  The population of known extrasolar planets includes giant and terrestrial
planets that closely orbit their host star. Such planets experience significant
tidal distortions that can force the planet into synchronous rotation. The
combined effects of tidal deformation and centripetal acceleration induces
significant asphericity in the shape of these planets, compared to the mild
oblateness of Earth, with maximum gravitational acceleration at the poles. Here
we show that this latitudinal variation in gravitational acceleration is
relevant for modeling the climate of oblate planets including Jovian planets
within the solar system, closely-orbiting hot Jupiters, and planets within the
habitable zone of white dwarfs. We compare first- and third-order
approximations for gravitational acceleration on an oblate spheroid and
calculate the geostrophic wind that would result from this asphericity on a
range of solar system planets and exoplanets. Third-order variations in
gravitational acceleration are negligible for Earth but become significant for
Jupiter, Saturn, and Jovian exoplanets. This latitudinal variation in
gravitational acceleration can be measured remotely, and the formalism
presented here can be implemented for use in general circulation climate
modeling studies of exoplanet atmospheres.
