Planetary Motion Research Articles

Pacing of the latest Ordovician and Silurian carbon cycle by a ~4.5 Myr orbital cycle

The cyclic eccentricity, precession and obliquity parameters of the Earth's orbit and axial motion have been demonstrated to have a large impact on climate on short (104 to 105 yr) timescales during the Cenozoic and Mesozoic. Amplitude modulation (AM) of these parameters on longer (106 yr) timescales induces “grand orbital cycles” that have also been detected for large parts of the Cenozoic and Mesozoic. However, the response of paleoclimatic variables to these cycles is unknown for the Paleozoic due to past chaotic transitions in the orbital motion of the inner planets. The Late Ordovician to Early Devonian remains an enigmatic period of geological time. During the Hirnantian, extensive Southern Hemisphere glaciation was associated with the second largest mass extinction in Earth's history. The subsequent Silurian was met with several high-amplitude (>4‰) carbon isotope (δ13C) excursions associated with equally erratic climatic, biotic and eustatic fluctuations. Here, I conduct spectral analysis of carbonate δ13C and conodont apatite oxygen isotope (δ18O) compilations for the Katian (~448 Ma) to mid-Lochkovian (~415 Ma). The resulting spectra document a prominent cyclicity of ~4.2 (3.7 to 4.8) Myr in the carbon and climate cycles, similar to dominant periods found in Cenozoic astronomical solutions related to the long-term AM of the 100-kyr eccentricity band, 400-kyr eccentricity band and axial obliquity. Variations in the ~4.5 Myr eccentricity and axial obliquity cycles respectively enhanced organic carbon burial or reservoir stability leading to fluctuations in the Paleozoic δ13C record. This process led to a decline in atmospheric CO2 to threshold levels, after which astronomical forcing triggered the onset of glaciation and extensive global cooling, associated with positive δ18O excursions during the Hirnantian, the early and late Llandovery, the Telychian-Sheinwoodian boundary, the Homerian, the late Ludfordian and the late Pridoli-early Lochkovian.

Intelligent Detection of a Planetary Gearbox Composite Fault Based on Adaptive Separation and Deep Learning.

Due to the existence of multiple rotating parts in the planetary gearbox—such as the sun gear, planet gears, planet carriers, and its unique planetary motion, etc.—the vibration signals generated under multiple fault conditions are time-varying and nonstable, thus making fault diagnosis difficult. In order to solve the problem of planetary gearbox composite fault diagnosis, an improved particle swarm optimization variational mode decomposition (IPVMD) and improved convolutional neural network (I-CNN) are proposed. The method takes as input the spectrum of the original vibration signal that contains rich information. First, the automatic feature extraction of signal spectrum is performed by I-CNN, while a classifier is used to diagnose the fault modes. Second, the composite fault signal is decomposed into multiple single fault signals by adaptive variational mode, and the signal is decomposed as a model input to diagnose the single fault component. Finally, a complete intelligent diagnosis of planetary gearboxes is conducted. Through experimental verification, the composite fault diagnosis method combining IPVMD and I-CNN will diagnose the composite fault and effectively diagnose the sub-fault included in the composite fault.

Planetary motion cross bar friction test for application in machining process

This paper describes a new method to evaluate the friction coefficient at the tool-work interface in machining process where high stress and temperature are caused. In order to examine the feasibility of the proposed method, the present report introduces the method and the results obtained only at room temperature. Ti6Al4V, SUS304, AISI1045, FCD 700, FCD 450 and FC300 were used as work materials, while TiN coated carbide tool, TiAlN coated carbide tool and P15 were used as tool materials. The proposed method provided the friction coefficients of different coatings against different work materials, and demonstrated the variability of friction coefficient and the anisotropy of surface roughness.

Stability of exoplanetary systems retrieved from scalar time series

Abstract We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time series are used to build up the high-dimensional phase space trajectory representing the dynamical evolution of planetary motion. The framework of nonlinear time series analysis and Poincaré recurrences allows us to transform the obtained univariate signals into complex networks whose topology carries the dynamical properties of the underlying system. The network-based analysis is able to distinguish the regular and chaotic behaviour not only for synthetic inputs but also for noisy and irregularly sampled real world observations. The proposed scheme does not require neither n-body integration nor best fitting planetary model to perform the stability investigation, therefore, the computation time can be reduced drastically compared to those of the standard numerical methods.

Exeter Book Riddle 95: ‘The Sun’, a New Solution

Abstract Elusive and fraught with textual difficulties, Riddle 95, the ‘last’ of the Old English verse riddles preserved in the tenth-century Exeter Book, has long baffled modern readers as one of a handful of thorny items in the collection that have so far defied solution. ‘Book’ is the answer that has found most acceptance with critics in the past, yet the speaking subject of Riddle 95 is unlike anything described in those items of the collection that actually deal with writing and the tools of the monastic scriptorium. Rather, the linguistic and thematic parallels between Riddle 95 on the one hand, and the cosmological riddles and poems in the Exeter Book on the other, strongly suggest that the subject of Riddle 95 is the sun, a frequent topic of early medieval enigmatography. The poem obliquely relates how the rising sun installs itself in the sky to shed its welcome light upon the earth before it sets and vanishes from sight, completing its daily orbit along unknown paths. The main clues helping to secure the solution ‘sun’ are based upon what was known in Anglo-Saxon England about the solar course and the planetary motions, especially from the astronomical writings of Isidore of Seville and Bede. Further evidence is provided by several analogues in the Anglo-Latin riddle tradition, including the Enigmata of Aldhelm and his followers.

Augmented Reality Applied in Astronomy Subject

Mobile augmented reality is one of the most potential technology for education. Science astronomy is one of the subject that need to develop by mobile augmented reality technology. Purpose in this research is to create mobile augmented reality based on astronomy subject in Indonesian curriculum in junior high school. Animation that has been show in this application follows Kepler’s law about planetary motion. This research is R&D research and it follow instructional design type ADDIE. This researcher collected the data qualitatively from 2 experts, 2 teachers and 2 students. Each of participant will give suggestion to improve the quality of the application. Finally the application has been made with 16 marker. 11 explain about member of solar system, 3 marker about rotation and revolution of earth and moon, and 2 marker is about solar eclipse and moon eclipse. The application size is 47 Mb with Apk format. It can be use at least in android version 4.1 jelly bean and camera 13 MP. This application is ready to use for more large participant.

Demonstrating the elliptical orbit of Mars using naked eye data

The discovery of Kepler's three laws of planetary motion served as a significant motivation to Newton to find the gravitational force law and explain why motion in an inverse square law force field produces orbits (or trajectories) that are conic sections. Kepler's discovery that Mars' orbit is an ellipse is one of the most significant in the history of astronomy. It relied on Tycho Brahe's observations, which were the most accurate data ever attained at that time. In this paper, we present an analysis of positional measurements carried out during two observing periods of ∼400 days centered on the 2016 and 2018 oppositions of Mars. Our observations were made with the naked eye and a simple cross staff. If we assume an elliptical orbit of Mars and simplify matters by adopting a circular orbit for the Earth, the data of the 2016 opposition indicate that the eccentricity of Mars' orbit is 0.093 ± 0.012. This is equal to the modern accepted value, but with a larger uncertainty. By adopting a more robust model that uses an ellipse for the Earth as well, we obtain a better fit, with an RMS residual of ±7.5 arc min for the ecliptic longitudes. The data of the 2018 opposition must be fit with an ellipse for Mars and the Earth.

Chronophilia; or, Biding Time in a Solar System

Abstract Having evolved in a dynamic solar system, all life on earth has adapted to and depends on recurring and repeating cycles of light, heat, and gravity. Our sleep cycles, reproductive cycles, and emotional cycles are all linked in varying ways to planetary motion even though we continually disrupt, modify, or extend these cycles to go about our personal and collective business. This essay explores how our sense of time is both physiological and cultural, with deep ramifications for confronting such challenges as jet lag, navigation, calendar construction, shift work, and even life span. Although chronobiologists have posited the existence of a Zeitgeber, or external master clock that serves to reset our internal clocks, it has become clear that any master clock relies as much on natural elements (such as a rising sun) as cultural elements (such as an alarm clock). Moreover the “circa” of circadian rhythms, suggests that our activities and emotions recur, not in exact twenty-four-hour cycles, but in more plastic and approximate cycles that, according to circumstance and individual, may span somewhat longer or shorter periods than one earthly rotation. Or as one chronobiologist explains, “Any one physiologic variable is characterized by a spectrum of rhythms that are genetically anchored, sociologically synchronized . . . and influenced by heliogeophysical effects.” As we contemplate faster and further travel and other activities that disrupt our biorhythms, we need to develop greater awareness of chronophilia, our attachment to rhythm, our love of familiar time.

Space test of the equivalence principle: first results of the MICROSCOPE mission

The weak equivalence principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of general relativity. The MICROSCOPE mission aims to test its validity to a precision of 10−15, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE’s first results show no hint for such a difference, expressed in terms of Eötvös parameter (both 1 uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7% of the current available data acquired during the whole mission. The quadratic combination of 1 uncertainties leads to a current limit on of about .

A review of reconstruction research for the lost gearing of antikythera astronomical calculator

This paper presented a review for the reconstruction research of the Antikythera mechanism, the mechanical calculator was made around the end of second century BC in ancient Greece. Under the concluded design specifications and constraints, all possible conceptual designs of the lost mechanical structures subject to the standard of technology and science at that time were synthesized based on a systematic design procedure. This oldest astronomical calculator excavated in 1900-1901 can display the solar, lunar and planetary motions, indicate the date of Egyptian calendar, calculate the luni-solar calendars and periods, and predict the eclipses by its interior gear trains. The structures for the solar and the planetary motions are completely lost in the excavation. Without surviving evidence, restoring the lost structures by computer tomography or X-ray detection is unfeasible. Here, the author applied a design procedure with four steps, which is based on the reconstruction design methodology of lost ancient machinery. Historical archives for reconstructing Antikythera mechanism are built based on historical records, ancient astronomy, ancient astronomical instruments, as well as the kinematic and mechanism analyses of gear trains. After identifying input conditions, three and two design specifications respectively for the solar and the planetary motions are concluded and their feasible designs are synthesized by the design procedure. For each design, the equations of teeth counting are derived based on the analysis of gear ratios. Finally, the possible teeth of gears are generated and then a new reconstruction design of Antikythera mechanism with complete interior structure is built through the constraints of space and assembly. These synthesized designs form a database of reconstruction work, and one of them can be the original structure. Once new evidence is discovered, these reconstruction designs can help archaeologists decode this mechanism further.

Analytical solution for the three-dimensional motion of a circumbinary planet around a binary star

By using the method of separating rapid and slow subsystem, we obtain an analytical solution for a stable three-dimensional motion of a circumbinary planet around a binary star. We show that the motion of the planet is more complicated than it was obtained for this situation analytically by Farago and Laskar (2010). Namely, in addition to the precession of the orbital plane of the planet around the angular momentum of the binary (found by Farago and Laskar (2010)), there is simultaneously the precession of the orbital plane of the planet within the orbital plane. We show that the frequency of this additional precession is different from the frequency of the precession of the orbital plane around the angular momentum of the binary. We demonstrate that this problem is mathematically equivalent both to the problem of the motion of a satellite around an oblate planet and to the problem of a hydrogen Rydberg atom in the field of a high-frequency linearly-polarized laser radiation, thus discovering yet another connection between astrophysics and atomic physics. We point out that all of the above physical systems have a higher than geometrical symmetry, which is a counterintuitive result. In particular, it is manifested by the fact that, while the elliptical orbit of the circumbinary planet (around a binary star) or of the satellite (around an oblate planet) or of the Rydberg electron (in the laser field) undergoes simultaneously two types of the precession, the shape of the orbit does not change. The fact that a system, consisting of a circumbinary planet around a binary star, possesses the hidden symmetry should be of a general physical interest. Our analytical results could be used for benchmarking future simulations.

Frequency analysis and representation of slowly diffusing planetary solutions

Context. Over short time-intervals, planetary ephemerides have traditionally been represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. This representation is not well adapted for the evolution of planetary orbits in the solar system over million of years which present drifts in their main frequencies as a result of the chaotic nature of their dynamics. Aims. We aim to develop a numerical algorithm for slowly diffusing solutions of a perturbed integrable Hamiltonian system that will apply for the representation of chaotic planetary motions with varying frequencies. Methods. By simple analytical considerations, we first argue that it is possible to exactly recover a single varying frequency. Then, a function basis involving time-dependent fundamental frequencies is formulated in a semi-analytical way. Finally, starting from a numerical solution, a recursive algorithm is used to numerically decompose the solution into the significant elements of the function basis. Results. Simple examples show that this algorithm can be used to give compact representations of different types of slowly diffusing solutions. As a test example, we show that this algorithm can be successfully applied to obtain a very compact approximation of the La2004 solution of the orbital motion of the Earth over 40 Myr ([−35 Myr, 5 Myr]). This example was chosen because this solution is widely used in the reconstruction of the past climates.

IDA software for investigating asteroid dynamics and its application to studying the motion of 2012 MF7

In this study, we developed a new version of the Investigating Dynamics of Asteroids (“IDA”) software for investigating the dynamics and probabilistic orbital evolution of asteroids. IDA allows the motions of asteroid to be predicted in order to determine close encounters, possible collisions, and orbital resonances with planets, as well as estimating the probability of impact, visualizing the motions of asteroid and planets on a computer screen, and solving some additional problems. The key features of the IDA software are its multifunctionality, high efficiency, and convenient interface. The motions of the asteroid 2012 MF7 were investigated to demonstrate use of the software, where the results showed that this object has a nonzero probability of colliding with the Earth in 2046.

Spectral Decomposition and Extremes of Atmospheric Meridional Energy Transport in the Northern Hemisphere Midlatitudes

AbstractThe atmospheric meridional energy transport in the Northern Hemisphere midlatitudes is mainly accomplished by planetary and synoptic waves. A decomposition into wave components highlights the strong seasonal dependence of the transport, with both the total transport and the contributions from planetary and synoptic waves peaking in winter. In both winter and summer months, poleward transport extremes primarily result from a constructive interference between planetary and synoptic motions. The contribution of the mean meridional circulation is close to climatology. Equatorward transport extremes feature a mean meridional equatorward transport in winter, while the planetary and synoptic modes mostly transport energy poleward. In summer, a systematic destructive interference occurs, with planetary modes mostly transporting energy equatorward and synoptic modes again poleward. This underscores that baroclinic conversion dominates regardless of season in the synoptic wave modes, whereas the planetary waves can be either free or forced, depending on the season.

Dynamic modeling and analysis of wind turbine drivetrain considering platform motion

For floating offshore wind turbines, platform motion is large under the impact of waves and currents leading to increasing system vibration and should be analyzed in the design phase to improve the survivability of wind turbine. However, most of the wind turbine drivetrain models lack the attention to the dynamic response caused by platform motions. In this work, a novel dynamic modeling method considering platform motion is proposed, which is suitable for any combinations of the planetary and parallel gear stages. A dynamic model of the drivetrain with platform motions is developed, which includes the concentrated mass components (CMCs) with the fixed-shaft and orbital revolution motions, the flexible gear meshes and bearings as well as the flexible shafts. The vibration modes of the drivetrain are investigated. Three kinds of platform motions are determined and applied to the drivetrain. The effects of these platform motions on the dynamic behaviors of the drivetrain are studied in-depth. The simulation results indicate that the platform motions not only introduce additional excitation frequencies to the drivetrain and increase system vibration but also increase the risk of the resonance. The proposed method can be utilized to guide the modeling and design of an offshore wind turbine drivetrain.

A Digital (3D) Reconstruction of a Lost Planetarium

After many years of research, it has been concluded that Antikythera mechanism is a more complicated device than initially was thought. Recently, the rapidly increasing development of 3D modeling and simulation software, resulted in attempts to recreate the mechanism's 3D construction. These 3D replicas are based on advanced knowledge, gathered by the study of the mechanism remnants or the deciphered inscription on its surfaces. The latest decrypted inscriptions on the back door of the mechanism refers to planetary motion, which might be illustrated by a planetarium formation, which is absent from the remains of Antikythera mechanism. The authors propose a 3D reconstruction of this alleged planetarium, as a possible sequence of the existed mechanism's remains, compatible with the surviving inscriptions. Specifically, the authors introduce a lot of constructional differentiations compared to the other suggested, focusing mainly on measurements accuracy which this planetary system could perform.

Effect of the Solar dark matter wake on planets

The Galaxy is conventionally thought to be surrounded by a massive dark matter (DM) halo. As the Sun goes through this halo, it excites a DM wake behind it. This local asymmetry in the DM distribution would gravitationally affect the motions of Solar System planets, potentially allowing the DM wake to be detected or ruled out. Hernandez (2019) recently calculated that the DM-induced perturbation to Saturn's position is 252 metres net of the effect on the Sun. No such anomaly is seen in Saturn's motion despite very accurate tracking of the Cassini spacecraft, which orbited Saturn for >13 years. Here, we revisit the calculation of how much Saturn would deviate from Keplerian motion if we fix its position and velocity at some particular time. The DM wake induces a nearly resonant perturbation whose amplitude grows almost linearly with time. We show that the Hernandez (2019) result applies only for an observing duration comparable to the ${\approx 250}$ million year period of the Sun's orbit around the Galaxy. Over a 100 year period, the perturbation to Saturn's orbit amounts to <1 cm, which is quite consistent with existing observations. Even smaller perturbations are expected for the terrestrial planets.

Kepler Orbits in Pairs of Disks Settling in a Viscous Fluid.

We show experimentally that a pair of disks settling at negligible Reynolds number (∼10^{-4}) displays two classes of bound periodic orbits, each with transitions to scattering states. We account for these dynamics, at leading far-field order, through an effective Hamiltonian in which gravitational driving endows orientation with the properties of momentum. This treatment is successfully compared against the measured properties of orbits and critical parameters of transitions between types of orbits. We demonstrate a precise correspondence with the Kepler problem of planetary motion for a wide range of initial conditions, find and account for a family of orbits with no Keplerian analog, and highlight the role of orientation as momentum in the many-disk problem.

Planetary Mill with Friction Wheels Transmission Aided by an Additional Degree of Freedom

Processing in planetary ball mills is well suited to a large number of applications because they are easy to operate and versatile, grinding faster than other mills. Research related to planetary mills are mainly about the process evaluation, and there are few studies on the mechanical design of such equipment. This paper describes the decision process in the design of an innovative planetary mill in which design for manufacture and assembly (DFMA) principles were used to provide compact equipment made of simple and standardized parts. We developed a friction wheel mechanism with an additional degree of freedom that improves transmission and facilitates assembly, reducing the need for adjustment. It can be applied to different equipment that relies on planetary motion or rotating devices. A prototype was built, and its grinding performance surpasses that of other types of traditional mill. The mean particle size of alumina powder was reduced from 4.2 µm to 0.9 µm in 60 minutes.

Nonlinear Estimation and Decision-Making Methods in Short Track Identification and Orbit Determination Problem

Typically, near-Earth space objects are observable for a small fraction of the orbit revolution. In this paper, we consider the problem of identification and fusion of two short optical tracks of near-Earth space objects, as well as the problem of estimation of the parameters of the corresponding orbits directly from these tracks in the absence of a priori information. The popular approach to solving these problems is based on admissible regions of orbital parameters, which is typically computationally demanding. It is shown that the solution of these problems does not require admissible regions and computationally and algorithmically difficult operations with admissible regions. A new, purely statistical method for solving these problems is proposed.