This thesis investigates the mathematical modeling of gas giant atmospheric dynamics using gravitational data from the Juno and Cassini missions. Focusing on Jupiter and Saturn, it explores how observed zonal wind structures may extend into planetary interiors and influence gravity fields. Building on concepts from inverse gravimetry, the study formulates these physical processes within a rigorous mathematical framework. It introduces orthonormal function bases, examines the gravitational potential and Helmholtz equation, and develops models linking zonal winds to gravitational perturbations. The work concludes by formulating an inverse problem and providing appendices on windinduced gravitational coefficients and Bessel function properties.