Models, figures and gravitational moments of Jupiter’s satellite Io: Effects of the second order approximation

Жарков, В. Н.; Гудкова, Т. В.

doi:10.1016/j.pss.2010.06.004

Cited by 7 publications

(10 citation statements)

References 13 publications

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“…We computed C h 2m from H h 2m using the second-order relations between shape and gravity (Eq. (49) of Zharkov and Gudkova [2010]). Our formalism for the harmonic coefficients of degree two is equivalent to the one of Zharkov and Gudkova [2010], except that their Eqs.…”

Section: Figure Of Equilibriummentioning

confidence: 98%

“…The geoid, to first order in the figure of equilibrium, is given by H h nm = R 0 C nm , except for the two components affected by the rotation and by the permanent static tide [Zharkov , 2004;Zharkov and Gudkova, 2010]:…”

Section: S2 Gravity Data (Tables S2 and S3)mentioning

confidence: 99%

“…(49) of Zharkov and Gudkova [2010]). Our formalism for the harmonic coefficients of degree two is equivalent to the one of Zharkov and Gudkova [2010], except that their Eqs. ( 51)-( 52) and ( 57)-( 58) are wrong and must be replaced by the two equations above.…”

Section: Figure Of Equilibriummentioning

confidence: 99%

See 2 more Smart Citations

Enceladus's and Dione's floating ice shells supported by minimum stress isostasy

Beuthe

Rivoldini

Trinh

2016

Geophysical Research Letters

152

182

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Enceladus's gravity and shape have been explained in terms of a thick isostatic ice shell floating on a global ocean, in contradiction of the thin shell implied by librations. Here we propose a new isostatic model minimizing crustal deviatoric stress and demonstrate that gravity and shape data predict a 38 ± 4 km thick ocean beneath a 23 ± 4 km thick shell agreeing with—but independent of—libration data. Isostatic and tidal stresses are comparable in magnitude. South polar crust is only 7 ± 4 km thick, facilitating the opening of water conduits and enhancing tidal dissipation through stress concentration. Enceladus's resonant companion, Dione, is in a similar state of minimum stress isostasy. Its gravity and shape can be explained in terms of a 99 ± 23 km thick isostatic shell overlying a 65 ± 30 km thick global ocean, thus providing the first clear evidence for a present‐day ocean within Dione.

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Section: Figure Of Equilibriummentioning

confidence: 98%

Section: S2 Gravity Data (Tables S2 and S3)mentioning

confidence: 99%

See 1 more Smart Citation

Enceladus's and Dione's floating ice shells supported by minimum stress isostasy

Beuthe

Rivoldini

Trinh

2016

Geophysical Research Letters

152

182

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show abstract

“…While Triton's mean density (2059±5 kg m 3 ) (Jacobson, 2009;Thomas, 2000) is consistent with a large rocky core overlain by a relatively thin icy shell, models of the radial mass distribution would be best constrained by radio science measurements of the non spherical part of the satellite's low-degree gravity field. As the latter is dominated by both spin and tidal contributions, a level-surface theory as developed by Hubbard and Anderson (1978), Dermott (1979), and more recently in a series of papers by Zharkov and Gudkova (2010) can be used to deduce the concentration of mass toward the center of a synchronously rotating satellite.…”

Section: Tritonmentioning

confidence: 99%

OSS (Outer Solar System): a fundamental and planetary physics mission to Neptune, Triton and the Kuiper Belt

Christophe

Spilker²,

Anderson³

et al. 2012

Exp Astron

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“…The most commonly used method, known as the theory of figures (Zharkov & Trubitsyn 1978), uses a perturbative approach to determine the planet's response to small deviations of the potential from spherical symmetry. Other works have extended the theory of figures to consider secondorder effects through higher-order perturbative theory (Zharkov 2004;Zharkov & Gudkova 2010;Correia & Rodríguez 2013). Padovan et al (2018) adapted a related perturbative method using a matrix-propagator approach, more common in geophysical applications to exoplanets.…”

Section: Introductionmentioning

confidence: 99%

Tidal Response and Shape of Hot Jupiters

Wahl

Thorngren

et al. 2021

ApJ

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We study the response of hot Jupiters to a static tidal perturbation using the concentric MacLaurin spheroid method. For strongly irradiated planets, we first performed radiative transfer calculations to relate the planet’s equilibrium temperature, T eq, to its interior entropy. We then determined the gravity harmonics, shape, moment of inertia, and static Love numbers for a range of two-layer interior models that assume a rocky core plus a homogeneous and isentropic envelope composed of hydrogen, helium, and heavier elements. We identify general trends and then study HAT-P-13b, the WASP planets 4b, 12b, 18b, 103b, and 121b, and Kepler-75b and CoRot-3b. We compute the Love numbers, k nm , and transit radius correction, ΔR, which we compare with predictions in the literature. We find that the Love number, k 22, of tidally locked giant planets cannot exceed a value of 0.6, and that the high T eq consistent with strongly irradiated hot Jupiters tends to further lower k 22. While most tidally locked planets are well described by a linear regime response of k 22 = 3J 2/q 0 (where q 0 is the rotation parameter of the gravitational potential), for extreme cases such as WASP-12b, WASP-103b, and WASP-121b, nonlinear effects can account for over 10% of the predicted k 22. The k 22 values larger than 0.6, as they have been reported for planets WASP-4b and HAT-P13B, cannot result from a static tidal response without extremely rapid rotation and thus are inconsistent with their expected tidally locked state.

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Models, figures and gravitational moments of Jupiter’s satellite Io: Effects of the second order approximation

Cited by 7 publications

References 13 publications

Enceladus's and Dione's floating ice shells supported by minimum stress isostasy

Enceladus's and Dione's floating ice shells supported by minimum stress isostasy

OSS (Outer Solar System): a fundamental and planetary physics mission to Neptune, Triton and the Kuiper Belt

Tidal Response and Shape of Hot Jupiters

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