  As a photon propagates along a null geodesic, the space-time curvature around
the geodesic distorts its wave function. We utilise the Fermi coordinates
adapted to a general null geodesic, and derive the equation for interaction
between the Riemann tensor and the photon wave function. The equation is solved
by being mapped to a time-dependent Schr\"odinger equation in $(2+1)$
dimensions. The results show that as a Gaussian time-bin wavepacket with a
narrow bandwidth travels over a null geodesic, it gains an extra phase that is
a function of the Riemann tensor evaluated and integrated over the propagation
trajectory. This extra phase is calculated for communication between satellites
around the Earth, and is shown to be measurable by current technology.
