Planetary Motion Research Articles

A harmonic oscillator model of atmospheric dynamics using the Newton-Kepler planetary approach

Projection of future meteorological patterns such as median temperature and precipitation are necessary for governments to facilitate civil aviation, forecast agricultural productions, and advise future public energy policies. Various models were proposed based on historical data such as the short-term 7-day forecast or the long-term Global Forecast System to study climate change over the coming decades. We strike a balance by examining the harmonic oscillator model in mid-term weather projections. This model is the starting point to provide general mathematical guidelines to inform governmental agencies to forecast levels of energy consumptions for residential cooling in summer and heating in winter to provide energy subsidies for low-income populations and for non-profit organizations to support countries needing energy assistance. Additionally, mid-term meteorological models are especially useful during time of global energy disruptions. A model is derived based on orbital mechanics, planetary science, and astronomy using Newton’s Law of Universal Gravitation and Kepler’s Laws of Planetary Motions. We optimize the model with historical data on a specific region. The model’s predictions were then statistically compared with the actual data in the same time period in the region in a reverse goodness of fit test. We also gave certain directions on the generalized harmonic oscillator model in the future. In sum, the current harmonic oscillator method can be beneficially utilized by governments to forecast natural phenomena in order to provide timely assistance to respective populations such as in the control of infectious diseases or predicting extreme temperature fluctuations in the planning of agricultural productions.

How Does Our Solar System Work? Tracking Planetary Motion in the Classroom by Using Video Analysis in Astronomical Model Experiments

How Does Our Solar System Work? Tracking Planetary Motion in the Classroom by Using Video Analysis in Astronomical Model Experiments

Numerical Analysis of Viscous Polymer Resin Mixing Processes in High-Speed Blade-Free Planetary Blender Using Smoothed Particle Hydrodynamics

High-speed planetary mixers can rapidly and efficiently combine rheological liquids, such as polymer resins and paste materials, because of the large centrifugal forces generated by the planetary motion of the mixing vessel. Only a few attempts have been made to computationally model and analyze the intricate mixing patterns of highly viscous substances. This paper presents meshless flow simulations of the planetary mixing of polymeric fluids. This research utilized the smoothed particle hydrodynamics (SPH) approach for numerical calculations. This method has advantages over the finite-volume method, which is a grid-based computational technique, when it comes to modeling interfacial and free surface flow problems. Newtonian rheology and interfacial surface force models were used to calculate the dissipative forces in the partial differential momentum equation of fluid motion. Simulations of the flow of an uncured polyurethane resin were carried out while it was mixed in a planetary mixer, under various operating conditions. Simulations using SPH were able to accurately reproduce the intricate flow and blending pattern, providing insight into mixing mechanics and mixing index evolution characteristics according to operating conditions for the planetary mixing of polymeric fluids. The simulation results showed that the spiral band, which promotes the mixing performance, is densely and distinctively formed under high-speed operation conditions.

Aristotle as an Astronomer? Sosigenes’ Account of Metaphysics Λ.8

Abstract I have argued elsewhere that the idea that Aristotle aspired to improve the theories of the planetary motions of Eudoxus and Callippus by adding the ‘counteracting’ spheres (ἀνελίττουσαι) first emerged with the Peripatetic exegete Sosigenes in the second century CE. This paper supplements that argument by contrasting two major lines of interpretation of the astronomical system set out in Metaphysics Λ.8: Adrastus of Aphrodisias’ widely ahistorical account, and Sosigenes’ attempt to save Aristotle against later developments of astronomical science.

Sub-m s−1 upper limits from a deep HARPS-N radial-velocity search for planets orbiting HD 166620 and HD 144579

ABSTRACT Minimizing the impact of stellar variability in radial velocity (RV) measurements is a critical challenge in achieving the 10 cm s−1 precision needed to hunt for Earth twins. Since 2012, a dedicated programme has been underway with HARPS-N, to conduct a blind RV rocky planets search (RPS) around bright stars in the Northern hemisphere. Here we describe the results of a comprehensive search for planetary systems in two RPS targets, HD 166620 and HD 144579. Using wavelength-domain line-profile decorrelation vectors to mitigate the stellar activity and performing a deep search for planetary reflex motions using a trans-dimensional nested sampler, we found no significant planetary signals in the data sets of either of the stars. We validated the results via data-splitting and injection recovery tests. Additionally, we obtained the 95th percentile detection limits on the HARPS-N RVs. We found that the likelihood of finding a low-mass planet increases noticeably across a wide period range when the inherent stellar variability is corrected for using scalpelsU-vectors. We are able to detect planet signals with Msin i ≤ 1 M⊕ for orbital periods shorter than 10 d. We demonstrate that with our decorrelation technique, we are able to detect signals as low as 54 cm s−1, which brings us closer to the calibration limit of 50 cm s−1 demonstrated by HARPS-N. Therefore, we show that we can push down towards the RV precision required to find Earth analogues using high-precision radial velocity data with novel data-analysis techniques.

Cosmological Constant as a Variable Parameter: Spring Theory

A spring term is added into Newton’s law of gravitation. The universe accelerates to luminal or superluminal speed at the outer rim of the Hubble sphere where no matters can be observed. Such a big bang is explained three dimensionally from which we obtain the Hubble constant 10-17.5 /s which is the square root of the cosmological constant   10-35 /s2  .  The missing mass of galaxies in the rotation curves can be clarified via the virial theorm in which galaxies mass 1041    kg and their spring constant 10-31 /s2 match with other authors. Under certain conditions in Sect.5, the Schroedinger equation can be reduced to 1st order for long range interaction and 2nd order(both time and spatial part) for micro interaction; whereas the latter has the same form as the Klein-Gordan equation. Upon a simple modification of the classical field theory, we derive the equation V(r) = a ln(1 + b/r) + C which is compatible with the well known Cornell potential in quark confinement. Such a modified field theory can furtherly apply to planetary motions by adding a spring term in the Binet equation to estimate different spring constants of the sun for the inner planets;they are  1��-14  /s2Mercury, 10-15/s2 Venus amd 10-16 /s2    (Earth). Since spring is a fluid which cannot break except its value k decreases at farther distance. A comparison with the Fischbach’s fifth force is also dicussed in the conclusion.

Kepler’s struggle with the problem of force obstruction

The paper examines how the scarcely discussed problem of force obstruction contributed to shaping Kepler’s concept of force, that is, the question whether corporeal forces are blocked when an intermediate body is interposed between the force source and the target body. We explore the role played by this problem in Kepler’s works, focusing on his Optics, Foundations of Astrology, Astronomia Nova and Epitome. While the problem is instrumental in abandoning an initially physicalistic framework for astrology, Kepler attempts at different solutions when discussing the forces responsible for planetary motion. These forces are first modelled upon light, and then magnetism (and gravity). However, after considering several ways to get rid of the problem, he is eventually unable to decide why observable effects of obstruction are usually absent. So he accepts this absence at face value, similarly to Newton in his most relevant passages, allowing for a new ontological category that is physical on the one hand, but non-material on the other.

Связи изменений ледовой обстановки на Северном морском пути с движением планет Солнечной системы

The paper considers the progress in the hydrographic support for navigation in various parts of the Northern Sea Route in terms of improving the methods for developing tentative forecasts of interannual changes of ice conditions. Among the approaches to solve the task the authors take into account factors that do not depend on the uncertainty of regional climate changes in the future. One of such factors is the main mechanical process in the Solar System — the orbital planetary motion. The paper goal is to confirm the existence of water areas in the seas under study, changes in the ice coverage of which in the summer-autumn period can be significantly associated with planetary orbital motion factor. The authors apply statistical methods to achieve the study goal. As factual material on changes in the ice coverage of the sections of the Northern Sea Route, they use information of GLORYS12v1 and ICDC global reanalysis databases for the period 1993—2019 and 1979—2020 respectively. As a result the authors have revealed locations of the water areas, for which the reliability of the conclusion about the significance of the relationship under consideration in certain months is at least 90%. They have stated that the reliability of such inference is the highest for some water areas of the East Siberian Sea in October and the Chukchi Sea in November. To confirm the suitability of the identified links for the development of tentative forecasts of trends in interannual changes in the ice conditions on the Northern Sea Route, the authors insist on additional testing to check the resistance to updating the actual material.

Secular orbital dynamics of the innermost exoplanet of the upsilon -Andromedæ system

We introduce a quasi-periodic restricted Hamiltonian to describe the secular motion of a small-mass planet in a multi-planetary system. In particular, we refer to the motion of upsilon -And textbf{b} which is the innermost planet among those discovered in the extrasolar system orbiting around the upsilon -Andromedæ A star. We preassign the orbits of the Super-Jupiter exoplanets upsilon -And textbf{c} and upsilon -And textbf{d} in a stable configuration. The Fourier decompositions of their secular motions are reconstructed by using the well-known technique of the (so-called) frequency analysis and are injected in the equations describing the orbital dynamics of upsilon -And textbf{b} under the gravitational effects exerted by those two external exoplanets (that are expected to be major ones in such an extrasolar system). Therefore, we end up with a Hamiltonian model having 2+3/2 degrees of freedom; its validity is confirmed by the comparison with several numerical integrations of the complete four-body problem. Furthermore, the model is enriched by taking into account also the effects due to the relativistic corrections on the secular motion of the innermost exoplanet. We focus on the problem of the stability of upsilon -And textbf{b} as a function of the parameters that mostly impact on its orbit, that are the initial values of its inclination and the longitude of its node (as they are measured with respect to the plane of the sky). In particular, we study the evolution of its eccentricity, which is crucial to exclude orbital configurations with high probability of (quasi)collision with the central star in the long-time evolution of the system. Moreover, we also introduce a normal form approach, that is based on the complete average of our restricted model with respect to the angles describing the secular motions of the major exoplanets. Therefore, our Hamiltonian model is further reduced to a system with 2 degrees of freedom, which is integrable because it admits a constant of motion that is related to the total angular momentum. This allows us to very quickly preselect the domains of stability for upsilon -And textbf{b}, with respect to the set of the initial orbital configurations that are compatible with the observations.

G.B. Riccioli’s geo-heliocentric use of Epicepicycles, ellipses and spirals

According to Giovanni Battista Riccioli (1598–1671), planets describe orbits in a fluid heaven in a helio-geocentric model of cosmos. In his Almagestum Novum (1651) he stresses the need for a novel and rigorous geometrical explanation for the motion of heavenly bodies, which considers a separate Primum Mobile as an unnecessary hypothesis. Riccioli rejects the standard eccentric-epicycle theory as unsatisfactory and argues for what he calls “Eccentrepicyclos” or “Epicepicycles.” He takes the Keplerian elliptical theory into account and includes a variable oscillation of both the mobile eccentric center and the variation of the epicycle’s diameter. As a result, planets move along spiral orbits that have variable sizes. The inequalities, which astronomers had always tried to explain, are now justified: the spiral trajectory, obtained by means of the oscillation of the eccentric center, warrants the first inequality, about the variation of the planets’ velocity. The variable amplitude of the spirals, obtained by the variation of the epicycle’s diameter, explains the second inequality, namely the apparent retrograde or progressive planetary motion. In the later work Astronomia Reformata (1665), Riccioli uses explicitly the term “ellipse.” Riccioli’s innovations are of great interest and help to understand the complexity of the astronomical debates about the best world-system.

Combining data and theory for derivable scientific discovery with AI-Descartes

Scientists aim to discover meaningful formulae that accurately describe experimental data. Mathematical models of natural phenomena can be manually created from domain knowledge and fitted to data, or, in contrast, created automatically from large datasets with machine-learning algorithms. The problem of incorporating prior knowledge expressed as constraints on the functional form of a learned model has been studied before, while finding models that are consistent with prior knowledge expressed via general logical axioms is an open problem. We develop a method to enable principled derivations of models of natural phenomena from axiomatic knowledge and experimental data by combining logical reasoning with symbolic regression. We demonstrate these concepts for Kepler’s third law of planetary motion, Einstein’s relativistic time-dilation law, and Langmuir’s theory of adsorption. We show we can discover governing laws from few data points when logical reasoning is used to distinguish between candidate formulae having similar error on the data.

The Influence of Configuration Parameters of the Planetary Drive of Crank Presses on its Dynamic and Energy-Consumption Characteristics

Introduction. The planetary drive has been widely found in the activation systems of crank presses as it improves working conditions of friction units and reduces press metal consumption and energy consumption.Problem Statement. For studying the planetary motion of its main parts, it is advisable to consider its operation as four periods characterized by different patterns of changes in external loads and, consequently, different patterns of motion of core parts. The periods between switching the brakes when one link has not stopped, while other one starts moving is of the greatest interest. The problem of dynamic and energy-consumption parameters of the drive in transient conditions still remain a little open.Purpose. The purpose of this research is to qualitatively assess the influence of configuration parameters on the dynamics of the processes of switching and stopping the planetary drive.Material and Methods. The parameters of the experimental pilot plant, a model planetary drive with a nominal load of 400 kN, have been calculated. The minimum speed of the central gear has been estimated depending on the moments of inertia of the leading mass and the outer gear. The obtained dependences have been processed with the use of a standard mathematical apparatus.Results. It has been found that the energy-consumption and dynamic parameters of the drive are significantly influenced by such characteristics as moments of inertia and braking moments, while decreasing angular velocity of the drive flywheel does not depend on the moments of inertia of the stopped links. The rate of braking processes is determined by the elastic properties of the friction materials and the parameters of the brake springs, not by the parameters of compressed air outflow.Conclusions. The obtained analytical and graphical dependences have allowed not only qualitative, but also quantitative assessment of the influence of the parameters on the dynamics of processes. These recommendations can be used at the design stage, to select the optimal parameters of the drive with the predicted properties.

Kepler optimization algorithm: A new metaheuristic algorithm inspired by Kepler’s laws of planetary motion

This study presents a novel physics-based metaheuristic algorithm called Kepler optimization algorithm (KOA), inspired by Kepler’s laws of planetary motion to predict the position and velocity of planets at any given time. In KOA, each planet with its position acts as a candidate solution, which is randomly updated through the optimization process with respect to the best-so-far solution (Sun). KOA allows for a more effective exploration and exploitation of the search space because the candidate solutions (planets) exhibit different situations from the Sun at different times. Four challengeable benchmarks, namely CEC 2014, CEC 2017, CEC 2020, and CEC2022, and eight constrained engineering design problems, in addition to the parameter estimation problem of photovoltaic modules, were used to assess the performance of KOA. To observe its effectiveness, it was compared with three classes of stochastic optimization algorithms, including: (i) the latest published algorithms, including Snake Optimizer (SO), Fick’s Law Algorithm (FLA), Coati Optimization Algorithm (COA), Pelican Optimization Algorithm (POA), Dandelion Optimizer (DO), Mountain Gazelle Optimizer (MGO), Artificial Gorilla Troops Optimizer (GTO), and Slime Mold Algorithm (SMA); (ii) well-studied and highly cited algorithms, such as Whale Optimization Algorithm (WOA) and Grey Wolf Optimizer (GWO); and (iii) two highly performing optimizers: LSHADE-cnEpSin and LSHADE-SPACMA. Results of the convergence curve and statistical information indicated that KOA is more promising than all the compared optimizers. The source code of KOA is publicly accessible at https://www.mathworks.com/matlabcentral/fileexchange/126175-kepler-optimization-algorithm-koa

A 20‐million‐year Early Jurassic cyclostratigraphic record and its implications for the chaotic inner Solar System and sea‐level changes

AbstractWe present high‐resolution (every 2 cm) magnetic susceptibility (MS) data from the Sancerre‐Couy drill core (Paris Basin), spanning the latest Sinemurian to the earliest Aalenian (Early Jurassic). This record allows to build a 20‐million‐year cyclostratigraphic interval using the stable 405 kyr (g2–g5) orbital eccentricity cycle and to focus on long‐period cyclicities and their potential implications for the chaotic diffusion in the inner Solar System and sea‐level changes. Time series analysis indicates evidence of two long‐period cyclicities of 1.6 and 3.4 Myr. These Early Jurassic cyclicities likely correspond to the Cenozoic orbital cyclicities of 2.4 Myr (g4–g3) and 4.7 Myr eccentricity terms. Shortening of eccentricity terms during the Early Jurassic is potentially related to the chaotic orbital motion of the inner planets expressed in the resonant argument θ = 2(g4–g3) − (s4–s3). The 1.6 Myr (g4–g3) cycle matches the third‐order eustatic sequences, whereas the 3.4 Myr cycle has no equivalent in the reference eustatic chart. These cycles of several million years are superimposed a cyclicity of ca. 7.5 Myr, which may correspond to the eccentricity term of 9.5 Myr, previously detected in the Cenozoic. Such cyclicity matches the global, ‘shorter’ second‐order sea‐level sequences and is strongly documented in the sedimentological and mineralogical proxy data, hence supporting the potential key role of orbitally paced climate and sea‐level changes at this timescale.

Approximations for Secular Variation Maxima of Classical Orbital Elements under Low Thrust

The reachability assessment of low-thrust spacecraft is of great significance for orbital transfer, because it can give a priori criteria for the challenging low-thrust trajectory design and optimization. This paper proposes an approximation method to obtain the variation maximum of each orbital element. Specifically, two steps organize the contribution of this study. First, combined with functional approximations, a set of analytical expressions for the variation maxima of orbital elements over one orbital revolution are derived. Second, the secular approximations for the variation maxima of the inclination and the right ascension of the ascending node are derived and expressed explicitly. An iterative algorithm is given to obtain the secular variation maxima of the other orbital elements the orbital elements other than the inclination and right ascension of the ascending node. Numerical simulations for approximating the variation maxima and a preliminary application in estimation of the velocity increment are given to demonstrate the efficiency and accuracy of the proposed method. Compared with the indirect method used alone for low-thrust trajectory optimization, the computation burden of the proposed method is reduced by over five orders of magnitude, and the computational accuracy is still high.

Multipurpose Laser Instrument for Interplanetary Ranging, Time Transfer, and Wideband Communications

In this paper, we discuss the design and feasibility of a multifunctional laser instrument capable of precision ranging, time transfer, and wideband communications over interplanetary distances throughout our solar system. To simplify the communications discussion, On-Off Keying (OOK) is assumed for the high bandwidth (MHz to GHz) modulation format, and the required laser powers and transmit and receive apertures are determined for each Earth–planet link as a function of data rate. Optimization of the transmitter and receiver antenna gains is reviewed. It is further assumed that the spacecraft is in orbit about the planet of interest in order to justify the need for large data downloads rates and that single-photon sensitive detector arrays can be utilized to aid in the acquisition, detection, and tracking of the opposite terminal. Satellite acquisition and tracking is complicated by the long one-way propagation distances (up to 40 AU), the finite speed of light, the orbital and rotational velocities of the two planets, and, if applicable, the spacecraft orbital speed about the planet. Taking advantage of the highly circular and coplanar planetary orbits within our solar system, point ahead angles are estimated for all combinations of possible Earth–planet positions revealing solar orbital geometries where planetary motion does not introduce a need for point ahead angles. Finally, possible methods for simplifying the initial mutual acquisition of the planetary and Earth terminals and maintaining the coalignment of their respective optical systems is discussed.

Solar Occultation Experiments (SOE) in the Venusian Atmosphere: effect of orbital parameters on the spatiotemporal distribution of measurements

AbstractSolar occultation is a satellite-based technique for high-resolution vertical profiling of planetary atmospheres. Owing to the distinctive observational geometry, the deduction of the spatiotemporal coverage of solar occultation measurements as a function of the spacecraft orbit is non-trivial. In this work, we have implemented python-based 3D simulations of the occultation-viewing geometry for a hypothetical Solar Occultation Experiment (SOE) to study the atmosphere of Venus. The simulations incorporate planetary motions and orbital propagation using the astropy and poliastro packages, and compute the instantaneous line-of-sight (LoS) tangent point using 3D vector algebra. SPICAV/SOIR data from Venus Express was used to validate the simulations, showing excellent agreement. Using the simulations, we conducted a first-of-its-kind theoretical study on the effect of varying different spacecraft orbital elements on the spatiotemporal distribution of solar occultation measurements in the Venusian atmosphere, confirming a highly sensitive dependence. The semimajor axis (a) and inclination (i) of the spacecraft orbit are found to influence the latitudinal extent of observations and the nature/duration of occultation seasons, while the eccentricity (e) and argument of periapsis (ω) determine the distinct regions of sparse observations. The spatiotemporal spread of individual SOE profiles is found to depend on the orbital parameters as well as the solar beta angle. Our results show that spacecraft orbits can be designed with appropriate parameters to optimize the coverage of SOE measurements in view of achieving specific science goals, providing valuable inputs for future missions to Venus that aim to implement the solar occultation technique.

Bounds on graviton mass and constraining Yukawa-like gravitational potential from planetary motion in the solar system

In this study we used the observed perihelion precession of planetary orbits in the Solar System in order to constrain theory of Yukawa-type gravity, and to bound mass of graviton. For that purpose we assumed that the precession angles of the planets in Yukawa-type gravity should be equal to their observed values, as well as to the corresponding predictions of General Relativity (GR). Starting from these requests we constrain Yukawa-like gravitational potential. The obtained results showed that our estimates for the range of Yukawa interaction ? at the Solar System scales are in good agreement with recent experimental constrains. Assuming that the estimated value of the range of ? corresponds to the Compton wavelength of graviton ?1, we then estimate the upper bound for its mass m1. We found that these estimates were in agreement with our previous results obtained from the observed stellar orbits around the Galactic Center (GC).

Модель движения колесного аппарата по неровной поверхности

The paper deals with two-dimensional model of wheeled planetary vehicle motion. The main features of the model are calculation of the vehicle position with high accuracy, interaction between wheels and surface and the possibility of real-time modeling. The model allows to investigate the geometric and dynamic patency of the wheeled vehicle in order to determine dimensions of the suspension elements and friction coefficients of the wheels to the ground, which provide the necessary conditions for overcoming a given surface relief.

Design and Analysis of a Novel Adjustable SVAWT for Wind Energy Harvesting in New Energy Vehicle

The new energy vehicle is a robust measure to solve the problem of global warming. However, the new energy vehicle generally has the disadvantages of short mileage and difficulty in finding public chargers. The combination of wind energy harvest and new energy vehicle can be conducive to the promotion of the new energy vehicle. This paper proposes a novel adjustable Savonius vertical axis wind turbine (SVAWT). It contains three parts: an energy absorption module, an energy recovery module, and an energy conversion module. The energy absorption module includes four blades with staggered distribution in two layers. The overlap ratio of the blades can be adjusted by the wind speed, which can ensure the SVAWT has a higher energy transfer efficiency. The energy recovery module adjusts the overlap ratio of the blades without interruption by utilizing the self-rotation and the orbital revolution of the gears. The energy conversion module converts mechanical energy into electric energy and supplies power for the vehicle after adjustment by the voltage regulator module. Based on actual operating data, it can be found that the variation trend of power of the blades absorbing is consistent with wind speed and increases with the wind speed. Under four actual operating conditions, the root mean square value of the blades absorbing power are 7.0 W, 7.1 W, 3.9 W, and 5.1 W, respectively. These results reveal that the proposed novel adjustable SVAWT has high recovery power potential and can provide a valuable solution to the practical applications of wind energy harvesting.