a wave-particle duality test that cannot be fully understood using
only classical concepts. Here, we implement Wheeler's idea along a
satellite-ground interferometer which extends for thousands of kilometers in
Space. We exploit temporal and polarization degrees of freedom of photons
reflected by a fast moving satellite equipped with retro-reflecting mirrors. We
observed the complementary wave-like or particle-like behaviors at the ground
station by choosing the measurement apparatus while the photons are propagating
from the satellite to the ground. Our results confirm quantum mechanical
predictions, demonstrating the need of the dual wave-particle interpretation,
at this unprecedented scale. Our work paves the way for novel applications of
quantum mechanics in Space links involving multiple photon degrees of freedom.
