Love numbers of the moon and of the terrestrial planets

Zhang, Chaozhi

doi:10.1007/bf00116287

Cited by 22 publications

(12 citation statements)

References 13 publications

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“…The same trend is expected for inclusion of solid-body effects, which will be important for colder super-Earth planets and those with less extended, less massive atmosphere. Theoretical k 2 values for the terrestrial objects are in good agreement with the observations when making the simplifying assumption of an elastic interior (Zhang 1992;Yoder et al 2003) (in which case the shear modulus becomes frequency-independent, i.e. k 2 a static Love number), while their observed moments of inertia are close to 0.4 indicating a nearly homogeneous interior, the theoretical Love number k 2 of which would approach 1.5 if the body were fluid and compressible.…”

Section: Compositionsupporting

confidence: 75%

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THERMAL EVOLUTION AND STRUCTURE MODELS OF THE TRANSITING SUPER-EARTH GJ 1214b

Nettelmann

Fortney

Kramm

et al. 2011

ApJ

188

167

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The planet GJ 1214b is the second known super-Earth with a measured mass and radius. Orbiting a quiet M-star, it receives considerably less mass-loss driving X-ray and UV radiation than CoRoT-7b, so that the interior may be quite dissimilar in composition, including the possibility of a large fraction of water. We model the interior of GJ 1214b assuming a two-layer (envelope+rock core) structure where the envelope material is either H/He, pure water, or a mixture of H/He and H 2 O. Within this framework we perform models of the thermal evolution and contraction of the planet. We discuss possible compositions that are consistent with M p = 6.55 M ⊕ , R p = 2.678 R ⊕ , an age τ = 3 − 10 Gyr, and the irradiation level of the atmosphere. These conditions require that if water exists in the interior, it must remain in a fluid state, with important consequences for magnetic field generation. These conditions also require the atmosphere to have a deep isothermal region extending down to 80−800 bar, depending on composition. Our results bolster the suggestion of a metal-enriched H/He atmosphere for the planet, as we find water-world models that lack an H/He atmosphere to require an implausibly large water-to-rock ratio of more than 6:1. We instead favor a H/He/H 2 O envelope with high water mass fraction (∼ 0.5−0.85), similar to recent models of the deep envelope of Uranus and Neptune. Even with these high water mass fractions in the H/He envelope, generally the bulk composition of the planet can have subsolar water:rock ratios. Dry, water-enriched, and pure water envelope models differ to an observationally significant level in their tidal Love numbers k 2 of respectively ∼ 0.018, ∼ 0.15, and ∼ 0.7. Subject headings: planets and satellites: general -planets and satellites: individual(GJ 1214b)

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Section: Compositionsupporting

confidence: 75%

“…The presence of an iron core could even enhance the central condensation. Therefore, although the H/He layer is low in mass, it significantly strengthens the property of central condensation compared to a closer to zero-mass atmosphere planetary object such as the Earth, the theoretical k 2 value of which is ∼ 0.3 (Zhang 1991).…”

Section: (D)mentioning

confidence: 95%

THERMAL EVOLUTION AND STRUCTURE MODELS OF THE TRANSITING SUPER-EARTH GJ 1214b

Nettelmann

Fortney

Kramm

et al. 2011

ApJ

188

167

View full text Add to dashboard Cite

show abstract

“…Historically, Goldreich and Soter (1966) estimated that Q < 17 for Venus, Lago and Cazenave (1979) More recently, Venus' tidal Love number was estimated by Konopliv and Yoder (1996) using Magellan and Pioneer Venus Orbiter data to be k 2 = 0.295±0.066 implying the core is liquid (Yoder, 1997). Work by Zhang (1992) and Xia and Xiao (2002) has estimated k 2 = 0.18-0.26. A smaller value (k 2 = 0.17) would imply a solidified iron core, which is not consistent with Konopliv and Yoder (1996).…”

Section: 1029/2019je006276mentioning

confidence: 99%

Venusian Habitable Climate Scenarios: Modeling Venus Through Time and Applications to Slowly Rotating Venus‐Like Exoplanets

2020

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One popular view of Venus' climate history describes a world that has spent much of its life with surface liquid water, plate tectonics, and a stable temperate climate. Part of the basis for this optimistic scenario is the high deuterium to hydrogen ratio from the Pioneer Venus mission that was interpreted to imply Venus had a shallow ocean's worth of water throughout much of its history. Another view is that Venus had a long-lived (∼100 million years) primordial magma ocean with a CO 2 and steam atmosphere. Venus' long-lived steam atmosphere would sufficient time to dissociate most of the water vapor, allow significant hydrogen escape, and oxidize the magma ocean. A third scenario is that Venus had surface water and habitable conditions early in its history for a short period of time (<1 Gyr), but that a moist/runaway greenhouse took effect because of a gradually warming Sun, leaving the planet desiccated ever since. Using a general circulation model, we demonstrate the viability of the first scenario using the few observational constraints available. We further speculate that large igneous provinces and the global resurfacing hundreds of millions of years ago played key roles in ending the clement period in its history and presenting the Venus we see today. The results have implications for what astronomers term "the habitable zone," and if Venus-like exoplanets exist with clement conditions akin to modern Earth, we propose to place them in what we term the "optimistic Venus zone." Plain Language SummaryWe have little data on our neighbor Venus to help us understand its climate history. Yet Earth and Venus are sister worlds: They initially formed close to one another and have nearly the same mass and radius. Despite the differences in their current atmospheres and surface temperatures, they likely have similar bulk compositions, making comparison between them extremely valuable for illuminating their distinct climate histories. We analyze our present data on Venus alongside knowledge about Earth's climate history to make a number of exciting claims. Evaluating several snapshots in time over the past 4+ billion years, we show that Venus could have sustained liquid water and moderate temperatures for most of this period. Cloud feedbacks from a slowly rotating world with surface liquid water reservoirs were the keys to keeping the planet clement. Contrast this with its current surface temperature of 450 • and an atmosphere dominated by carbon dioxide and nitrogen. Our results demonstrate that it was not the gradual warming of the Sun over the eons that contributed to Venus present hothouse state. Rather, we speculate that large igneous provinces and the global resurfacing hundreds of millions of years ago played key roles in ending the clement period in its history.

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“…for the equatorial deformation; see Appendix C. Here h 2 is the tidal Love number (h 2 ≈ 2k 2 [61]), while the other constants are as defined after (B.3). If we are interested only in orders of magnitude, we can express the equatorial deformation according to (B.4) with h 2 = 1 for the systems with Jupiter or Saturn as primary.…”

Section: B Parameters ε and γ For The Spin-orbit Modelmentioning

confidence: 99%

Attractiveness of periodic orbits in parametrically forced systems with time-increasing friction

Bartuccelli

Deane

Gentile

2012

Journal of Mathematical Physics

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We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven cubic oscillator in the presence of friction. We find that, if the damping coefficient increases in time up to a final constant value, then the basins of attraction of the leading resonances are larger than they would have been if the coefficient had been fixed at that value since the beginning. From a quantitative point of view, the scenario depends both on the final value and the growth rate of the damping coefficient. The relevance of the results for the spin-orbit model are discussed in some detail.

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Love numbers of the moon and of the terrestrial planets

Cited by 22 publications

References 13 publications

THERMAL EVOLUTION AND STRUCTURE MODELS OF THE TRANSITING SUPER-EARTH GJ 1214b

THERMAL EVOLUTION AND STRUCTURE MODELS OF THE TRANSITING SUPER-EARTH GJ 1214b

Venusian Habitable Climate Scenarios: Modeling Venus Through Time and Applications to Slowly Rotating Venus‐Like Exoplanets

Attractiveness of periodic orbits in parametrically forced systems with time-increasing friction

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