  Quantum interference arising from superposition of states is a striking
evidence of the validity of Quantum Mechanics, confirmed in many experiments
and also exploited in applications. However, as for any scientific theory,
Quantum Mechanics is valid within the limits in which it has been
experimentally verified. In order to extend such limits, it is necessary to
observe quantum interference in unexplored conditions such as moving terminals
at large distance in Space. Here we experimentally demonstrate single photon
interference at a ground station due to the coherent superposition of two
temporal modes reflected by a rapidly moving satellite thousand kilometers
away. The relative speed of the satellite induces a varying modulation in the
interference pattern. The measurement of the satellite distance in real time by
laser ranging allowed us to precisely predict the instantaneous value of the
interference phase. We then observed the interference patterns with visibility
up to $67\%$ with three different satellites and with path length up to 5000
km. Our results attest the viability of photon temporal modes for fundamental
tests of Physics and Quantum Communications in Space.
