Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially

With the aim of improving the Jupiter equilibrium liquid model consisting of two distorted spheroids (“spheroidals”) of our last paper, we generalize it here to any number l of layers, demanding that the calculated gravitational moments, J2n (n=1,.., 4), agree with those surveyed by the Juno mission, which is fulfilled with a much higher accuracy than for l=2. The layers are of constant density and concentric (but otherwise free from any specific constriction between their semi-axes), each rotating with its own distribution of differential angular velocity, in accordance with our law in a past work. We point out that the angular velocity profiles are a consequence of the equilibrium itself, rather than being imposed ad initio. Although planetary structure aspects are not contemplated in our models, we arrange matters so that they can be compared with Gudkova’s and Guillot’s, paying attention on the distributions of mass and pressure. Our procedure is exact, in contrast with the self-consistent CMS (Concentric Maclaurin Spheroids) method developed by Hubbard, whose inexactitude resides in maintaining a single constant angular velocity while the spheroids are deformed. Our model predicts a differential rotation for Jupiter with periods for pole and equator of 9h38m and 10h14m corresponding to a mean period of 9h55m.