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Geostrophic wind induced by latitudinal variation in gravitational acceleration on oblate planets

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.