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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.

An inverse method is devised to probe Earth's thermal state without assuming its mineralogy. This constrains thermal conductivity (κ) in the lower mantle (LM) by combining seismologic models of bulk modulus (B) and pressure (P) vs. depth (z) with a new result, ∂ln(κ) / ∂P ∼ 7.33/BT, and available high temperature (T) data on κ for lengths exceeding millimeters. Considering large samples accounts for the recently revealed dependence of heat transport properties on length scale. Applying separation of variables to seismologic ∂B/∂P vs. depth isolates changes with T. The resulting LM dT / dz depends on ∂2B/∂P2 and ∂B/∂T, which vary little among dense phases. Because seismic ∂B/∂P is discontinuous and model dependent ∼ 200 km above the core, unlike the LM, our results are extrapolated through this tiny layer (D′′). Flux and power are calculated from dT / dz for cases of high (oxide) and low (silicate) κ. Geotherm calculations are independent of κ, and thus of LM mineralogy, but require specifying a reference temperature at some depth: a wide range is considered. Limitations on deep melting are used to ascertain which of our geotherm, flux, and power curves best represent Earth's interior. Except for an oxide composition with miniscule ∂2B/∂P2, the LM heats the core, causing it to melt. Deep heating is attributed to cyclical stresses from > 1000 km daily and monthly fluctuations of the barycenter inside the LM.

Thermal conductivity (K) describes the response of matter to temporal or spatial variations in temperature (T). To quantify the effect of varying mineralogy on heat transport of rocks, an accurate (±2%) contact-free heat transfer method was applied at ambient T to multiple sections from 33 different low porosity, continental, igneous and metamorphic rocks. Thermal diffusivity (Dheat) was measured using laser-flash analysis, which was previously used to construct our large mineralogical database and which mitigates spurious radiative transfer found in other techniques. These measurements constrain K, because K is the product of Dheat with the known (or calculable) properties of density and specific heat measured at constant pressure (P). Compositions, proportions, and orientations of minerals, plus rock density, average grain-size (L), and porosity were characterized for 61 sections from 29 silicate rocks plus 5 sections from 3 marbles. Our database was used to evaluate component summation (averaging) formulae that were recently developed by considering Fourier’s laws, and to quantify the dependence of K and/or Dheat on key rock descriptors. We found that: (1) phase proportions and compositions are the main cause of variations; (2) minor porosity and foliation have minor effects; and (3) within ~5%, isotropic rocks follow Dheat = ½{[Σ(fi/Di)]−1 + Σ(fiDi)} where fi is volumetric mineral fraction, analogous to the Voigt-Reuss-Hill average for elastic moduli. Using this formula predictively depends on the accuracy of fi and Di. Quartzo-feldspathic rocks can be described by a new formula that uses only quartz fraction and plagioclase composition. Combining our mineralogical model with a universal formula for Dheat(T) and a thermodynamic identity for K(P) accurately constrains conductive thermal transport for Earth’s low porosity, crystalline rock layers.

Igneous intrusions are important to the thermomechanical evolution of continents because they inject heat into their relatively cold host rocks, and potentially change the distribution of radiogenic heat production and thermal properties within the crust. To explore one aspect of the complex evolution of the continental crust, this paper investigates the local thermal effects of two intrusive rock types (carbonatites and anorthosites) on the Archean Superior Province of the Canadian shield. We provide new data on their contrasting properties: rock density near 298 K, thermal diffusivity, and heat capacity up to 800 K (which altogether yield thermal conductivity), plus radiogenic element contents. The volumetrically small carbonatites have widely varying radiogenic heat production (2–56 µW m−3) and moderate thermal conductivity at 298 K (~ 1 to 4 W m−1 K−1) which decreases with temperature. The massive Shawmere anorthosite has nearly negligible radiogenic heat production (

Most differences in the gross surface morphologies, tectonic styles, overall geologic histories, and atmospheres of the rocky bodies in the solar system can be explained by contributions and dissipation of gravitational and radiogenic energy over geologic time. These two energy sources are large and measurable and can be extrapolated back in time. Accretion was likely cold, and directly converted gravitational potential energy into axial spin, a prominent feature of planets that is otherwise unexplained. Impact heating was mostly limited to planetary surfaces in the final stages of accretion. Frictional dissipation of spin contributed sufficient energy to ignite the primordial Sun and heated Earth and Venus by nearly as much as has the radioactive decay of K, U, and Th over geologic time. Energy inputs have been continuously offset by loss of heat to the surroundings. The magnitudes of most important energy contributions depend on the planet radius R and also on the distance r to the Sun. Quantitative, albeit approximate, relationships show that the net specific energy (kJ/kg) contributed to the rocky bodies over geologic time goes as: Earth ~ Venus >> Mars ~ Mercury ~ Moon >> asteroids. Net energy inputs increased the average internal temperatures of Earth and Venus by ~3000 K but heated asteroids by only a few hundred kelvins.

Lateral accelerations require lateral forces. We propose that force imbalances in the unique Earth-Moon-Sun system cause large-scale, cooperative tectonic motions. The solar gravitational pull on the Moon, being 2.2× terrestrial pull, causes lunar drift, orbital elongation, and an ~1000 km radial monthly excursion of the Earth-Moon barycenter inside Earth’s mantle. Earth’s spin superimposes an approximately longitudinal 24 h circuit of the barycenter. Because the oscillating barycenter lies 3500–5500 km from the geocenter, Earth’s tangential orbital acceleration and solar pull are imbalanced. Near-surface motions are enabled by a weak low-velocity zone underlying the cold, brittle lithosphere: The thermal states of both layers result from leakage of Earth’s internal radiogenic heat to space. Concomitantly, stress induced by spin cracks the lithosphere in a classic X-pattern, creating mid-ocean ridges and plate segments. The inertial response of our high-spin planet with its low-velocity zone is ~10 cm yr–1 westward drift of the entire lithosphere, which largely dictates plate motions. The thermal profile causes sinking plates to thin and disappear by depths of ~200–660 km, depending on angle and speed. Cyclical stresses are effective agents of failure, thereby adding asymmetry to plate motions. A comparison of rocky planets shows that the presence and longevity of volcanism and tectonism depend on the particular combination of moon size, moon orbital orientation, proximity to the Sun, and rates of body spin and cooling. Earth is the only rocky planet with all the factors needed for plate tectonics.

Major pandemics involving respiratory viruses develop semi-regularly and require a large flux of novel viruses, yet their origination is equivocal. This paper explores how natural processes could give rise to this puzzling combination of characteristics. Our model is based on available data regarding the emergence of historic influenzas, early COVID-19 cases and spreading, the microbiome of permafrost, long-distance airborne transport of viruses reaching stratospheric levels, ultraviolet immunosuppression, sunlight variations, weather patterns, Arctic thawing, and global warming. Atmospheric conveyance is supported by hemispheric distribution disparities, ties of COVID-19 cases to air pollution particulate concentrations, and contemporaneous animal infections. The following sequence is proposed: (1) virus emergence after hot Arctic summers, predominantly near solar irradiance maxima or involving wildfires, indicates release of large amounts of ancient viruses during extensive permafrost melting, which are then incorporated in autumn polar air circulation, where cold storage and little sunlight permit survival. (2) Pandemics onset in winter to spring at rather few locations: from climate data on Wuhan, emergence occurs where the North Polar Jet stream hovers while intersecting warmer, moist air, producing rain which deposits particulates with the viral harvest on a vulnerable human population. (3) Spring and summer increases in COVID-19 cases link to high solar irradiance, implicating ultraviolet immune suppression as one means of amplification. (4) Viruses multiplied by infected humans at close range being incorporated in atmospheric circulation explains rapid global spread, periodic case surges (waves), and multi-year durations. Pollution and wind geography affect uptake and re-distribution. Our model can be tested, e.g., against permafrost stored in laboratories as well as Artic air samples, and suggests mitigating actions.

Proposed explanations of galactic rotation curves (RC = tangential velocity vs. equatorial radius, determined from Doppler measurements) involve dramatically different assumptions. A dominant, original camp invoked huge amounts of unknown, non-baryonic dark matter (NBDM) in surrounding haloes to reconcile RC simulated using their Newtonian orbital models (NOMs) for billions of stars in spiral galaxies with the familiar Keplerian orbital patterns of the few, tiny planets in our Solar System. A competing minority proposed that hypothetical, non-relativistic, non-Newtonian forces govern the internal motions of galaxies. More than 40 years of controversy has followed. Other smaller groups, unsatisfied by explanations rooted in unknown matter or undocumented forces, have variously employed force summations, spin models, or relativistic adaptations to explain galactic rotation curves. Some small groups have pursued inverse models and found no need for NBDM. The successes, failures, and underlying assumptions of the above models are reviewed in this paper, focusing on their mathematical underpinnings. We also show that extractions of RC from Doppler measurements need revising to account for the effect of galaxy shape on flux-velocity profiles and for the possible presence of a secondary spin axis. The latter is indicated by complex Doppler shift patterns. Our findings, combined with independent evidence such as hadron collider experiments failing to produce non-baryonic matter, suggest that a paradigm shift is unfolding.

The low thermal diffusivity of Earth’s rocks and its large size signify that even today, thermal transport in the lower mantle and core are independent of that in the outer layers. This situation permits construction of thermal profiles of the deep Earth from internal constraints: namely, the two-phase metallic core follows the solidus of iron alloy, and the top of the lower mantle lies below the dry peridotite solidus. Thermal conductivity of the core is irrelevant. Without samples, mantle thermal conductivity is estimated considering data and models for dense solids, leading to “hot silicate” and “cold oxide” geotherms. Temperatures are reasonably constrained, except for the height and position of the local maximum in the lower mantle. Meteoritic values for radionuclide contents of the lower mantle are consistent with present-day temperatures and progressive melting of the core.

This chapter summarizes diverse observations pertaining to heat flow inside the Earth. Information on temperatures, flux, various material properties, heat sources, internal layering, and lateral differences are summarized because they pertain to the boundary and initial conditions used to construct thermal models of planets. We show how the presence and location of molten layers constrain both temperatures and flux, and discuss the implications for Earth’s thermal structure and evolution. Problems in assuming adiabatic gradients and internal homogeneity are discussed. Energy sources in addition to radionuclide decay are covered: we show that an important gravitational source, dissipation of spin via friction during differential rotation, has been overlooked. Spin exerts crucial control on plate tectonics, as proved by abundant evidence reviewed here.

Chondritic meteorites are detrital aggregates that can include both high- and low-temperature materials, one of many characteristics they share with clastic sedimentary rocks. Their distinctive chondrules are rounded, well-sorted, sand-sized grains whose quantitative size distribution indicates aeolian processing. High-speed winds are consistent with the rapid spin rates and huge Coriolis forces of accreting planets. Most grains originally formed in the nebula, possibly by cold welding. Upon deposition on the surface of an accreting planet, chondrules plus dusty matrix were variously subjected to compaction, fluid infiltration, recrystallization, overgrowth development, cementation, and other processes that produced the textural and petrographic variety of chondrites. Impacts ejected some consolidated material into space and provided shock structures and some melting. A sedimentary origin of chondrites is consistent with their petrographic character, their large relative abundance, and the assembly of the rocky planets from the diverse types of solid phases known to exist in nebulae.

Pyroxene crystals are common in meteorites but few compositions have been recognized in astronomical environments. We present quantitative room-temperature spectra of 17 Mg-- Fe-- and Ca--bearing ortho- and clinopyroxenes, and a Ca-pyroxenoid in order to discern trends indicative of crystal structure and a wide range of composition. Data are produced using a Diamond Anvil Cell: our band strengths are up to 6 times higher than those measured in KBr or polyethylene dispersions, which include variations in path length (from grain size) and surface reflections that are not addressed in data processing. Pyroxenes have varied spectra: only two bands, at 10.22~$\mu$m and 15.34~$\mu$m in enstatite (En$_{99}$), are common to all. Peak-wavelengths generally increase as Mg is replaced by Ca or Fe. However, two bands in MgFe-pyroxenes shift to shorter wavelengths as the Fe component increases from 0 to 60 per cent. A high-intensity band shifts from 11.6~$\mu$m to 11.2~$\mu$m and remains at 11.2~$\mu$m as Fe increases to 100~per~cent; it resembles an astronomical feature normally identified with olivine or forsterite. The distinctive pyroxene bands between 13~ and 16~$\mu$m show promise for their identification in MIRI spectra obtained with JWST. The many pyroxene bands between 40 and 80~$\mu$m could be diagnositic of silicate mineralogy if data were obtained with the proposed SPICA telescope. Our data indicate that comparison between room-temperature laboratory bands for enstatite and cold $\sim 10-K$ astronomical dust features at wavelengths $\gtrsim 28~\mu$m can result in the identification of (Mg,Fe)- pyroxenes that contain 7--15 % less Fe-- than their true values because some temperature shifts mimic some compositional shifts. Therefore some astronomical silicates may contain more Fe, and less Mg, than previously thought., Comment: 16 pages, 10 figures.accepted in MNRAS

Formation of the Solar System is discussed to constrain the initial conditions of thermal models. Large amounts of primordial heat are unexpected because accretion predominantly converts gravitational potential energy into orbital and axial spin energies. This deduction is supported by measured characteristics of the planets being close to those expected from the Virial Theorem. Any heat produced was lost to the surroundings during accretion to meet second law requirements. Late stage impacts added heat to the outer layers of planets and so did not raise interior temperatures. Subsequent dissipation of spin gradually released heat. We argue that the iron cores of planets accreted first due to magnetic attraction and friction welding, which addresses a key problem in accretionary models. These early cores grew subsequently due to gravitational sorting of subsequently accreted, heterogeneous material. Sorting sent radionuclides upward, cooling the Earth, as did outgassing, consistent with energy minimization and entropy maximization.

Thermal histories of the rocky bodies are controlled by their initial inventories of energy, and by the subsequent production and loss of heat. This chapter places constraints on these inventories and processes of large rocky bodies of the inner Solar System, which began with cold accretion, as demonstrated by the icy-rocky bodies of the outer Solar System. Inventories per unit mass of heat generated over geologic time by radionuclides vary tenfold for these bodies, whereas the inventory generated by spin dissipation varies from near zero to significant. Both correlate with body mass, and the power generated has decreased exponentially with time. Distance from the Sun controls heat supplied to the surface by impacts and radiation, and thus volatile speciation, which affects thermo-chemical evolution. Planetary interiors are cooler than commonly imagined, and some may be warming even as their outer zones are cooling. The tectonic and magmatic activity of the rocky bodies is weak and shallow, and is declining with time.

This chapter evaluates mechanisms for heat transfer in large bodies, which include several processes that occur on scales and/or conditions that cannot be reproduced in the laboratory. Planetary interiors contrast with laboratory conditions by being layered, self-compressed spheroids, and moreover are open systems with internally graded gravitational acceleration, high temperatures, and high pressures. The large time- and length-scales of planets permit diffusion of visible radiation, even within their metallic cores. Advection of fluids coexisting with solids is very important in planets, due to fluid buoyancy, mobility, low viscosity, and their ability to carry latent heat and heat-producing elements: such behavior is covered in detail in this chapter. Theoretical problems in mantle convection models are reviewed, which include not conserving mass, and incorrectly representing the response of condensed matter to differential stress as the diffusion of momentum, rather than as elastic and plastic deformation.

Plate models, which purportedly describe cooling of oceanic lithosphere, violate conservation of mass and do not solve Fourier’s 2-dimensional equation. Steady-state conditions are a valid description of Earth’s lithosphere over the last 0.3 Ga. We use surface flux measurements and thermal conductivity for a layered lithosphere to calculate geotherms. Thermal boundary thicknesses of ~69 km agree with various seismic determinations. From petrologic evidence, the low velocity zone is buffered by the peridotite solidus where water content decreases downwards to nothing by 320 km. We show that most subducting slabs thermally equilibrate above 320 km, which involves thinning, but the few which are thick, steep, and fast reach 660 km. Inferred times for upper mantle recycling are consistent with ophiolite ages and modest chemical inhomogeneity. Our findings show that layers above and below 660 km are independent systems, thermally, mechanically, and probably chemically.

Forces external to the oblate spheroid shape, observed from planetary to galactic scales, are demonstrably non-central, which has important ramifications for planetary science. We simplify historic formulae and derive new analytical solutions for the gravitational potential and force outside a constant density oblate. Numerical calculations that sum point mass contributions in a >109 element mesh confirm our equations. We show that contours of constant force and potential about oblate bodies are closely approximated by two confocal families whose foci (f) respectively are (9/10)½ae and (3/5)½ae for a body with f = ae. This leads to useful approximations that address internal density variations. We demonstrate that the force on a general point is not directed towards the oblate's center, nor are forces simply proportional to the inverse square of that distance, despite forces in the equatorial and axial directions pointing towards the center. Our results explain complex dynamics of galactic systems. Because most planets and stars have an aspect ratio >0.9, the spherical approximation is reasonable except for orbits within ∼2 body radii. We show that applying the “generalized” potential, which assumes central forces, yields J2 values half those expected for oblate bodies, and probably underestimates masses of Uranus and Neptune by ∼0.2%. We show that the inner Saturnian moons are subject to non-central forces, which may affect calculations of their orbital precession. Our new series should improve interpretation of flyby data.

The large magnitude of the dimensionless Rayleigh number (Ra ∼108) for Earth’s ∼3 000 km thick mantle is considered evidence of whole mantle convection. However, the current formulation assumes behavior characteristic of gases and liquids and also assumes Cartesian geometry. Issues arising from neglecting physical properties unique to solids and ignoring the spherical shapes for planets include: (1) Planet radius must be incorporated into Ra, in addition to layer thickness, to conserve mass during radial displacements. (2) The vastly different rates for heat and mass diffusion in solids, which result from their decoupled transport mechanisms, promote stability. (3) Unlike liquids, substantial stress is needed to deform solids, which independently promotes stability. (4) High interior compression stabilizes the mantle in additional minor ways. Therefore, representing conditions for convection in solid, self-gravitating spheroids, requires modifying formulae developed for bottomheated fluids near ambient conditions under an invariant gravitational field. To derive stability criteria appropriate to solid spheres, we use dimensional analysis, and consider the effects of geometry, force competition, and microscopic behavior. We show that internal heating has been improperly accounted for in the Ra. We conclude that the lower mantle is stable for two independent reasons: heat diffusion far outpaces mass diffusion (creep) and yield strength of solids at high pressure exceeds the effective deviatoric stress. We discuss the role of partial melt in lubricating plate motion, and explain why the Ra is not applicable to the multi-component upper mantle. When conduction is insufficient to transport heat in the Earth, melt production and ascent are expected, not convection of solid rock.

Spiral galaxies are discrete spheroidal objects with highly organized, circular internal motions about a special axis. Available models do not describe these key features or explain why the central regions rotate like a solid body. Practically all previous models describe galaxies as a collection of orbiting test particles, utilize numerous fitting parameters, and require either copious amounts of surrounding dark matter that have not been detected, or modifications to Newton’s law, to fit the observed dependence of equatorial velocity on radius. Our paper probes the reasonable alternative that galaxies are discrete, spinning objects. Our analytical forward models, constructed by applying the virial theorem and Newton’s law to Maclaurin’s spinning spheroids with varying internal density, explain why galactic rotation is organized into this three-dimensional shape. Without invoking dark matter, our spin model explains why the outermost rotational velocities are nearly constant, yet depend on galaxy size, and, with no free parameters, provides masses of 14 important galaxies consistent with their luminosities. We show that proposed modifications to Newton’s law compensate for the dynamical differences between a flattened, spinning, Newtonian spheroid, and a collection of orbits.

Recent work discloses shortcomings in models for heat transport properties. Some errors involve simple numerical factors, but others are substantial, such as not accounting for the finite lifetimes of interactions, nor weighting thermal conductivity in summations, nor realizing that thermal diffusivity depends on thickness. This chapter discusses the consequences in view of the ambiguities contributed by multiplied parameters in models, and provides an improved model for heat transport in solids. We show that radiative diffusion describes all heat transfer, when the association of various processes in matter with limited frequency ranges of light is addressed. Dimensionless thermal conductivity of solids from 0 to ~300K, including the cryogenic peak, is fit by one parameter; but including high temperature data requires more. Theoretical pressure derivatives agree well with reliable data. To better understand heat transport requires measuring transport properties as a function of length and spectra at low frequencies and temperatures.