  Europa's surface reflectance exhibits a pronounced hemispheric dichotomy,
which is hypothesized to form due to enhanced irradiation of the trailing
hemisphere by energetic particles entrained in the jovian magnetosphere. We
propose that this pattern can only persist if the timescale for discoloration
is much shorter than that of Europa's rotation relative to the synchronous
state, and provide a means for constraining the rotation rate using the
observed color pattern. By decomposing the longitudinal ultraviolet and visible
color variations from Voyager data into sine and cosine terms, we find no
detectable signature of non-synchronous rotation (NSR). This same conclusion is
reached with two observational models of discoloration: one representing an
actively discoloring surface, and the other assuming that the present-day
exogenic discoloration on the surface is in steady-state. Magnitudes of the
expected signature are presented as functions of the age of the crater Pwyll,
which is used to constrain the timescale of discoloration. Furthermore, we
develop a physical model of discoloration to validate the geometric models,
producing consistent results. The failure to identify a signature of NSR using
Europa's hemispheric color dichotomy magnifies the outstanding problem of the
origin of the stress to explain Europa's pervasive tectonic features.
