Probing the Jovian Interior via its Gravitational Field: Mathematical Theory and Applications

Alternating, fast cloud level zonal winds on Jupiter have been accurately measured for several decades but their depth of penetration into the Jovian interior, which is closely associated with the origin of the winds, still remains highly controversial. The Juno spacecraft, now on its way to Jupiter and will arrive there in 2016, will probe the depth of penetration of the zonal winds by accurately measuring their effects on the high-order zonal gravitational coefficients at unprecedentedly high precision. Interpretation of these gravitational measurements requires an accurate description of the shape, density structure and internal wind profile. We shall discuss the mathematical theory and accurate numerical simulation for the gravitational field of rapidly rotating, non-spherical gaseous Jupiter.