Analytics of planetary rotation: Improved physics with implications for the shape and super-rotation of Earth's core

Criss, Robert E.

doi:10.1016/j.earscirev.2019.01.024

Cited by 11 publications

(5 citation statements)

References 6 publications

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“…Regarding rigidity, even layers in the dense and highly viscous Earth are decoupled, as demonstrated by westward drift of Earth's outermost lithospheric plates relative to its interior [16]. Decoupling of motions between layers is referred to as differential rotation, and may also exist for Earth's core [17,18]. The precise term is differential spin.…”

Section: Introductionmentioning

confidence: 99%

Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves

Criss

Hofmeister

2020

Galaxies

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Spiral galaxies and their rotation curves have key characteristics of differentially spinning objects. Oblate spheroid shapes are a consequence of spin and reasonably describe galaxies, indicating that their matter is distributed in gravitationally interacting homeoidal shells. Here, previously published equations describing differentially spinning oblate spheroids with radially varying density are applied to 51 galaxies, mostly spirals. A constant volumetric density (ρ, kg m−3) is assumed for each thin homeoid in these formulae, after Newton, which is consistent with RCs being reported simply as a function of equatorial radius r. We construct parameter-free inverse models that uniquely specify mass inside any given r, and thus directly constrain ρ vs. r solely from velocity v (r) and galactic aspect ratios (assumed as 1:10 for spirals when data are unavailable). Except for their innermost zones, ρ is proven to be closely proportional to rn, where the statistical average of n for all 36 spirals studied is −1.80 ± 0.40. Our values for interior densities compare closely with independently measured baryon density in appropriate astronomical environments: for example, calculated ρ at galactic edges agrees with independently estimated ρ of intergalactic media (IGM). Our finding that central densities increase with galaxy size is consistent with behavior exhibited by diverse self-gravitating entities. Our calculated mass distributions are consistent with visible luminosity and require no non-baryonic component.

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Section: Introductionmentioning

confidence: 99%

Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves

Criss

Hofmeister

2020

Galaxies

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“…or ε ≈ constant × ω (10b) [32], which therefore holds to significantly larger ε than the planets of our solar system. The small deviation between the exact relationship and the approximation (Figure 6a) is insignificant, given that real bodies have radially varying density.…”

Section: Ellipticity and Spin Ratementioning

confidence: 86%

“…Therefore, differential rotation could exist between the strong mantle and the inner core. Super-rotation of the core has been considered, but its small size (<1 • y −1 ) makes quantification difficult (see [32] and the review of [39]). A tangential velocity similar to continental drift is well below the limit of detection.…”

Section: Oversimplified Case: Conservation Of Spin Angular Momentum H...mentioning

confidence: 99%

“…In particular, the molten outer core flows (shears) without resistance, so a faster rotating, more oblate solid inner core could be accommodated while the mantle rotates more slowly and is rounder. Criss [32] provides analytical formulae for spinning stratified bodies along with calculations for several endmember cases.…”

Section: Oversimplified Case: Conservation Of Spin Angular Momentum H...mentioning

confidence: 99%

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Theoretical and Observational Constraints on Lunar Orbital Evolution in the Three-Body Earth-Moon-Sun System

Hofmeister

Criss

2022

Astronomy

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Extremely slow recession of the Moon from the Earth has been recently proposed and attributed to conversion of Earth’s axial spin to lunar orbital momentum. This hypothesis is inconsistent with long-standing recognition that the Moon’s orbit involves three-body interactions. This and other short-comings, such as Earth’s spin loss being internal, are summarized here. Considering point-masses is justified by theory and observational data on other moons. We deduce that torque in the Earth-Moon-Sun system increases eccentricity of the lunar orbit but decreases its inclination over time. Consequently, the average lunar orbital radius is decreasing. We also show that lunar drift is too small to be constrained through lunar laser ranging measurements, mainly because atmospheric refraction corrections are comparatively large and variations in lunar cycles are under-sampled. Our findings support co-accretion and explain how orbits evolve in many-body point-mass systems.

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“…Importantly, the theory predicting an oblate shape describes fluid matter (gases or liquids). Although the resistance of solid matter to deformation is neglected in this formulation, solids such as the Earth are also reasonably represented (e.g., [53]).…”

Section: Gravitational Assessment Of Baryonic Mass and Density In And...mentioning

confidence: 99%

Baryonic Mass Inventory for Galaxies and Rarefied Media from Theory and Observations of Rotation and Luminosity

Hofmeister,

Criss,

Chou

2023

Galaxies

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Available inventories of baryonic mass in the universe are based largely on galactic data and empirical calculations made >20 years ago. Values falling below cosmological estimates underlie proposals that certain rarified gassy regions could have extremely high T, which motivated absorption measurements and hydrodynamic models. Yet, the shortfall remains. We inventory the total baryonic mass, focusing on gravitational interactions and updated measurements. A recent analytical inverse method for analyzing galactic rotation curves quantified how baryon mass and associated volumetric density (ρ) depend on distance (r) from galactic centers. The model is based on the dynamical consequences of the observed oblate shape of galaxies and the Virial Theorem. The parameter-free solution provides ρ(r) ∝ 1/r2 which describes star-rich galactic interiors, gas-rich outer discoids, circumgalactic media, and gradation into intergalactic media. Independent observational determinations of baryonic ρ validate that our 1/r2 result describes baryons alone. This solution shows that total baryonic mass associated with any galaxy is 2.4 to 40 times detectable luminosity, depending on galaxy size and spacing. Luminosity data within 50 Mpc show that Andromeda equivalents separated by ~1 Mpc represent the local universe. Combining the above yields (6 ± 2) × 10−25 kg m−3 for the present-day universe. Three other approaches support this high density: (1) evaluating trends and luminosity data near 1000 Mpc; (2) using a recent estimate for the number of galaxies in the universe; (3) calculating an energy balance. We discuss uncertainties in the critical density. Implications of large baryonic ρ are briefly discussed.

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Analytics of planetary rotation: Improved physics with implications for the shape and super-rotation of Earth's core

Cited by 11 publications

References 6 publications

Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves

Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves

Theoretical and Observational Constraints on Lunar Orbital Evolution in the Three-Body Earth-Moon-Sun System

Baryonic Mass Inventory for Galaxies and Rarefied Media from Theory and Observations of Rotation and Luminosity

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