Planetary Model Research Articles

On the Equant Point for the Planets and the Moon

The introduction of the equant point signified a major improvement in the history of planetary models. Thanks to its incorporation in ancient planetary hypotheses, Greek astronomy reached a higher degree of accuracy in its predictive capabilities than any of its predecessors, an accuracy that would not be surpassed until as late as the seventieth century, when Kepler postulated his laws. In the Almagest, Ptolemy explains how he arrived at the necessity of the introduction of the equant point for Venus and Mercury. There is, however, some unsolved matter surrounding the argument Ptolemy gives and most scholars dispute that his observations of Venus were in fact the empirical basis from which Ptolemy built his model. These considerations led scholars to wonder about the real path Ptolemy took to discover the equant. In this paper, we present a simple argument through which Ptolemy might have arrived to the conclusion of the existence of an equant for the models of the planets, and to his conclusion of the bisection of the equant’s eccentricity by the centre of the deferent. Moreover, we show that this same argument could have been used to solve the problems posed by the second lunar anomaly.

Application of an evolution strategy in planetary ephemeris modeling

Classical planetary ephemeris construction comprises three major steps which are to be performed iteratively: numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of observations (reduction step), and optimization of model parameters (adjustment step). In future, this approach may become challenged by further refinements in force modeling (e.g. inclusion of much more significant minor bodies than in the past), an ever-growing number of planetary observations (e.g. the vast amount of spacecraft tracking data), and big data issues in general. In order to circumvent the need for both the inversion of normal equation matrices and the determination of partial derivatives, and to prepare the ephemeris for applications apart from stand-alone solar-system planetary orbit calculations, here we propose an alternative ephemeris construction method. The main idea is to solve it as an optimization problem by straightforward direct evaluation of the whole set of mathematical formulas, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and potential numerical difficulties. The usual gradient search is replaced by a stochastic search, namely an evolution strategy, the latter of which is perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach allows for multi-criteria optimization and time-varying optima. These issues will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of a generalized physical state (orbit, size, shape, rotation, gravity, …) of celestial bodies (planets, satellites, asteroids, or comets), and/or if one seeks near real-time solutions. Here, we outline the general idea and exemplarily optimize high-correlated asteroidal ring model parameters (total mass and heliocentric radius), and individual asteroid masses, based on simulated observations.

Equation of State of SiC at Extreme Conditions: New Insight Into the Interior of Carbon‐Rich Exoplanets

AbstractThere is a direct relation between the composition of a host star and that of the planets orbiting around it. As such, the recent discovery of stars with unusual chemical composition, notably enriched in carbon instead of oxygen, supports the existence of exoplanets with a chemistry dominated by carbides instead of oxides. Accordingly, several studies have been recently conducted on the Si–C binary system at high pressure and temperature. Nonetheless, the properties of carbides at the pressure‐temperature conditions of exoplanets interiors are still inadequately constrained, effectively hampering reliable planetary modeling. Here we present an in situ X‐ray diffraction study of the Si–C binary system up to 200 GPa and 3,500 K, significantly enlarging the pressure range explored by previous experimental studies. The large amount of collected data allows us to properly investigate the phase diagram and to refine the Clapeyron slope of the transition line from the zinc blende to the rock salt structure. Furthermore, the pressure‐volume‐temperature equation of state is provided for the high‐pressure phase, characterized by low compressibility and thermal expansion. Our results are used to model idealized C‐rich exoplanets of end‐members composition. In particular, we derived mass‐radius relations and performed numerical simulations defining rheological parameters and initial conditions which lead to onset of convection in such SiC planets. We demonstrate that if restrained to silicate‐rich mantle compositions, the interpretation of mass‐radius relations may underestimate the interior diversity of exoplanets.

MOA-2015-BLG-337: A Planetary System with a Low-mass Brown Dwarf/Planetary Boundary Host, or a Brown Dwarf Binary

Abstract We report on the discovery and analysis of the short-timescale binary-lens microlensing event, MOA-2015-BLG-337. The lens system could be a planetary system with a very low-mass host, around the brown dwarf (BD)/planetary-mass boundary, or a BD binary. We found two competing models that explain the observed light curves with companion/host mass ratios of q ∼ 0.01 and ∼0.17, respectively. A significant finite source effect in the best-fit planetary model (q ∼ 0.01) reveals a small angular Einstein radius of θ E ≃ 0.03 mas, which favors a low-mass lens. We obtain the posterior probability distribution of the lens properties from a Bayesian analysis. The results for the planetary models strongly depend on a power-law index in planetary-mass regime, α pl, in the assumed mass function. In summary, there are two solutions of the lens system: (1) a BD/planetary-mass boundary object orbited by a super-Neptune (the planetary model with α pl = 0.49) and (2) a BD binary (the binary model). If the planetary models are correct, this system can be one of a new class of planetary system, having a low host mass and also a planetary-mass ratio (q < 0.03) between the companion and its host. The discovery of the event is important for the study of planetary formation in very low-mass objects. In addition, it is important to consider all viable solutions in these kinds of ambiguous events in order for the future comprehensive statistical analyses of planetary/binary microlensing events.

The Spectral Analysis of Labor Force and Profit of Construction Materials Distribution Companies in Romania Analogue Spectrum of Light in Physics

In physics, spectral studies have been observed and quantified since 1822 when Fourier J. (1822) used them in his analysis of thermal conduction. Further, Balmer (1885), studying the hydrogen atom, noticed the existence of the four lengths waveform which characterize the spectrum of the hydrogen atom. Following the research, it determined the number of 364.6 nm that was identified in each hydrogen spectral line. Therefore, Balmer determined the equation to determine the wavelength of the emission or absorption lines. Three years later, physicist Johannes Rydberg generalized Balmer's equation, thus determining the constant Rydberg. Rutherford's model was later improved and in 1913 was introduced Bohr's model and converts justify empirical results in terms of fundamental physical constants. Subsequently, a significant number of physicists approached the spectral analyzes of electromagnetic radiation (in different fields: ultraviolet, X-rays, infrared) and analyzed their characteristics: frequency, amplitude, spectral density. In the economy, the first papers that dealt with spectral analysis emerged in 1960 and consisted of the analysis of seasonal adjustment procedures for time series at macroeconomic level. Starting from the cross-spectral methods were developed methods such as analysis of the movement in the series, the time-frequency methods, etc. The fluctuating nature of the activities of different sectors of activity involves different oscillations in terms of amplitude and frequency, but also oscillations characterized by a higher or lower propagation period, which determines the evolution of economic indicators. We can classify the propagation periods of activities according to the level of the characteristics that determine them in time units (time intervals). Thus, the oscillation frequency will be given by the number of periods of propagation activities. Depending on the oscillation period will determine their average, and the amplitude of oscillation is determined by peak line and the average determined. Starting from the ultraviolet spectrum in physics and the spectral analyzes made by physicists, analogy we find in the economy elements that refer to the fervent oscillations and form "color strips" and "spectrum". To make "spectral analysis" of such a fluctuating process in terms of frequency and amplitude need a sufficient number of numerical data on the evolution of an economic process.

Insulator-metal transition in dense fluid deuterium.

Dense fluid metallic hydrogen occupies the interiors of Jupiter, Saturn, and many extrasolar planets, where pressures reach millions of atmospheres. Planetary structure models must describe accurately the transition from the outer molecular envelopes to the interior metallic regions. We report optical measurements of dynamically compressed fluid deuterium to 600 gigapascals (GPa) that reveal an increasing refractive index, the onset of absorption of visible light near 150 GPa, and a transition to metal-like reflectivity (exceeding 30%) near 200 GPa, all at temperatures below 2000 kelvin. Our measurements and analysis address existing discrepancies between static and dynamic experiments for the insulator-metal transition in dense fluid hydrogen isotopes. They also provide new benchmarks for the theoretical calculations used to construct planetary models.

Buildup of Abiotic Oxygen and Ozone in Moist Atmospheres of Temperate Terrestrial Exoplanets and Its Impact on the Spectral Fingerprint in Transit Observations

Abstract We investigate the abiotic production of oxygen and its photochemical byproduct ozone through water vapor photolysis in moist atmospheres of temperate terrestrial exoplanets. The amount of water vapor available for photolysis in the middle atmosphere of a planet can be limited by an atmospheric cold-trap, the formation of which largely depends on the amount of noncondensable gases. We study this effect using a photochemical model coupled to a 1D radiative-convective equilibrium model in atmospheres with N2, CO2, and H2O as the main constituents. We find that in atmospheres with a low N2 inventory, water vapor mixing ratios in the middle atmosphere can be more than two orders of magnitude higher compared to atmospheres with an Earth-like N2 inventory. Without a strong surface sink, the noncondensable oxygen can build up rapidly, drying out the upper atmosphere. With a moderate surface sink, the planet can approach a steady state with significant oxygen mixing ratios in which oxygen production is balanced by surface uptake. We use a radiative transfer model to study the spectroscopic fingerprint of these atmospheres in transit observations. Spectral signatures of abiotic oxygen and ozone can be of comparable magnitude as in spectra of Earth seen as an exoplanet. Middle atmospheric water vapor is unlikely to be a usable indicator of the abiotic origin of oxygen because of the influence of oxygen on the water vapor distribution. This suggests that atmospheric oxygen and ozone cannot be used as binary bioindicators and that their interpretation will likely require atmospheric and planetary models.

UV Surface Environments and Atmospheres of Earth-like Planets Orbiting White Dwarfs

Abstract An Earth-like exoplanet orbiting a white dwarf (WD) would be exposed to different UV environments than Earth, influencing both its atmospheric photochemistry and UV surface environment. Through the use of a coupled 1D climate-photochemistry code, we model atmospheres of Earth-like planets in the habitable zone (HZ) of WDs for surface temperatures between 6000 and 4000 K, corresponding to about 7 billion years of WD evolution, and discuss the evolution of planetary models in the HZ during that evolution.

On the Feasibility of Intense Radial Velocity Surveys for Earth-Twin Discoveries

This work assesses the potential capability of the next generation of high-precision Radial Velocity (RV) instruments for Earth-twin exoplanet detection. From the perspective of the importance of data sampling, the Terra Hunting Experiment aims to do this through an intense series of nightly RV observations over a long baseline on a carefully selected target list, via the brand-new instrument HARPS3. This paper describes an end-to-end simulation of generating and processing such data to help us better understand the impact of uncharacterised stellar noise in the recovery of Earth-mass planets with orbital periods of the order of many months. We consider full Keplerian systems, realistic simulated stellar noise, instrument white noise, and location-specific weather patterns for our observation schedules. We use Bayesian statistics to assess various planetary models fitted to the synthetic data, and compare the successful planet recovery of the Terra Hunting Experiment schedule with a typical reference survey. We find that the Terra Hunting Experiment can detect Earth-twins in the habitable zones of solar-type stars, in single and multi-planet systems, and in the presence of stellar signals. Also that it out-performs a typical reference survey on accuracy of recovered parameters, and that it performs comparably to an uninterrupted space-based schedule.

Spitzer Opens New Path to Break Classic Degeneracy for Jupiter-mass Microlensing Planet OGLE-2017-BLG-1140Lb

Abstract We analyze the combined Spitzer and ground-based data for OGLE-2017-BLG-1140 and show that the event was generated by a Jupiter-class planet orbiting a mid-late M dwarf that lies in the foreground of the microlensed Galactic-bar source star. The planet–host projected separation is , i.e., well beyond the snow line. By measuring the source proper motion from ongoing long-term OGLE imaging and combining this with the lens-source relative proper motion derived from the microlensing solution, we show that the lens proper motion is consistent with the lens lying in the Galactic disk, although a bulge lens is not ruled out. We show that while the Spitzer and ground-based data are comparably well fitted by planetary (i.e., binary-lens (2L1S)) and binary-source (1L2S) models, the combination of Spitzer and ground-based data decisively favors the planetary model. This is a new channel to resolve the 2L1S/1L2S degeneracy, which can be difficult to break in some cases.

Ptolemaic Orbs in Twelfth-Century England: A Study and Edition of the Anonymous Liber de motibus planetarum

This article offers the first study and critical edition of the Liber de motibus planetarum (Lmp), a neglected Latin text on planetary theory that appears anonymously and without any clear indication of date or place of origin in nine manuscripts of the thirteenth to fifteenth centuries. An analysis of its sources and parallels to other Latin treatises and translations from Arabic indicates that the Lmp originated in England in the third quarter of the twelfth century. A plausible terminus post quem is provided by the appearance of similar passages in the anonymous treatise Ptolomeus et multi sapientum (1145), which can be linked to Abraham Ibn Ezra and his astronomical tables for the meridian of Pisa. The Lmp would appear to be historically significant for its relatively detailed textual and diagrammatic presentations of Ptolemy’s planetary models as composed of multipart physical orbs. While it is generally accepted that physicalized or ‘orbed’ versions of these models entered Latin astronomy through the influence of Ibn al-Haytham’s Maqāla fī hayʾat al-ʿālam (On the Configuration of the World), the early history of this idea in a Latin context has not been studied to any deeper extent. In this regard, the Lmp offers clear evidence that Ptolemaic orbs and diagrams representing them already were a part of Latin astronomy three centuries before Peuerbach’s Theoricae novae planetarum (1454).

Development and validation of an integrated planetary gear set permanent magnet electric motor power loss model

Abstract This study proposes a methodology to predict power losses of traction motor having an integrated planetary gear set permanent magnet electric motor, including both load-dependent and load-independent power loss components. The methodology combines a planetary gear set loss model which accounts for sliding and rolling losses at the external and internal gear mesh contact interfaces, a bearing mechanical and drag loss model, a gear drag loss model, an external and internal gear mesh pocketing loss model, a permanent magnet synchronous machine iron, and copper loss model. Power loss measurements from a developed prototype traction motor having integrated planetary gear set permanent magnet electric motor is compared to model predictions to successfully demonstrate the accuracy of the proposed methodology.

A third way: Developing a planetary spirituality

AbstractGlobalization has brought the world closer together, but it has come with a cost. Over the past several decades, it seems our only two options for moving ahead are through continued globalization of a neoliberal model of economics as usual, or some sort of return to nationalism. Many countries are facing the challenges of globalization and opting for one or the other of these models to deal with a globalized world. Might there be a third way? Perhaps religious leaders can help bring about a third, planetary model that helps us to navigate between the ills of neoliberalism and nationalism, and toward an understanding of a planetary vision of spirituality, ethics, and citizenship.

Dynamical models to explain observations with SPHERE in planetary systems with double debris belts

Context.A large number of systems harboring a debris disk show evidence for a double belt architecture. One hypothesis for explaining the gap between the debris belts in these disks is the presence of one or more planets dynamically carving it. For this reason these disks represent prime targets for searching planets using direct imaging instruments, like the Spectro-Polarimetric High-constrast Exoplanet Research (SPHERE) at the Very Large Telescope.Aim.The goal of this work is to investigate this scenario in systems harboring debris disks divided into two components, placed, respectively, in the inner and outer parts of the system. All the targets in the sample were observed with the SPHERE instrument, which performs high-contrast direct imaging, during the SHINE guaranteed time observations. Positions of the inner and outer belts were estimated by spectral energy distribution fitting of the infrared excesses or, when available, from resolved images of the disk. Very few planets have been observed so far in debris disks gaps and we intended to test if such non-detections depend on the observational limits of the present instruments. This aim is achieved by deriving theoretical predictions of masses, eccentricities, and semi-major axes of planets able to open the observed gaps and comparing such parameters with detection limits obtained with SPHERE.Methods.The relation between the gap and the planet is due to the chaotic zone neighboring the orbit of the planet. The radial extent of this zone depends on the mass ratio between the planet and the star, on the semi-major axis, and on the eccentricity of the planet, and it can be estimated analytically. We first tested the different analytical predictions using a numerical tool for the detection of chaotic behavior and then selected the best formula for estimating a planet’s physical and dynamical properties required to open the observed gap. We then apply the formalism to the case of one single planet on a circular or eccentric orbit. We then consider multi-planetary systems: two and three equal-mass planets on circular orbits and two equal-mass planets on eccentric orbits in a packed configuration. As a final step, we compare each couple of values (Mp,ap), derived from the dynamical analysis of single and multiple planetary models, with the detection limits obtained with SPHERE.Results.For one single planet on a circular orbit we obtain conclusive results that allow us to exclude such a hypothesis since in most cases this configuration requires massive planets which should have been detected by our observations. Unsatisfactory is also the case of one single planet on an eccentric orbit for which we obtained high masses and/or eccentricities which are still at odds with observations. Introducing multi planetary architectures is encouraging because for the case of three packed equal-mass planets on circular orbits we obtain quite low masses for the perturbing planets which would remain undetected by our SPHERE observations. The case of two equal-mass planets on eccentric orbits is also of interest since it suggests the possible presence of planets with masses lower than the detection limits and with moderate eccentricity. Our results show that the apparent lack of planets in gaps between double belts could be explained by the presence of a system of two or more planets possibly of low mass and on eccentric orbits whose sizes are below the present detection limits.

Habitable Evaporated Cores and the Occurrence of Panspermia Near the Galactic Center

Abstract Black holes growing via the accretion of gas emit radiation that can photoevaporate the atmospheres of nearby planets. Here, we couple planetary structural evolution models of sub-Neptune-mass planets to the growth of the Milky Way’s central supermassive black hole, Sgr A*, and investigate how planetary evolution is influenced by quasar activity. We find that, out to ∼20 pc from Sgr A*, the XUV flux emitted during its quasar phase can remove several percent of a planet’s H/He envelope by mass; in many cases, this removal results in bare rocky cores, many of which are situated in the habitable zones of G-type stars. Near the Galactic Center, the erosion of sub-Neptune-sized planets may be one of the most prevalent channels by which terrestrial super-Earths are created. As such, the planet population demographics may be quite different close to Sgr A* than in the galactic outskirts. The high stellar densities in this region (about seven orders of magnitude greater than the solar neighborhood) imply that the distance between neighboring rocky worlds is short (500–5000 au). The proximity between potentially habitable terrestrial planets may enable the onset of widespread interstellar panspermia near the nuclei of our galaxy. More generally, we predict these phenomena to be ubiquitous for planets in nuclear star clusters and ultra-compact dwarfs. Globular clusters, on the other hand, are less affected by the central black holes.

Mapping the Wind Hazard of Global Tropical Cyclones with Parametric Wind Field Models by Considering the Effects of Local Factors

Tropical cyclones (TCs) cause catastrophic loss in many coastal areas of the world. TC wind hazard maps can play an important role in disaster management. A good representation of local factors reflecting the effects of spatially heterogeneous terrain and land cover is critical to evaluation of TC wind hazard. Very few studies, however, provide global wind hazard assessment results that consider detailed local effects. In this study, the wind fields of historical TCs were simulated with parametric models in which the planetary boundary layer models explicitly integrate local effects at 1 km resolution. The topographic effects for eight wind directions were quantified over four types of terrain (ground, escarpment, ridge, and valley), and the surface roughness lengths were estimated from a global land cover map. The missing TC parameters in the best track datasets were reconstructed with local regression models. Finally, an example of a wind hazard map in the form of wind speeds under a 100-year return period and corresponding uncertainties was created based on a statistical analysis of reconstructed historical wind fields over seven of the world’s ocean basins.

Magnetic properties of Proxima Centauri b analogues

The discovery of a planet around the closest star to our Sun, Proxima Centauri, represents a quantum leap in the testability of exoplanetary models. Unlike any other discovered exoplanet, models of Proxima b could be contrasted against near future telescopic observations and far future in-situ measurements. In this paper we aim at predicting the planetary radius and the magnetic properties (dynamo lifetime and magnetic dipole moment) of Proxima b analogues (solid planets with masses of ∼1−3M⊕, rotation periods of several days and habitable conditions). For this purpose we build a grid of planetary models with a wide range of compositions and masses. For each point in the grid we run the planetary evolution model developed in Zuluaga et al. (2013). Our model assumes small orbital eccentricity, negligible tidal heating and earth-like radiogenic mantle elements abundances. We devise a statistical methodology to estimate the posterior distribution of the desired planetary properties assuming simple lprior distributions for the orbital inclination and bulk composition. Our model predicts that Proxima b would have a mass 1.3≤Mp≤2.3M⊕ and a radius Rp=1.4−0.2+0.3R⊕. In our simulations, most Proxima b analogues develop intrinsic dynamos that last for ≥4 Gyr (the estimated age of the host star). If alive, the dynamo of Proxima b have a dipole moment ℳdip>0.32÷2.9×2.3ℳdip,⊕. These results are not restricted to Proxima b but they also apply to earth-like planets having similar observed properties.

Dynamic characteristics of charging effects on the dielectric constant due to E-beam irradiation: a numerical simulation

A series of synthetic variations of material intrinsic properties always come with charging phenomena due to electron beam irradiation. The effects of charging on the dielectric constant will influence the charging dynamic in return. In this paper, we propose a numerical simulation for investigating the dynamic characteristics of charging effects on the dielectric constant due to electron beam irradiation. The scattering process between electrons and atoms is calculated considering elastic and inelastic collisions via the Rutherford model and the fast secondary electron model, respectively. Internal charge drift due to E-field, density gradient caused diffusion, charges trap by material defect, free electron and hole neutralization, and variation in the internal dielectric constant are considered when simulating the transport process. The dynamics of electron and hole distributions and charging states are demonstrated during E-beam irradiation. As a function of material nonlinear susceptibility and primary energy, the dynamics of charging states and dielectric constants are then presented in the charging process. It is found that the variation in the internal dielectric constant is more with respect to the depth and irradiation time. Material with a larger nonlinear susceptibility corresponds a faster charging enhancement. In addition, the effective dielectric constant and the surface potential have a linear relationship in the charging balance. Nevertheless, with shrinking charging affect range, the situation with a higher energy primary electron comes with less dielectric constant variation. The proposed numerical simulation mode of the charging process and the results presented in this study offer a comprehensive insight into the complicated charging phenomena in electron irradiation related fields.

Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice.

Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H. Hele et al., J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot be used as a practical method without further approximation. Recently, Smith et al. [J. Chem. Phys. 142, 244112 (2015)] developed a "planetary" model dynamics which conserves the Feynman-Kleinert (FK) approximation to the quantum-Boltzmann distribution. Here, we show that for moderately anharmonic potentials, the planetary dynamics gives a good approximation to Matsubara trajectories on the FK potential surface by decoupling the centroid trajectory from the locally harmonic Matsubara fluctuations, which reduce to a single phase-less fluctuation particle (the "planet"). We also show that the FK effective frequency can be approximated by a direct integral over these fluctuations, obviating the need to solve iterative equations. This modification, together with use of thermostatted ring-polymer molecular dynamics, allows us to test the planetary model on water (gas-phase, liquid, and ice) using the q-TIP4P/F potential surface. The "planetary" fluctuations give a poor approximation to the rotational/librational bands in the infrared spectrum, but a good approximation to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid.

Расчет планетарных и региональных гравитационных моделей коры и мантии Земли с учетом ее сферической формы

Расчет планетарных и региональных гравитационных моделей коры и мантии Земли с учетом ее сферической формы