The Juno spacecraft has measured Jupiter's low‐order, even gravitational moments, J2–J8, to an unprecedented precision, providing important constraints on the density profile and core mass of the planet. Here we report on a selection of interior models based on ab initio computer simulations of hydrogen‐helium mixtures. We demonstrate that a dilute core, expanded to a significant fraction of the planet's radius, is helpful in reconciling the calculated Jn with Juno's observations. Although model predictions are strongly affected by the chosen equation of state, the prediction of an enrichment of Z in the deep, metallic envelope over that in the shallow, molecular envelope holds. We estimate Jupiter's core to contain a 7–25 Earth mass of heavy elements. We discuss the current difficulties in reconciling measured Jn with the equations of state and with theory for formation and evolution of the planet.

The depth to which Jupiter's observed east-west jet streams extend has been a long-standing question. Resolving this puzzle has been a primary goal for the Juno spacecraft, which has been in orbit around the gas giant since July 2016. Juno's gravitational measurements have revealed that Jupiter's gravitational field is north-south asymmetric, which is a signature of the planet's atmospheric and interior flows. Here we report that the measured odd gravitational harmonics J, J, J and J indicate that the observed jet streams, as they appear at the cloud level, extend down to depths of thousands of kilometres beneath the cloud level, probably to the region of magnetic dissipation at a depth of about 3,000  kilometres. By inverting the measured gravity values into a wind field, we calculate the most likely vertical profile of the deep atmospheric and interior flow, and the latitudinal dependence of its depth. Furthermore, the even gravity harmonics J and J resulting from this flow profile also match the measurements, when taking into account the contribution of the interior structure. These results indicate that the mass of the dynamical atmosphere is about one per cent of Jupiter's total mass.

The interior structure of Saturn, the depth of its winds, and the mass and age of its rings constrain its formation and evolution. In the final phase of the Cassini mission, the spacecraft dived between the planet and its innermost ring, at altitudes of 2600 to 3900 kilometers above the cloud tops. During six of these crossings, a radio link with Earth was monitored to determine the gravitational field of the planet and the mass of its rings. We find that Saturn’s gravity deviates from theoretical expectations and requires differential rotation of the atmosphere extending to a depth of at least 9000 kilometers. The total mass of the rings is (1.54 ± 0.49) × 1019 kilograms (0.41 ± 0.13 times that of the moon Mimas), indicating that the rings may have formed 107 to 108 years ago.