Planetary Motion Research Articles

Visualization of simulated coating efficiency and uniformity.

For a line-of-sight coating uniformity model, the source distribution is normalized such that all material can be traced. This is validated for a point source in an empty coating chamber. We can now quantify the source utilization of a coating geometry to determine what fraction of the evaporated source material is collected on the optics of interest. For the example of a planetary motion system, we calculate this utilization and two nonuniformity parameters for a large range of two input parameters, here the distance between the source and the rotary drive system and the lateral displacement of the source from the machine centerline. Contour plot visualizations in this 2D parameter space assist understanding geometry trade-offs.

Jovian encounter manifolds

AbstractRecent numerical studies have shown that the entire solar system is permeated with arch-like structures originating from all planets. Particles placed on such arches experience planetary close encounters after only one or few orbital revolutions. In this work, we are interested how thece arches, which we associate to encounter manifolds of Jupiter, appear in three dimensions for higher inclinations.Our results show that about 0.5% of the observed domain [a, e, i] = [2 AU, 11.5 AU] × [0, 0.7] × [0°, 90°] is covered by the manifolds. For inclinations up to ∼5°, the arch-like structures are almost unchanged compared to those initially observed in the orbital plane of Jupiter. At higher inclinations, the number of encounter orbits rapidly decreases to narrow domains where the manifolds stretch up to inclinations of 90° (and above) in a very steep manner.

Secular dynamics of a coplanar, non-resonant planetary system, consisting of a star and two planets

AbstractWe consider an exoplanetary system consisting of a star and two planets. The masses of the planets are significantly less than the mass of the star. The evolution of the orbital motion of exoplanets is studied within the framework of a double averaged unrestricted three-body problem. The main attention is paid to coplanar configurations, when the star and planets move in a certain plane that preserves a constant position. The possibility of reversing the orbital motion of the inner planet is noted.

Evolution equations of multi-planet systems with variable masses

In celestial mechanics and astrodynamics, the study  of the  dynamical evolution of exoplanetary systems is the   relevant topics.    For today more than 3,000 exoplanetary systems are known. In this paper, we study the dynamic evolution of extrasolar systems, when the leading factor of evolution  is the variability of the masses of gravitating bodies. The problem of spherically symmetric bodies with  variable masses is considered in a relative coordinate system, this bodies inter-gravitating according to Newton's law. The quasi-elliptical motions of planets whose orbits do not intersect during evolution are investigated. It is believed that the mass of bodies under consideration  varies isotropically by various known laws with different velocities. The mass of the parent star is considered to be the most massive than its planets and the origin of the relative coordinate system is in the center of the parent star.. Due to the variability of the masses, the differential equations of motion become non-autonomous and the task is difficult. The problem is investigated by methods of perturbation theory. The canonical perturbation theory based on a periodic motion over a quasi-canonical section is used.  Canonical equations of motion are obtained in analogues of the second Poincare system, which are effective in the case when the analogues of eccentricities and the analogues of the inclination of the orbital plane of planets are sufficiently small.  The secular perturbations of the planets, which determine the behavior of the orbital parameters over long time intervals, are studied. The evolutionary equations of many planetary systems with isotropically varying masses in analogues of the second system of Poincare variables are derived in an analytical form which are obtained using the Wolfram Mathematica computer algebra system. This takes into account the effects of the decreasing mass of the parent star and the growth of the masses of the planets due to the accretion of matter from the remnants of the protoplanetary disk. For the three-planetary problem of four bodies with variable masses, the evolutionary equations in dimensionless variables are obtained explicitly. In the future, these results will be used to study the dynamics of the three-planet system K2-3 in the non-stationary stage of its evolution.

Evolution of pits at the surface of 67P/Churyumov-Gerasimenko

Context. The observation of pits at the surface of comets offers the opportunity to take a glimpse into the properties and the mechanisms that shape a nucleus through cometary activity. If the origin of these pits is still a matter of debate, multiple studies have recently suggested that known phase transitions (such as volatile sublimation or amorphous water ice crystallization) alone could not have carved these morphological features on the surface of 67P/Churyumov-Gerasimenko (hereafter 67P). Aims. We want to understand how the progressive modification of 67P’s surface due to cometary activity might have affected the characteristics of pits and alcoves. In particular, we aim to understand whether signatures of the formation mechanism of these surface morphological features can still be identified. Methods. To quantify the amount of erosion sustained at the surface of 67P since it arrived on its currently observed orbit, we selected 380 facets of a medium-resolution shape model of the nucleus, sampling 30 pits and alcoves across the surface. We computed the surface energy balance with a high temporal resolution, including shadowing and self-heating contributions. We then applied a thermal evolution model to assess the amount of erosion sustained after ten orbital revolutions under current illumination conditions. Results. We find that the maximum erosion sustained after ten orbital revolutions is on the order of 80 m, for facets located in the southern hemisphere. We thus confirm that progressive erosion cannot form pits and alcoves, as local erosion is much lower than their observed depth and diameter. We find that plateaus tend to erode more than bottoms, especially for the deepest depressions, and that some differential erosion can affect their morphology. As a general rule, our results suggest that sharp morphological features tend to be erased by progressive erosion. Conclusions. This study supports the assumption that deep circular pits, such as Seth_01, are the least processed morphological features at the surface of 67P, or the best preserved since their formation.

Teaching planetary retrograde motion using a local positioning system

For millennia, humans have observed planetary retrograde motion and attempted to explain the phenomena. Our modern understanding of the motions of bodies within the Solar System is built up from a rich history of past models, each of which tried to explain astronomical observations while also being influenced by the contemporary belief system. One of the pivotal observations that assisted astronomers in the development of our current planetary model is planetary retrograde motion. Complexities in heliocentric and geocentric planetary models coupled with the change of reference frame required to visualize retrograde can be challenging for students. For this reason, we developed a kinaesthetic learning activity for introductory physics and astronomy courses that requires students to physically walk planetary orbits and allows them to see apparent motions across a virtual sky in real-time. In this paper, we present multiple activities using a local positioning system that are based on changing historical models for the retrograde phenomenon. We aim for these activities to culminate in students’ holistic understanding of how astronomically observed retrograde patterns were explained by models stemming from the existing scientific knowledge and beliefs available at the time.

A New Physical Description of Planetary Motion-Spinvector Motion I

A new planetary motion theory, spin-vector motion is developed, based on Kepler's second laws of planetary motion that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. The planetary motion follows the same Schrodinger wave equation as quantum particles. The planets have same particle-wave duality, wave length and momentum relation, energy and wave frequency relation as quantum particles too. Based on our deduction we conclude that the Schrodinger equation can be applied successfully to photons, quantum particles, and celestial bodies, but with different energy constant for celestial bodies. Even though these objects are with different masses, sizes and with different wave speeds. And we predict that the wave speed exceeding light speed will not have any impacts on the wave equation form. This spin-vector in motion theory or Spin-vector Mechanics will be a candidate theory leading to the theory of everything.

The Laws of Planetary Motion (A Teaching Method Inspired by the History of Physics)

In high school, and also in introductory physics courses in higher levels of schooling, the law of universal gravitation of planets is introduced by postulating Johannes Kepler’s three laws, and later Isaac Newton’s law of the inverse of the square of the distance to the Sun. The justification of the laws is only achieved in advanced courses in mechanics. We present material to teach the law of areas and the law of attraction, which is inspired by Newton’s analysis of motions under central forces, as done in Mathematical Principles of Natural Philosophy. The method is geometric, so that the dynamics behind the laws can be discussed with a ruler, triangles, and compass, or some software, without appeal to equations, and can be used on levels of instruction that dispense with analytic treatment.

Stability analysis of planetary systems via second-order Rényi entropy

ABSTRACT The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data are continuously growing and the precision allows us to obtain accurate planetary orbits, the canonical stability analysis still requires N-body simulations and phase space trajectory investigations. We propose a method for stability analysis of planetary motion based on the generalized Rényi entropy obtained from a scalar measurement. The radial velocity data of the central body in the gravitational three-body problem are used as the basis of a phase space reconstruction procedure. Then, Poincaré’s recurrence theorem contributes to finding a natural partitioning in the reconstructed phase space to obtain the Rényi entropy. It turns out that the entropy-based stability analysis is in good agreement with other chaos detection methods, and it requires only a few tens of thousands of orbital period integration time.

Drift Rates of Narrowband Signals in Long-term SETI Observations for Exoplanets

The Doppler shift of a radio signal is caused by the relative motion between the transmitter and receiver. The change in frequency of the signal over time is called the drift rate. In the studies of radio search for extraterrestrial intelligence (SETI), extraterrestrial narrowband signals are expected to appear “chirped” since both the exoplanet and Earth are moving. Such planet rotation and orbital revolution around the central star can cause a nonzero drift rate. Other relative motions between the transmitter and receiver, such as the gravitational redshift and galactic potential, are negligible. In this paper, we mainly consider the common cases in which the drift rate is contributed by the rotations and orbits of Earth and the exoplanet in the celestial mechanics perspective, and we briefly discuss other cases different from the Earth–exoplanet one. We can obtain the expected pseudosinusoidal drifting result with long-term observations and shorter orbital periods of exoplanets. Exoplanets with higher orbital eccentricities can cause asymmetric drifting. The expected result should be intermittent pseudosinusoidal curves in long-term observations. The characteristics of pseudosinusoidal curves, as another new criterion for extraterrestrial signals, can be applied to long-term SETI reobservations in future research.

The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics

<i>The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics</i>

Wavier jet streams driven by zonally asymmetric surface thermal forcing

Recent studies have argued that global warming is responsible for a wavier jet stream, thereby driving midlatitude extreme flooding and drought. Polar amplification-the relative enhancement of high-latitude temperatures under global warming-is argued to be the principal climate state driving midlatitude extremes. Namely, the decreased meridional temperature gradient suppresses the mean zonal winds, leading to wavier midlatitude jets. However, although observations are consistent with such a linkage, a detailed dynamical mechanism is still debated. Here, we argue that the Northern Hemisphere land-sea thermal forcing contrast that underlies zonally asymmetric forcing drives a response in the planetary geostrophic motion, which provides balanced mean fields for synoptic eddies in midlatitudes and thus for wavier jet streams. We show that when the barotropic zonal mean wind U is smaller than a threshold, proportional to the β-plane effect and dry static stability, the flow field exhibits a dramatic transition from a response confined near the surface to one reaching the upper atmosphere. As global warming enhances polar amplification, the midlatitude jet stream intensity is suppressed. The confluence of these effects leads to wavier jet streams.

Symplectic Effect for the Numerical Solution of Conservative Systems

The focus of this paper is to use those numerical tools for conservative systems that provides an approximation flow for the Hamiltonian system, which defines a worldwide physical systems including planetary motion, simple Pendulum and several models. It has been observed that the symplectic scheme is found very effective for astronomical many body systems. We are particularly interested in those numerical schemes that possess the qualitative behavior of such systems and symplecticity of the flow. In this paper, we investigate the Hamiltonian systems for its symplecticity and G-symplecticity numerically and show explicitly how these techniques be effective for the preservation of energy. Since we have applied this scheme for the planetary body motion and found that the results are very much effective and the energy preserves during the motion of the planetary bodies. Since the aim of this paper is to investigate the energy preservation adopted by the symplectic methods.

Inverse-Square Orbits Revisited

Kepler’s laws are an essential part of any mechanics course at the introductory level. They are commonly used to illustrate the power of Newton’s laws at explaining and predicting the motion of planets and comets around the sun. While the derivation of the second and third laws are outlined in every standard textbook, that of the first law (and the shape of orbits in general) is invariably omitted, due mainly to the insufficient proficiency of the targeted students in differential equations. The paper offers a workaround this difficulty. Assuming familiarity with the basic properties of conics and employing Newton’s law of universal gravitation, we manage to obtain, with very little calculus, the classic result: orbits are conic sections whose nature is determined by the body’s total energy.

Exoplanet Radio Transits as a Probe for Exoplanetary Magnetic Fields—Time-dependent MHD Simulations

We perform a series of time-dependent magnetohydrodynamic simulations of the HD 189733 star–planet system in order to predict radio transit modulations due to the interaction between the stellar wind and planetary magnetic field. The simulation combines a model for the stellar corona and wind with an exoplanet that is orbiting the star in a fully dynamic, time-dependent manner. Our simulations generate synthetic radio images that enable us to obtain synthetic radio light curves in different frequencies. We find a clear evidence for the planetary motion in the radio light curves. Moreover, we find specific repeated features in the light curves that are attributed to the passage of the planetary magnetosphere in front of the star during transit. More importantly, we find a clear dependence in magnitude and phase of these light-curve features on the strength of the planetary magnetic field. Our work demonstrates that if radio transits could be observed, they could indeed provide information about the magnetic field strength of the transiting exoplanet. Future work to parameterize these light-curve features and their dependence on the planetary field strength would provide tools to search for these features in radio observation data sets. As we only consider the thermal radio emission from the host star for our study, very sensitive radio interferometers are necessary to detect these kinds of planetary transits in radio.

Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks

Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural networks can assist us in exploring the fundamental laws of classical mechanics from data of planetary motion. Firstly, we predict the orbits of planets in the geocentric system using the gate recurrent unit, one of the common neural networks. We find that the precision of the prediction is obviously improved when the information of the Sun is included in the training set. This result implies that the Sun is particularly important in the geocentric system without any prior knowledge, which inspires us to gain Copernicus’ heliocentric theory. Secondly, we turn to the heliocentric system and make successfully mutual predictions between the position and velocity of planets. We hold that the successful prediction is due to the existence of enough conserved quantities (such as conservations of mechanical energy and angular momentum) in the system. Our research provides a new way to explore the existence of conserved quantities in mechanics system based on neural networks.

Optimizing the Clearance Fit of a Progressive Cavity Pump for the Thermal Recovery of Petroleum Using Fluid-Structure Thermal Coupling.

It is important to incorporate the effects of fluid–structure thermal coupling and the boundary conditions when calculating the thermal dynamics and response of progressive cavity pumps. This study develops a fluid–structure thermal coupling model of the progressive cavity pump to improve the accuracy of its measured field of deformation and the temperature field of the stator. A function for the macroscopic motion of a rigid body is written in a typical fluid domain, and the user-defined function (UDF) in FLUENT is used to load the boundary of the rotor to realize its planetary motion. Local remeshing is used to update the moving grid, and the viscoelastic hysteretic heat of the stator is treated as the internal source of heat. One-way decoupling is used based on tire slip theory, and heat flux on the surface of the stator is calculated by the ANSYS Parametric Design Language (APDL). The sequential fluid–structure thermal coupling of the progressive cavity pump is calculated by using the ANSYS workbench. A scheme for optimizing the fit clearance of the stator and rotor is given to improve the volumetric efficiency of the progressive cavity pump and prevent the stator from being stuck owing to a large deformation, and the calculations are verified by experiments on volumetric efficiency. The average deviation in the calculated volumetric efficiency was less than 5% compared with the experimental values. The proposed scheme provides a theoretical basis for the optimal design of the progressive cavity pump for the thermal production of petroleum.

Effect of Some Modified Models of Gravity on the Radial Velocity of Binary Systems

For many classes of astronomical and astrophysical binary systems, long observational records of their radial velocity V, which is their directly observable quantity, are available. For exoplanets close to their parent stars, they cover several full orbital revolutions, while for wide binaries such as, e.g., the Proxima/α Centauri AB system, only relatively short orbital arcs are sampled by existing radial velocity measurements. Here, the changes ΔV induced on a binary’s radial velocity by some long-range modified models of gravity are analytically calculated. In particular, extra-potentials proportional to r−N,N=2,3 and r2 are considered; the Cosmological Constant Λ belongs to the latter group. Both the net shift per orbit and the instantaneous one are explicitly calculated for each model. The Cosmological Constant induces a shift in the radial velocity of the Proxima/α Centauri AB binary as little as ΔV≲10−7ms−1, while the present-day accuracy in measuring its radial velocity is σV≃30ms−1. The calculational scheme presented here is quite general, and can be straightforwardly extended to any other modified gravity.

ОПРЕДЕЛЕНИЕ КИНЕМАТИЧЕСКИХ И ДИНАМИЧЕСКИХ ХАРАКТЕРИСТИК ТЕХНОЛОШИЧЕСКИХ МАШИН ПЛАНЕТАРНОГО ТИПА

The article deals with issues related to the study of planetary machines. It is demonstrated that they are able to significantly intensify most of the processes applicable to them. This is due to the complication of the trajectory of the movement of the working body and the increase in inertial forces. In addition, planetary units are energy efficient. The influence of the mutual action of grinding bodies on their power characteristics in a planetary mill with external and internal running of the drums is presented. The dependence of destructive forces on the angular velocity, the degree of filling of the grinding drums, the geometric ratios of the mill itself is shown. Sufficiently simple dependences have been obtained for calculating the total speed at any point of the planetary working body of the smoothing machine. Their use makes it possible to analyze the change in speed over a wide range, depending on a number of design and technological parameters. The proposed method allows to calculate the speeds of the working bodies that make planetary motion. Using the methods of classical mechanics, using the instantaneous center of velocities, a formula is obtained for calculating the speed at any point of the mixing blade. It is established that the speed of the blade changes in time according to a sinusoidal law. The total power gradually increases with increasing angular velocity. The results obtained in this article can be applied in the design and operation of planetary units.

The Planetary Theory of Solar Activity Variability: A Review

Commenting the 11-year sunspot cycle, Wolf (1859, MNRAS 19, 85–86) conjectured that “the variations of spot-frequency depend on the influences of Venus, Earth, Jupiter, and Saturn.” The high synchronization of our planetary system is already nicely revealed by the fact that the ratios of the planetary orbital radii are closely related to each other through a scaling-mirror symmetry equation (Bank and Scafetta, Front. Astron. Space Sci. 8, 758184, 2022). Reviewing the many planetary harmonics and the orbital invariant inequalities that characterize the planetary motions of the solar system from the monthly to the millennial time scales, we show that they are not randomly distributed but clearly tend to cluster around some specific values that also match those of the main solar activity cycles. In some cases, planetary models have even been able to predict the time-phase of the solar oscillations including the Schwabe 11-year sunspot cycle. We also stress that solar models based on the hypothesis that solar activity is regulated by its internal dynamics alone have never been able to reproduce the variety of the observed cycles. Although planetary tidal forces are weak, we review a number of mechanisms that could explain how the solar structure and the solar dynamo could get tuned to the planetary motions. In particular, we discuss how the effects of the weak tidal forces could be significantly amplified in the solar core by an induced increase in the H-burning. Mechanisms modulating the electromagnetic and gravitational large-scale structure of the planetary system are also discussed.