  We show that changes in the orientation of the inner accretion disk of Cygnus
X-1 affect the shape of the broad Fe K$\alpha$ emission line emitted from this
object, in such a way that eV-level spectral resolution observations (such as
those that will be carried out by the {\it ASTRO-E2} satellite) can be used to
analyze the dynamics of the disk. We here present a potential diagnostic tool,
supported by numerical simulations, by which a few observations of Cygnus X-1,
separated in time, can determine whether its accretion disk actually precesses,
and if so, determine its period and precession angle. This approach could also
be used for similar studies in other microquasar systems.
