Spherical approximation is often adopted in modeling planetary and stellar fluid dynamics, which implicitly assumes the rotational flattening effect is small. This simplification, to the leading order of the basic reference state, makes gravity, pressure, chemical, and thermal variables only depend on the radial coordinate. However, a rotating and self-gravitating fluid body is necessarily nonspherical. In order to represent fundamental mechanical equilibrium and thermal state of rapidly rotating planets or stars, where rotational flattening is not to be neglected, we construct a nonspherical, stably stratified Boussinesq fluid model of uniform rotation. Closed-form gravity and temperature formulations of the basic reference state are derived in terms of oblate spheroidal coordinates. The key emphasis of this paper is that the uniformly heated model is mathematically confirmed to be motionless in the corotating frame of reference. Based on this hydrostatic model of rotating stable stratification, we show that although treating the centrifugal terms within a spherical geometry context is convenient, it can lead to incorrect flows. The neglected terms produced by the oblateness are of the same order as the baroclinic terms included, and can indeed cancel them out in some circumstances. This paper proposes a foundation for the analysis of thermally driven flows in nonspherical geometries, which will be carried on in a series of future papers.

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• Astrophysical fluid dynamics
• Geophysical fluid dynamics
• Rotating geophysical flows
• Stratified geophysical flows