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

TL;DR

This work analyzes how a Uranus Orbiter and Probe could extract Uranus's gravity-field multipoles beyond the current $J_2$ and $J_4$ limits by combining simulated UOP trajectories with interior structure and wind models. It demonstrates that wind-induced perturbations to $J_n$ depend strongly on wind depth, with the most informative probes being the even $J_8$ and the odd $J_5$/$J_7$, while $J_6$ is largely dominated by bulk rotation. The study identifies that achieving constraints on wind depth requires a highly inclined, ring-crossing orbit featuring >~10 pericenter passages inward of the $\zeta$ ring (roughly 1,000–2,500 km above the cloud tops). These results inform trajectory planning and demonstrate the potential to significantly reduce interior–wind degeneracies in Uranus by leveraging higher-degree gravity moments. The methodology blends gradient interior models, a cylinder-extended wind profile with a sigmoid decay, and on-the-fly wind solves to assess the measurability and utility of $J_n$ in disentangling Uranus's interior structure from atmospheric dynamics.

Abstract

Close orbits by a Uranus Orbiter and Probe (UOP) could be used to deduce Uranus's multipolar gravity field to higher precision and angular degree than the J2 and J4 currently measured from ground-based ring occultations and the Voyager 2 flyby. We examine Jn sensitivity limits obtained from 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. Present knowledge of J2 and J4 permits a fairly wide range of possible wind depths in Uranus, up to 1,800 km or 7% by radius. Measuring additional gravity moments is essential to separate this unknown wind depth from other interior properties of interest, but J6 is found to be too dominated by bulk rotation to be a useful probe of the wind depth. Odd moments arising from Uranus's observed north-south asymmetric flow are strong functions of the wind depth, but the usefulness of J3 is hindered by its sensitivity to present uncertainties in the wind profile. The even moment J8, or the odd moments J5 and J7, are the best probes of the depth of Uranus's winds. J8, and most likely J5 and J7, are measurable in a highly inclined orbit making >~10 pericenter passages inward of the $ζ$ ring, approximately 1,000-2,500 km above Uranus's cloud tops.