Tilting Uranus via the migration of an ancient satellite

Saillenfest, Melaine; Rogoszinski, Zeeve; Lari, Giacomo; Baillié, K.; Boué, G.; Crida, A.; Lainey, V.

doi:10.48550/arxiv.2209.10590

Cited by 1 publication

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“…The angular momentum of a giant planet must be accurately known to calculate the planet's precession rate, which is the crucial quantity to determine whether it is in a spin-orbit resonance. Such resonances have been invoked, along with additional assumptions to explain the obliquities of Saturn, 27 • (Saillenfest et al 2021;Wisdom et al 2022), Jupiter, 3 • (Ward & Canup 2006), and Uranus, 98 • (Saillenfest et al 2022). The planetary spin angular momentum contributes 99% of the angular momenta of the Jovian or Saturnian systems, the rest coming from the most massive satellites.…”

Section: Introductionmentioning

confidence: 99%

Relation of Gravity, Winds, and the Moment of Inertia of Jupiter and Saturn

Militzer

Hubbard

2023

Planet. Sci. J.

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We study the relationship of zonal gravity coefficients, J 2n , zonal winds, and axial moment of inertia (MoI) by constructing models for the interiors of giant planets. We employ the nonperturbative concentric Maclaurin spheroid method to construct both physical (realistic equation of state and barotropes) and abstract (small number of constant-density spheroids) interior models. We find that accurate gravity measurements of Jupiter’s and Saturn’s J 2, J 4, and J 6 by the Juno and Cassini spacecraft do not uniquely determine the MoI of either planet but do constrain it to better than 1%. Zonal winds (or differential rotation (DR)) then emerge as the leading source of uncertainty. For Saturn they are predicted to decrease the MoI by 0.4% because they reach a depth of ∼9000 km, while on Jupiter they appear to reach only ∼3000 km. We thus predict DR to affect Jupiter’s MoI by only 0.01%, too small by one order of magnitude to be detectable by the Juno spacecraft. We find that winds primarily affect the MoI indirectly via the gravity harmonic J 6, while direct contributions are much smaller because the effects of pro- and retrograde winds cancel. DR contributes +6% and −0.8% to Saturn’s and Jupiter’s J 6 value, respectively. This changes the J 6 contribution that comes from the uniformly rotating bulk of the planet that correlates most strongly with the predicted MoI. With our physical models, we predict Jupiter’s MoI to be 0.26393 ± 0.00001. For Saturn, we predict 0.2181 ± 0.0002, assuming a rotation period of 10:33:34 hr that matches the observed polar radius.

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