  Atmospheres are not spatially homogeneous. This is particularly true for hot,
tidally locked exoplanets with large day-to-night temperature variations, which
can yield significant differences between the morning and evening terminators
-- known as limb asymmetry. Current transit observations with the James Webb
Space Telescope (JWST) are precise enough to disentangle the separate
contributions of these morning and evening limbs to the overall transmission
spectrum in certain circumstances. However, the signature of limb asymmetry in
a transit light curve is highly degenerate with uncertainty in the planet's
time of conjunction. This raises the question of how precisely transit times
must be measured to enable accurate studies of limb asymmetry, particularly
with JWST. Although this degeneracy has been discussed in the literature, a
general description of it has not been presented. In this work, we show how
this degeneracy results from apparent changes in the transit contact times when
the planetary disk has asymmetric limb sizes. We derive a general formula
relating the magnitude of limb asymmetry to the amount which it would cause the
apparent time of conjunction to vary, which can reach tens of seconds.
Comparing our formula to simulated observations, we find that numerical fitting
techniques add additional bias to the measured time, of generally less than a
second, resulting from the occultation geometry. We also derive an analytical
formula for this extra numerical bias. These formulae can be applied to
planning new observations or interpreting literature measurements, and we show
examples for commonly studied exoplanets.
