  We utilize the well-established properties of the solar gravitational lens
(SGL) to consider realistic observational scenarios. Actual exoplanets, which
may be the target of an SGL observational campaign, are not stationary. Their
appearance changes as a result of their diurnal rotation and varying
illumination due to their orbital motion around their host star. The nature of
the SGL is such that imaging with one telescope is accomplished with a cadence
of one pixel at a time, with substantial per-pixel integration times.
Therefore, capturing a single snapshot of the target planet with a
realistically-sized telescope is not possible. Instead, the planetary surface
must be reconstructed by inverting the combined effect of the SGL's
point-spread function and temporal changes induced by the planetary dynamics.
Using the Earth as a stand-in, we demonstrate practical feasibility of this
approach, by simulating a dynamical system and then recovering topographic
images of acceptable quality. The dynamics-induced temporal variability of the
exoplanet represents an added challenge, but even in the presence of such
dynamics, use of the SGL for exoplanet imaging remains feasible.
