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Algorithms for computing neutrino oscillation probabilities in sharply varying matter potentials such as the Earth are becoming increasingly important. As the next generation of experiments, DUNE and HyperK as well as the IceCube upgrade and KM3NeT, come online, the computational cost for atmospheric and solar neutrinos will continue to increase. To address these issues, we expand upon our previous algorithm for long-baseline calculations to efficiently handle probabilities through the Earth for atmospheric, nighttime solar, and supernova neutrinos. The algorithm is fast, flexible, and accurate. It can handle arbitrary Earth models with two different schemes for varying density profiles. We also provide a c++ implementation of the code called NuFast-Earth along with a detailed user manual. The code intelligently keeps track of repeated calculations and only recalculates what is needed on each successive call which can also help provide significant speed-ups.

The possibility of the emergence of a stratified region in the uppermost part of the Earth's outer core with long-term magnetic field generation is assessed, taking into account uncertainties in the thermal conductivity of the Earth's core and the present-day heat flow across the core-mantle boundary (CMB). The radial structures of the Earth's outer core are calculated for various values of thermal conductivity and CMB heat flow using a one-dimensional thermo-chemical model. The results show that there exist solutions that allow both emergence of stable stratification and long-term magnetic field generation although their thickness of stratified region is thinner than 100 km. In order to satisfy both emergence of stratified region and long-term magnetic field generation, possible value of the present-day CMB heat flow (13-15 TW) suggests a thermal conductivity of 77-121 W/m/K at CMB, which is in good agreement with the values estimated from the electrical conductivity measurements under the Earth' s core condition. The thickness of the stratified region in this case is about 50 km, which is also consistent with the thickness of the stratified region estimated from the geomagnetic s

Migration of bodies under the gravitational influence of almost formed planets was studied, and probabilities of their collisions with the Earth and other terrestrial planets were calculated. Based on the probabilities, several conclusions on the accumulation of the terrestrial planets have been made. The outer layers of the Earth and Venus could accumulate similar planetesimals from different regions of the feeding zone of the terrestrial planets. The probabilities of collisions of bodies during their dynamical lifetimes with the Earth could be up to 0.001-0.01 for some initial semi-major axes between 3.2 and 3.6 AU, whereas such probabilities did not exceed 10^-5 at initial semi-major axes between 12 and 40 AU. The total mass of water delivered to the Earth from beyond Jupiter's orbit could exceed the mass of the Earth's oceans. The zone of the outer asteroid belt could be one of the sources of the late-heavy bombardment. The bodies that came from the zone of Jupiter and Saturn typically collided with the Earth and the Moon with velocities from 23 to 26 km/s and from 20 to 23 km/s, respectively.

This article investigates long-term orbits within the Earth's magnetosphere, specifically focusing on orbits where the argument of periapsis is synchronized with changes induced by lunar gravity assists and the Earth's argument of latitude over a complete orbital period in Earth-Moon resonance. In the Earth-Moon rotating frame, resonance orbits appear repetitive; however, the argument of periapsis shifts due to the third-body effects from lunar flybys. The extent of this shift is influenced by the Jacobi integral associated with the resonance orbit. To identify feasible resonance orbits and the optimal Jacobi integral, we map the argument of periapsis change against the Jacobi integral for each prospective orbit. This synchronization allows the spacecraft to remain within a confined region in space when observed from the Sun-Earth rotating frame. Finally, the article discusses the applications of these long-term Earth magnetosphere science orbits, including orbit-orientation reconfiguration (station keeping) and stability.

Light volatile elements in lunar regolith are thought to be a mixture of the solar wind and Earth's atmosphere, the latter sourced in the absence of geomagnetic field. However, the extent to which both the current and primitive geodynamo influence the transport of terrestrial ions still remains unclear, and this uncertainty is further complicated by the enigmatic composition and poorly constrained location of the Eoarchean exosphere. Here we use 3-D MHD numerical simulations with present-day magnetized and Archean unmagnetized atmospheres to investigate how Earth's intrinsic magnetic field affects this transfer, aiming to constrain how and when the lunar isotopic signature provides a record of Earth's paleoatmosphere. We find that atmospheric transfer is efficient only when the Moon is within Earth's magnetotail. The non-solar contribution to the lunar soil is best explained by implantation during the long history of the geodynamo, rather than any short, putatively unmagnetized epoch of early Earth. This further suggests the history of the terrestrial atmosphere, spanning billions of years, could be preserved in buried lunar soils. Our results indicate that the elemental abundances

The Earth's mantle has elevated Fe$^{3+}$ relative to those of other rocky bodies, yet the oxidation- and electronic state of iron at extreme pressures is poorly known. We present in-situ energy-domain synchrotron Mössbauer spectra of $^{57}$Fe-enriched silicate glasses at 298 K from 1 bar to 174 GPa in a diamond anvil cell. Glasses were synthesised with Fe$^{3+}$/[Fe$^{3+}$ + Fe$^{2+}$] from 0.02 $\pm$ 0.02 to 1.00 $\pm$ 0.02, as determined by colourimetry. While pure Fe$^{3+}$-basaltic glass shows minimal changes up to 174 GPa, the spectra of Fe$^{2+}$-peridotitic and basaltic glasses are fit by two doublets, D$_1$ and D$_2$. At 1 bar, their relative intensities are $\sim$92 % and $\sim$8 %, respectively, but the integral area ratio, D$_2$/(D$_1$ + D$_2$), reaches 0.65 by 172 GPa. Because this transition is reversible with pressure and no metallic iron is detected, the D$_2$ feature is Fe$^{2+}$ low spin (LS), whereas D$_1$ is Fe$^{2+}$ high spin (HS). Consequently, the Fe$^{3+}$/[Fe$^{3+}$+Fe$^{2+}$] of planetary mantles reach a maximum near $\sim$40 GPa, before decreasing at higher pressures due to the stabilisation of Fe$^{2+}_{\mathrm{LS}}$. This peak coincides with estimated

The bulk silicate Earth (BSE) is depleted in moderately volatile elements, indicating Earth formed from a mixture of volatile-rich and -poor materials. To better constrain the origin and nature of Earth's volatile-rich building blocks, we determined the mass-dependent isotope compositions of Ge in carbonaceous (CC) and enstatite chondrites. We find that, similar to other moderately volatile elements, the Ge isotope variations among the chondrites reflect mixing between volatile-rich, isotopically heavy matrix and volatile-poor, isotopically light chondrules. The Ge isotope composition of the BSE is within the chondritic range and can be accounted for as a ~2:1 mixture of CI and enstatite chondrite-derived Ge. This mixing ratio appears to be distinct from the ~1:2 ratio inferred for Zn, reflecting the different geochemical behavior of Ge (siderophile) and Zn (lithophile), and suggesting the late-stage addition of volatile-rich CC materials to Earth. On dynamical grounds it has been argued that Earth accreted CC material through a few Moon-sized embryos, in which case the Ge isotope results imply that these objects were volatile-rich, presumably because they were either undifferentia

Earth's surface is deficient in available forms of many elements considered limiting for prebiotic chemistry. In contrast, many extraterrestrial rocky objects are rich in these same elements. Limiting prebiotic ingredients may, therefore, have been delivered by exogenous material; however, the mechanisms by which exogeneous material may be reliably and non-destructively supplied to a planetary surface remains unclear. Today, the flux of extraterrestrial matter to Earth is dominated by fine-grained cosmic dust. Although this material is rarely discussed in a prebiotic context due to its delivery over a large surface area, concentrated cosmic dust deposits are known to form on Earth today due to the action of sedimentary processes. Here we combine empirical constraints on dust sedimentation with dynamical simulations of dust formation and planetary accretion to show that localized sedimentary deposits of cosmic dust could have accumulated in arid environments on early Earth, in particular glacial settings that today produce cryoconite sediments. Our results challenge the widely held assumption that cosmic dust is incapable of fertilizing prebiotic chemistry. Cosmic dust deposits may

The main idea of this challenging research is to revisit the solar-centric dynamics of Earth around the Sun in analysis of its position on 13 April 2029 close to asteroid Apophis which is supposed to be moving in fly-by near the Earth on its orbit. As of now, we can be sure that trajectory of Apophis is well-known with respect to the center of Sun. Also, NASA experts calculated that relative distance between center of Earth and Apophis should be less than 38 thousands of kilometers during closest Apophis approach to the Earth. But the reasonable question is: will the center of Earth be at the predicted position at the beginning of April 2029? The matter is that NASA solving procedure disregards influence of Milankovich cycles to the orbit of Earth but alternative concept suggests another solution (with additional quasi-periodic deviation from their solution, proportional to square of eccentricity of Earth orbit around the Sun equals to ~ 0.017). So, possible perturbation of Earth orbit is likely to be proportional to (0.017)$^2$ ~ 0.03% from 1 a.e. or ~ 43 200 km which could be compared with gap between Earth and Apophis during closest Apophis approach to Earth in April 2029.

The Hadean, once thought to be uninhabitable and tumultuous, has more recently been recontextualized as a clement time in which oceans, land, and life likely appeared on Earth. This non-exhaustive chapter follows multiple threads from planet formation to the origin of life. We place significant emphasis on the solar system context for the Earth, the timing and nature of crustal formation and the evolution of the surface and atmosphere. Several scenarios for prebiotic chemistry are also discussed including atmospheric photochemistry, wet-dry and freeze-thaw cycles, and hydrothermal vent systems. We attempt to draw connections between the large-scale, planetary processes and various origin of life pathways to illustrate possible overlaps and correlations. In detail, we conclude with and discuss the "impact of impacts" to show how asteroid and comet impacts during the Hadean may have affected many of these processes and scenarios, from generating land to altering the chemical composition and oxidation state of the early Earth's atmosphere and surface.

One in every two atoms in the Earth, Mars, and the Moon is oxygen; it is the third most abundant element in the solar system. The oxygen isotopic compositions of the terrestrial planets are different from those of the Sun and demonstrate that these planets are not direct compositional analogs of the solar photosphere. Likewise, the Suns O/Fe, Fe/Mg and Mg/Si values are distinct from those of inner solar system chondrites and terrestrial planets. These four elements (O, Fe, Mg, Si) make up about 94% by mass of the rocky planets and their abundances are determined uniquely using geophysical, geochemical and cosmochemical constraints. The rocky planets grew rapidly from planetesimals, most of which were differentiated, having a core and a mantle, before being accreted. Planetary growth in the early stages of protoplanetary disk evolution was rapid and was only partially recorded by the meteoritic record. The noncarbonaceous meteorites (NC) provide insights into the early history of the inner solar system and are used to construct a framework for how the rocky planets were assembled. NC chondrites have chondrule ages that are two to three million years younger than t_zero (the age of c

Astronomical solutions provide calculated orbital and rotational parameters of solar system bodies based on the dynamics and physics of the solar system. Application of astronomical solutions in the Earth sciences has revolutionized our understanding in at least two areas of active research. (i) The Astronomical (or Milankovic) forcing of climate on time scales > ~10 kyr and (ii) the dating of geologic archives. The latter has permitted the development of the astronomical time scale, widely used today to reconstruct highly accurate geological dates and chronologies. The tasks of computing vs. applying astronomical solutions are usually performed by investigators from different backgrounds, which has led to confusion and recent inaccurate results on the side of the applications. Here we review astronomical solutions and Milankovic forcing in the Earth sciences, primarily aiming at clarifying the astronomical basis, applicability, and limitations of the solutions. We provide a summary of current up-to-date and outdated astronomical solutions and their valid time span. We discuss the fundamental limits imposed by dynamical solar system chaos on astronomical calculations and geologi

Understanding planetary habitability is one of the major challenges of the current scientific era, particularly given the discovery of a large and diverse terrestrial exoplanet population. Discerning the primary factors that contribute to planetary habitability may be extracted through a detailed examination of the terrestrial planets within the Solar System, most particularly Venus, Earth, and Mars, and the evolution of their interiors and atmospheres through time. Here, we provide a detailed description of the fundamental properties of these three planets, the effects of solar evolution, and the potential contributions of these various aspects toward driving their evolutionary pathways. We argue that evolution of Venus, Earth, and Mars provide essential templates from which a more comprehensive approach toward the study of planetary habitability may be derived.

Super-Earths, objects slightly larger than Earth and slightly smaller than Uranus, have found a special place in exoplanetary science. As a new class of planetary bodies, these objects have challenged models of planet formation at both ends of the spectrum and have triggered a great deal of research on the composition and interior dynamics of rocky planets in connection to their masses and radii. Being relatively easier to detect than an Earth-sized planet at 1 AU around a G star, super-Earths have become the focus of worldwide observational campaigns to search for habitable planets. With a range of masses that allows these objects to retain moderate atmospheres and perhaps even plate tectonics, super-Earths may be habitable if they maintain long-term orbits in the habitable zones of their host stars. Given that in the past two years a few such potentially habitable super-Earths have in fact been discovered, it is necessary to develop a deep understanding of the formation and dynamical evolution of these objects. This article reviews the current state of research on the formation of super-Earths and discusses different models of their formation and dynamical evolution.

Quantifying the energy budget of Earth in the first few million years following the Moon-forming giant impact is vital to understanding Earth's initial thermal state and the dynamics of lunar tidal evolution. After the impact, the body was substantially vaporized and rotating rapidly, very different from the planet we know today. The subsequent evolution of Earth's energy budget, as the body cooled and angular momentum was transferred during lunar tidal recession, has not been accurately calculated with all relevant energy components included. Here, we use giant impact simulations and planetary structure models to calculate the energy budget at stages in Earth's evolution. We show that the figure and internal structure of Earth changed substantially during its post-impact evolution and that changes in kinetic, potential, and internal energy were all significant. These changes have important implications for the dynamics of tidal recession and the thermal structure of early Earth.

The search for extrasolar Earth-like planets is underway. Over 100 extrasolar giant planets are known to orbit nearby sun-like stars, including several in multiple-planet systems. These planetary systems are stepping stones for the search for Earth-like planets; the technology development, observational strategies, and science results can all be applied to Earth-like planets. Stars much less massive than the sun the most common stars in our Galaxy are being monitored for the gravitational influence of Earth-like planets. Although Earth-like planets orbiting sun-like stars are much more difficult to detect, space missions are being built to detect them indirectly due to their effects on the parent star and to quantify fundamental factors such as terrestrial planet frequency, size distribution, and mass distribution. Extremely ambitious space programs are being developed to directly detect Earth-like planets orbiting sun-like stars, and must tackle the immense technological challenge of blocking out the light of the parent star, which is brighter than the planet by six to ten orders of magnitude. Direct detection of radiation from the planet is necessary for the definitive goal of th

Carbon is an essential element for the existence and evolution of life on Earth. Its abundance in Earth's crust and mantle (the Bulk Silicate Earth, BSE) is surprisingly high given that carbon is strongly siderophile (metal-loving) at low pressures and temperatures, and hence should have segregated almost completely into Earth's core during accretion. Estimates of the concentration of carbon in the BSE lie in the range 100-260 ppm and are much higher than expected based on simple models of core-mantle differentiation. Here we show through experiments at the putative conditions of Earth's core formation (49-71 GPa and 3600-4000 K) that carbon is significantly less siderophile at these conditions than at the low pressures ($\leq$13 GPa) and temperatures ($\leq$2500 K) of previous large volume press studies, but at least an order of magnitude more siderophile than proposed recently based on an experimental approach that is similar to ours. Using our new data along with previously published results, we derive a new parameterization of the pressure-temperature dependence of the metal-silicate partitioning of carbon. We apply this parameterization in a model that combines planet formatio

Conventional planet formation theory suggests that chondritic materials have delivered crucial atmospheric and hydrospheric elements such as carbon (C), nitrogen (N), and hydrogen (H) onto primitive Earth. However, recent measurements highlight the significant elemental ratio discrepancies between terrestrial parent bodies and the supposed planet building blocks. Here we present a volatile evolution model during the assembly of Earth and Earth-like planets. Our model includes impact losses, atmosphere-mantle exchange, and time dependent effects of accretion and outgassing calculated from dynamical modeling outcomes. Exploring a wide range of planetesimal properties (i.e., size and composition) as well as impact history informed by N-body accretion simulations, we find that while the degree of CNH fractionation has inherent stochasticity, the evolution of C/N and C/H ratios can be traced back to certain properties of the protoplanet and projectiles. Interestingly, the majority of our Earth-like planets acquire superchondritic final C/N ratios, implying that the volatile elemental ratios on terrestrial planets are driven by the complex interplay between delivery, atmospheric ablation

Using PREM as a reference model for the Earth density distribution we investigate in the present article the sensitivity of the ORCA detector to deviations of the Earth i) outer core (OC) density, ii) inner core (IC) density, iii) total core density, and iv) mantle density, from their respective PREM densities. The analysis is performed by studying the effects of the Earth matter on the oscillations of atmospheric $ν_μ$, $ν_e$, $\barν_μ$ and $\barν_e$. We present results which, in particular, illustrate the dependence of the ORCA sensitivity to the OC, IC, core and mantle densities on the type of systematic uncertainties used in the analysis, on the value of the atmospheric neutrino mixing angle $θ_{23}$, on whether the Earth mass constraint is implemented or not, and on the way it is implemented, and on the type - with normal ordering (NO) or inverted ordering (IO) - of the light neutrino mass spectrum. We show, in particular, that in the "most favorable" NO case of implemented Earth mass constraint, "minimal" systematic errors and $\sin^2θ_{23}=0.58$, ORCA can determine, e.g., the OC (mantle) density at $3σ$ C.L. after 10 years of operation with an uncertainty of (-18\%)/+15\% (o