The Uranus system from occultation observations (1977–2006): Rings, pole direction, gravity field, and masses of Cressida, Cordelia, and Ophelia

• Published in: Icarus (New York, N.Y. 1962) N.Y. 1962), 2024-03, Vol.411, p.115957, Article 115957
• Main Authors: French, Richard G., Hedman, Matthew M., Nicholson, Philip D., Longaretti, Pierre-Yves, McGhee-French, Colleen A.
• Format: Article
• Language: English
• Subjects: Occultations; Planets; Rings; Sciences of the Universe
• ISSN: 0019-1035; 1090-2643
• DOI: 10.1016/j.icarus.2024.115957

From an analysis of 31 Earth-based stellar occultations and three Voyager 2 occultations spanning 1977–2006 (French et al. 2023a), we determine the keplerian orbital elements of the centerlines of the nine main Uranian rings to high accuracy, with typical RMS residuals of 0.2–0.4 km and 1-σ formal errors in a,ae, and asini of order 0.1 km, registered on an absolute radius scale accurate to 0.2 km at the 2-σ level. The λ ring shows more substantial scatter, with few secure detections. We identify a host of free and forced normal modes in several of the ring centerlines and inner and outer edges. In addition to the previously-known free modes m=0 in the γ ring and m=2 in the δ ring, we find two additional outer Lindblad resonance (OLR) modes (m=−1 and −2) and a possible m=3 inner Lindblad resonance (ILR) mode in the γ ring. No normal modes are detected for rings 6, 5, 4, α, or β. Five separate normal modes are forced by small moonlets: the 3:2 inner ILR of Cressida with the η ring, the 6:5 ILR of Ophelia with the γ ring, the 23:22 ILR of Cordelia with the δ ring, the 14:13 ILR of Ophelia with the outer edge of the ϵ ring, and the counterpart 25:24 OLR of Cordelia with the ring’s inner edge. The phases of the modes and their pattern speeds are consistent with the mean longitudes and mean motions of the satellites, confirming their dynamical roles in the ring system. We find no evidence of normal modes excited by internal planetary oscillations. We determine the width–radius relations for nearly all of the detected modes, with positive width–radius slopes for ILR modes (including the m=1 elliptical orbits) and negative slopes for most of the detected OLR modes, supporting the standard self-gravity model for ring apse alignment. We find no convincing evidence for librations of any of the rings. The Uranus J2000 pole direction at epoch TDB 1986 Jan 19 12:00 is αP=77.311327±0.000141° and δP=15.172795±0.000618°. The slight pole precession predicted by Jacobson (2023) is not detectable in our orbit fits, and the absolute radius scale is not strongly correlated with the pole direction. From Monte Carlo fits to the measured apsidal precession and nodal regression rates of the eccentric and inclined rings, we determine the zonal gravitational coefficients J2=(3509.291±0.412)×10−6,J4=(−35.522±0.466)×10−6, and J6 fixed at 0.5×10−6, with a correlation coefficient ρ(J2,J4)=0.9861, for a reference radius R=25559 km. This result differs significantly from both earlier and m