  Using a shallow water model with time-dependent forcing we show that the peak
of an exoplanet thermal phase curve is, in general, offset from secondary
eclipse when the planet is rotating. That is, the planetary hot-spot is offset
from the point of maximal heating (the substellar point) and may lead or lag
the forcing; the extent and sign of the offset is a function of both the
rotation rate and orbital period of the planet. We also find that the system
reaches a steady-state in the reference frame of the moving forcing. The model
is an extension of the well studied Matsuno-Gill model into a full spherical
geometry and with a planetary-scale translating forcing representing the
insolation received on an exoplanet from a host star.
  The speed of the gravity waves in the model is shown to be a key metric in
evaluating the phase curve offset. If the velocity of the substellar point
(relative to the planet's surface) exceeds that of the gravity waves then the
hotspot will lag the substellar point, as might be expected by consideration of
forced gravity wave dynamics. However, when the substellar point is moving
slower than the internal wavespeed of the system the hottest point can lead the
passage of the forcing. We provide an interpretation of this result by
consideration of the Rossby and Kelvin wave dynamics as well as, in the very
slowly rotating case, a one-dimensional model that yields an analytic solution.
Finally, we consider the inverse problem of constraining planetary rotation
rate from an observed phase curve.
