DIFFERENTIAL ROTATION OF CELESTIAL BODIESAND THE CORIOLIS FORCE

Abstract

Differential rotation is a central organising mechanism in rotating planets, stars, and magnetised plasma envelopes. This article treats the problem as a comparative dynamical analysis and asks how latitudinal and radial shear, Coriolis deflection, and wave-mediated angular-momentum transport form a single physical chain across planetary atmospheres, the solar convection zone, and magnetically active stellar interiors. Starting from the momentum equation in a rotating frame, the paper derives the role of the Coriolis term, introduces the Rossby number and the latitudinal beta effect as diagnostic parameters, and relates these quantities to observed solar differential rotation, tachocline shear, solar-like stellar rotation, and Rossby or r-mode oscillations. The analysis shows that differential rotation should not be interpreted simply as a surface rotation law; it is a maintained non-equilibrium state in which Reynolds stresses, baroclinicity, meridional circulation, Lorentz forces, and global waves compete to redistribute angular momentum. The Sun is used as the principal astrophysical case because helioseismology constrains its internal angular velocity profile, while the Earth-atmosphere system provides the clearest geophysical analogue for Corioliscontrolled wave dynamics. A synthesis table is proposed to classify rotating celestial systems according to dominant force balance, expected shear morphology, and wave response. The resulting framework clarifies why Rossby-type modes can appear in both neutral planetary fluids and magnetised stellar plasmas, although their restoring mechanisms and observational tracers differ.