Inferring the depth of the zonal jets on Jupiter and Saturn from odd gravity harmonics

The low-order even gravity harmonics J₂, J₄, and J₆ are well constrained for Jupiter and Saturn from spacecraft encounters over the past few decades. These gravity harmonics are dominated by the oblate shape and radial density distribution of these gaseous planets. In the lack of any north-south asymmetry, odd gravity harmonics will be zero. However, the winds on these planets are not hemispherically symmetric, and therefore can contribute to the odd gravity harmonics through dynamical variations to the density field. Here it is shown that even relatively shallow winds (reaching ~ 40 bars) can cause considerable odd gravity harmonics that can be detectable by NASA's Juno and Cassini missions to Jupiter and Saturn. Moreover, these measurements will have better sensitivity to the odd harmonics than to the high-order even harmonics, which have been previously proposed as a proxy for deep winds. Determining the odd gravity harmonics will therefore help constrain the depth of the jets on these planets, and may provide valuable information about the planet's core and structure. Key Points Measurable odd harmonics due to atmospheric circulation exist on giant planets Odd harmonics provide a pure dynamical gravity signal (no solid-body component) Juno/Cassini will have better sensitivity to odd harmonics than high even ones