The shape of Jupiter and Saturn based on atmospheric dynamics, radio occultations and gravity measurements

The shape of two gas giants, Jupiter and Saturn, is determined primarily by their rotation rate, and interior density distribution. It is also affected by their zonal winds, causing a perturbation of O(10 km) at low latitudes. However, uncertainties in the observed cloud-level wind and the polar radius, translate to uncertainty in the shape with the same order of magnitude. This prevents an exact comparison against the shape based on radio-occultation measurements, the only other available data. The Juno (Jupiter) and Cassini (Saturn) missions gave unprecedentedly accurate gravity measurements, constraining better the uncertainty in the wind structure. Using an accurate shape calculation, and a joint optimization, given both gravity and radio-occultation measurements, we calculate the possible range of dynamical height for both planets. We find that for Saturn there is an excellent match to the radio-occultation measurements, while at Jupiter the shape does not reflect the radio-occultations measurements on that scale.