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

TL;DR

Close orbital passes of a Uranus orbiter can improve gravity field measurements, helping to better understand Uranus's interior and wind depths, with specific gravity moments like J8, J5, and J7 being most informative.

Contribution

This study identifies the most sensitive gravity moments for probing Uranus's wind depth and assesses the feasibility of measuring them through close orbital passes.

Findings

J8, J5, and J7 are the best gravity moments to measure for wind depth.

J6 is too dominated by bulk rotation to be useful for wind depth analysis.

Multiple close passes inward of the rings are needed to measure these moments.

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 $\zeta$ ring, approximately 1,000-2,500 km above Uranus's cloud tops.