Reconstructing wind fields from gravitational data on gas giants: an investigation of mathematical methods

Abstract The atmospheric structure of gas giants, especially those of Jupiter and Saturn, has been an object of scientific studies for a long time. The measurement of the gravitational fields by the Juno mission for Jupiter and the Cassini mission for Saturn offered new possibilities to study the interior structure of these planets. Accordingly, the reconstruction of the wind velocities from gravitational data on gas giants has been the subject of many research papers over the years, yet the mathematical foundations of this inverse problem and its numerical resolution have not been studied in detail. This article suggests a rigorous mathematical theory for inferring the wind fields of gas giants. In particular, an orthonormal basis is derived which can be associated to models of the gravitational potential and the interior wind velocity field. Moreover, this approach provides the foundations for existing resolution concepts of the inverse problem.