Isolating the gravitational influence of Uranus’s winds requires close passages inward of the rings

Close orbits by a Uranus Orbiter and Probe (UOP) could be used to deduce Uranus's multipolar gravity field to higher precision and higher angular degree than the existing $J_2$ and $J_4$ measurements from ground-based ring occultations and the Voyager 2 flyby. We consider the $J_n$ sensitivity limits set by simulations of candidate UOP trajectories, pairing these with Uranus interior and wind models to perform retrievals from the gravity moments. We consider zonal wind profiles derived from recent feature tracking data, assuming that zonal winds extend into the planet along cylinders, with a radial decay function similar to those that explain Jupiter and Saturn gravity. We find that present knowledge of $J_2$ and $J_4$ permits a fairly wide range of possible wind depths in Uranus, up to 2,000 km or $8\%$ of the planet's radius. The measurement of additional gravity moments is essential to separate this unknown wind depth from other interior properties of interest, but $J_6$ is found to be too dominated by bulk rotation to be a useful probe of the wind depth. Odd moments arising from the observed north-south asymmetry in the zonal flow are a strong function of wind depth, but the usefulness of $J_3$ is limited by its sensitivity to which feature tracking data are incorporated into the global fit. The even moment $J_8$, or the odd moments $J_5$ and $J_7$, are the most useful probes of the depth of Uranus's winds. $J_8$, and most likely $J_5$ and $J_7$, are measurable in a polar orbit making $\gtrsim10$ pericenter passages inside the rings approximately $\sim1,000$ km above Uranus's cloud tops.