Planetary Motion Research Articles

Spatial planetary movements for multi-axis EDM

Spatial planetary movements for multi-axis EDM

Attempt to obtain the general relativistic planet's motion by special relativity techniques

AbstractIt is attempted to derive the general relativistic equation of motion for a planet and its solution solely by the special relativity techniques. The motion of a planet relative to the Sun and that of the Sun to the planet are solved independently in a special relativistic framework using the perturbation theory in celestial mechanics. The solution reveals a nature of the structure of the spacetime under the gravitation of the Sun, and then its effect on the planet's motion is examined. When the motion thus examined are compared with the one obtained by the general relativity theory in post‐Newtonian approximation, both are different concerning the mean motion and the radius of the orbit but exactly the same as for the perihelion precession.

Analysis of Principle Behind the Stability, Self-Revolution and Orbital Formation of Planets around the Sun

Abstract: There are lots of moving parts in the Universe, as nothing exists in isolation. There are trillions of large masses in our Solar System, all orbiting around the galactic centre on timescales of hundreds of millions of years. In this paper, I present the idea of the Existence of the force of attraction by the Sun due to its constituents. Same as that, the debris of the sun due to the big bang may also possess some characteristics of the sun since all these objects possess similar origins. This means “Every object possesses a force of attraction that has the tendency to attract every other object of the universe but this tendency is limited to a certain extent based upon the constituent, size and distance between the object”. This force of attraction is exhibited in multiple axis by every object. It altogether results in the formation of a closed-circuit form of connection between every object present inside this cluster of objects in space. The same principle applies to the galactic centre of the universe also. This force of attraction is responsible for the stability, Self revolution and orbital revolution of planets around the sun.

Law of Gravity Blurred by Perturbed Planetary Orbits for Alien Observers

The Fermi paradox is the contradiction between the high probability for aliens and its lack of evidence. This is perhaps the most significant of all questions in astronomy. Nowadays, thousands of exoplanets have been detected, providing us more information directly from alien planets to revisit Fermi paradox. Over recent years, the detection of habitable exoplanets has grown rapidly, and most of them in multi-planet system with fairly compact structures, which is partly due to our observational techniques. In such systems, planets’ orbits are significantly perturbed by gravitational interactions from each other. To travel within or out of a planetary system, one must understand the law governing planetary motion, but can extraterrestrials deduce the universal law of gravitation by observing planets in their system, as Johannes Kepler and Isaac Newton had done? Here we show that due to the close planetary orbits in systems hosting habitable exoplanets, planetary orbits significantly deviate from the Keplerian orbit. In our N-body simulation over a period of 300 days, out of the ten planetary systems which all include habitable exoplanets in our sample, the mean anomaly deviates from a Keplerian orbit by more than 5 degrees while the system remains stable as the semi-major axis remains relatively constant. This would significantly complicate what the observers on those planets observe as the motion in the system would not appear to have a pattern periodically. Although planets indeed affect each other in all systems, the compact nature of these systems have magnified the effect and provide no way for the extraterrestrials inhabiting those planets to discover the universal law of gravitation. Extraterrestrials lacking the law of gravity definitely cannot facilitate traveling beyond their planets. That could be one possible resolution of Fermi paradox, reducing the population of high-developed civilization in Universe.

An efficient Planet Optimization Algorithm for solving engineering problems

In this study, a meta-heuristic algorithm, named The Planet Optimization Algorithm (POA), inspired by Newton's gravitational law is proposed. POA simulates the motion of planets in the solar system. The Sun plays the key role in the algorithm as at the heart of search space. Two main phases, local and global search, are adopted for increasing accuracy and expanding searching space simultaneously. A Gauss distribution function is employed as a technique to enhance the accuracy of this algorithm. POA is evaluated using 23 well-known test functions, 38 IEEE CEC benchmark test functions (CEC 2017, CEC 2019) and three real engineering problems. The statistical results of the benchmark functions show that POA can provide very competitive and promising results. Not only does POA require a relatively short computational time for solving problems, but also it shows superior accuracy in terms of exploiting the optimum.

Johannes Kepler. The Sun as the Heart of the World

In two early unpublished texts (a Disputation in favor of Copernicus of 1593 and the Apologia pro Tychone against Ursus of 1600), Kepler argued with the Pythagoreans that, contrary to Aristotle ( De caelo, ii, 13), the geometrical center of the cosmos coincides with its natural center. Since the Sun is the body that occupies this central position, Kepler conceives it as the heart of the world and the principle of planetary motion. In the following study, we examine how Kepler further develops this pivotal theme in a letter to Herwart von Hohenburg of 25 March 1605 and later in the Dissertatio cum nuncio sidereo (Prague, 1610) as well as in a German translation and critical commentary of the Aristotelian chapter, which ultimately remained unpublished as well.

Kinematics and Dynamics of a Particle in Gravitation Field

It is accepted that three-dimensional physical space is a hypersurface with a Riemannian metric in four-dimensional space. The metric tensor of this three-dimensional space is defined by Einstein's equations. Another coordinate of four-dimensional space is time. In this space, the equations of the world line of a particle with a mass m are defined under certain initial conditions: the starting point of the space and the vector of the particle's initial velocity. This approach removes all the problems and contradictions noted in the monograph [1], and the resulting equations adequately describe, for example, the curvilinear motion of planets without energy change.

N-body Interactions will be Detectable in the HR-8799 System within 5 yr with VLTI-GRAVITY

Abstract While Keplerian orbits account for the majority of the astrometric motion of directly-imaged planets, perturbations due to N-body interactions allow us to directly constrain exoplanet masses in multiplanet systems. This has the potential to improve our understanding of massive directly-imaged planets, which nearly all currently have only model-dependent masses. The VLTI-GRAVITY instrument has demonstrated that interferometry can achieve 100x better astrometric precision than existing methods, a level of precision that makes detection of planet–planet interactions possible. In this study, we show that in the HR-8799 system, planet–planet deviations from currently used Keplerian approximations are expected to be up to one-quarter of a milliarcsecond within five years, which will make them detectable with VLTI-GRAVITY. Modeling of this system to directly constrain exoplanet masses will be crucial in order to make precise predictions.

Design and contact characteristics analysis of a new internal twin-screw pump

This paper designs a new internal meshing twin-screw pump (new twin-screw pump). To study the new twin-screw pump in the principle, performance parameters, and contact characteristics of the differences with the single-screw pump, the mathematical method of motion conversion is used to convert the planetary motion of the single-screw pump into the fixed-axis rotation of the internally intermeshing twin-screw pump. It is found that the movement relationship of the two pumps is similar. When the structural parameters of the two pumps are the same, the flow per revolution of the single-screw pump is N+1 times that of the new twin-screw pump. To obtain the force transmission characteristics in the internal meshing process, a numerical method was used to analyze the structure of the new twin-screw pump statically. Due to the existence of the meshing relationship, the influence of the screw meshing fit clearance, progression, and pitch on the contact stress is further explored. The results of the study show that the internal and external rotor contact stresses show a trend of small in the middle and large at the ends, the stress distribution coefficient [Formula: see text] increases with the increase of the mating clearance, and the stress distribution becomes uneven with the increase of the number of screw stages and pitch. The results of this study provide a basis for the reasonable selection of structural parameters of the new twin-screw pump.

Sidereal Astrology in Medieval Europe (Twelfth and Thirteenth Centuries): Traces of a Forgotten Tradition

Abstract Sets of astronomical tables available in Latin Europe during the Middle Ages can be classified based on whether they imitated Ptolemy in using a tropical zodiac for displaying planetary mean motions or followed an Indian tradition of preferring a sidereal reference frame. While this basic bifurcation in medieval computational astronomy is well known to modern scholars, there has so far been no systematic research concerning its consequences for the practice of astrology in this period. This article makes a first step by documenting cases from the twelfth and thirteenth centuries where Latin astrologers employed the sidereal zodiac for their calculations or expressly recommended its use for astrological purposes. Basing itself on printed sources as well as unpublished manuscript material, it provides evidence that a commitment to sidereal coordinates united several important figures during the early phases of the assimilation of Islamic mathematical astronomy in Latin Europe, but largely disappeared after 1250. As will be argued in the conclusion, this move away from sidereal astrology may possibly be linked to the thirteenth-century emergence of Paris as a major European center for the study of astrology.

Spin–orbit gravitational locking—an effective potential approach

The objective of this paper is to study the tidally locked 3:2 spin–orbit resonance of Mercury around the Sun. In order to achieve this goal, the effective potential energy that determines the spinning motion of an ellipsoidal planet around its axis is considered. By studying the rotational potential energy of an ellipsoidal planet orbiting a spherical star on an elliptic orbit with fixed eccentricity and semi-major axis, it is shown that the system presents an infinite number of metastable equilibrium configurations. These states correspond to local minima of the rotational potential energy averaged over an orbit, where the ratio between the rotational period of the planet around its axis and the revolution period around the star is fixed. The configurations in which this ratio is an integer or an half integer are of particular interest. Among these configurations, the deepest minimum in the average potential energy corresponds to a situation where the rotational and orbital motion of the planet are synchronous, and the system is tidally locked. The next-to-the deepest minimum corresponds to the case in which the planet rotates three times around its axis in the time that it needs to complete two orbits around the Sun. The latter is indeed the case that describes Mercury’s motion. The method discussed in this work allows one to identify the integer and half-integer ratios that correspond to spin–orbit resonances and to describe the motion of the planet in the resonant orbit.

Analysis of Factors Influence on the Efficiency of the Burnishing Rolling Process

Abstract Burnishing is a cold processing process that produces a good quality of the surface by the planetary motion of rolls hardened on turned or perforated surfaces. The result is a mirror surface with high wear and corrosion resistance, the surface of the part depends on several factors such as: ductility of the material, tensile strength, roughness of the workpiece surface before rolling, diameter and shape of the rollers (https://sinotech.com/resources/). Burnishing is the most suitable process to improve the fatigue resistance of dynamically requested parts. Because cold rolling does not remove material, then only the surface roughness rolls, influences the obtained roughness. That is why the roughness of the rolls will be equal to the roughness of the part. The cold rolling finishing method does not require the use of special machines, they can be used existing machines in the production sections such as: milling machines, lathes, drilling machines, lathes with numerical control (https://en.wikipedia.org/wiki/).

Cover Feature: Post‐Synthetic Macrocyclization of Rotaxane Building Blocks (ChemPlusChem 3/2022)

The Cover Feature shows a night sky photo from dusk until dawn illustrating relative orbital motions of planets and stars in universe due to gravitational interactions. Far in the whirl of light patterns are [2]rotaxane scaffolds that may undergo cyclization. Coming to the foreground, the resulting appealing cyclic interlocked molecular architectures are the real star molecular targets of the review, furthermore acting as molecular shuttles for some of them. More information can be found in the Review by Frédéric Coutrot, and co-workers.

Apparent retrograde motions of planets

Thanks to the COVID-19 pandemic, virtually all in-person instruction was shut down across the country in 2020 and beyond. This posed special problems for laboratory-based science courses, as those are defined by the conducting of experiments in person and often with specialized equipment unavailable outside of the classroom. Here I discuss a semester-long project for introductory astronomy that can be performed at home with very basic and inexpensive equipment. And, thanks to the vagaries of the orbits of the planets, variations of this activity can be carried out in many future semesters.

Relativistic Precession of Elliptical Orbits of a Circumbinary Planet can be Cancelled

In publications presenting analytical results on the non-coplanar motion of a circumbinary planet it was shown that the unperturbed elliptical orbit of the planet undergoes simultaneously two kinds of the precession: the precession of the orbital plane and the precession of the orbit in its own plane. It is also well-known that there is also the relativistic precession of the planetary orbit in its own plane. In the present paper we study a combined effect of the all of the above precessions. For the general case, where the planetary orbit is not coplanar with the stars orbits, we analyzed the dependence of the critical inclination angle ic, at which the precession of the planetary orbit in its own plane vanishes, on the angular momentum L of the planet. We showed that the larger the angular momentum, the smaller the critical inclination angle becomes. We presented the analytical result for ic(L) and calculated the value of L, for which the critical inclination value becomes zero. For the particular case, where the planetary orbit is not coplanar with the stars orbits, we demonstrated analytically that at a certain value of the angular momentum of the planet, the elliptical orbit of the planet would become stationary: no precession. In other words, at this value of the angular momentum, the relativistic precession of the planetary orbit and its precession, caused by the fact that the planet revolves around a binary (rather than single) star, cancel each other out. This is a counterintuitive result.

Attitude determination and control for the deployment preparation phase of a space tether mission

A compact and low-cost architecture for the sensor and actuators of a deorbit device based on an electrodynamic tether, together with the corresponding attitude determination and control algorithms, is proposed and studied through numerical simulations. The solution, aimed at the tether deployment preparation phase, is based on four sensors (gyroscope, magnetometer, coarse sun sensors and GNSS), magnetorquers for the attitude control, a multiplicative Extended Kalman Filter, and the construction of two independent control laws for the detumbling of the deorbit device and the subsequent deployment pointing stabilization phase. The latter involves the alignment of the longitudinal axis of the deorbit device along a given direction different from nadir with an error below 10°. Monte Carlo analysis revealed the existence of an optimal gain for the control law in the detumbling phase that yields a detumbling time of around one orbit revolution only. The deployment pointing phase was also investigated through Monte Carlo analysis, for which initial conditions, errors in the attitude sensors, and uncertainties in the inertial properties of the device and the residual magnetic dipole were varied. The numerical results indicate that the proposed architecture and algorithms fit the requirements and are suitable for space tether missions in Low Earth Orbit.

The Effect of Post-Newtonian Spin Precessions on the Evolution of Exomoons’ Obliquity

Abstract Putative natural massive satellites (exomoons) have gained increasing attention when they orbit Jupiter-like planets within the habitable zone of their host main-sequence star S. An exomoon s is expected to move within the equatorial plane of its host planet p, with its spin S s aligned with its orbital angular momentum L , which, in turn, is parallel to the planetary spin S p. If, in particular, the common tilt ε of such angular momenta to the plane of the satellite–planet motion about the star, assumed fixed, has certain values, the stellar latitudinal irradiation experienced on the exomoon may allow it to sustain life as we know it, at least for certain orbital configurations. An Earth analog (similar in mass, radius, oblateness, and obliquity) is considered, which orbits within 5–10 planetary radii R p from its Jupiter-like host planet. The de Sitter and Lense–Thirring spin precessions due to the general relativistic post-Newtonian (pN) field of the host planet have an impact on an exomoon’s habitability for a variety of different initial spin–orbit configurations. Here I show it by identifying long-term variations in the satellite’s obliquity ε s, where variations can be ≲10°–100°, depending on the initial spin–orbit configuration, with a timescale of ≃0.1–1 million years. Also the satellite’s quadrupole mass moment J 2 s induces obliquity variations that are faster than the pN ones but do not cancel them. Tidal dissipations, which may potentially have a relevant impact on the outlined pattern, are not included in the present analysis.

Eviction-like resonances for satellite orbits

The motion of a satellite can experience secular resonances between the precession frequencies of its orbit and the mean motion of the host planet around the star. Some of these resonances can significantly modify the eccentricity (evection resonance) and the inclination (eviction resonance) of the satellite. In this paper, we study in detail the secular resonances that can disturb the orbit of a satellite, in particular the eviction-like ones. Although the inclination is always disturbed while crossing one eviction-like resonance, capture can only occur when the semi-major axis is decreasing. This is, for instance, the case of Phobos, the largest satellite of Mars, that will cross some of these resonances in the future because its orbit is shrinking owing to tidal effects. We estimate the impact of resonance crossing in the orbit of the satellite, including the capture probabilities, as a function of several parameters, such as the eccentricity and the inclination of the satellite, and the obliquity of the planet. Finally, we use the method of the frequency map analysis to study the resonant dynamics based on stability maps, and we show that some of the secular resonances may overlap, which leads to chaotic motion for the inclination of the satellite.

The Investigation of the Dynamical Evolution of Extrasolar Three-planetary System GJ 3138

This article is devoted to studying the dynamical evolution and orbital stability of compact extrasolar three-planetary system GJ 3138. In this system, all semimajor axes are less than 0.7 au. The modeling of planetary motion is performed using the averaged semi-analytical motion theory of the second order in planetary masses, which the authors construct. Unknown and known with errors orbital elements vary in allowable limits to obtain a set of initial conditions. Each of these initial conditions is applied for the modeling of planetary motion. The assumption about the stability of observed planetary systems allows to eliminate the initial conditions leading to excessive growth of the orbital eccentricities and inclinations and to identify those under which these orbital elements conserve moderate values over the whole modeling interval. Thus, it becomes possible to limit the range of possible values of unknown orbital elements and determine their most probable values in terms of stability.

Mechanism research and field test of a novel axial vibratory tool for friction reduction in long horizontal wells

When drilling long horizontal wells, the axial vibration generated by the drilling string at the bottom hole will effectively alleviate the phenomenon of “frictional drag of the drill bit”, which can reduce the friction and enhance the penetration rate. Based on the principle of vibration impact, the axial vibratory tool for friction reduction with a diameter of 127 mm was designed, and the mechanical structure and working principle of this tool were also introduced in detail. First, the planar planetary motion of the throttle valve was described, and a model for calculating the cross-flow area at different moving valve and fixed valve sizes was established. Then, considering the effect of local head loss, the mechanical analysis of the working pressure drop generated by the fluid at each site within the dynamic short connector was carried out, and the relationship curves of the working pressure drop with time and cross-flow area were obtained. After that, the Viscous-Realizable k-ε turbulence model was used to simulate the water hammer pressure of the dynamic short connector, and the variation of water hammer pressure with time, cross-flow area, and cross-sectional flow velocity under 3D/2D conditions was obtained. Based on the undamped vibration differential equation, the axial impact force and axial vibration displacement generated by the vibratory tool were solved. The calculated results are in good agreement with the experimental test results. The field test of this vibratory tool was conducted in well FNHW4084 of the Mahu oil field in Xinjiang, China. The tool was in the well for 10.68 days. The drilling fluid was circulated for 202 h. The pure drilling time was 125.83 h. The drilling footage of a single tool is 596 m with an average penetration rate of 4.74 m/h. Rate of penetration in the test section was increased by 254% compared with the upper section. Compared with the same kick-off section of the neighboring well FNHW4026, the one-trip drilling footage of the test section was increased by 150% and the penetration rate was increased by 126%. The field test results present that this vibratory tool can significantly increase the drilling footage and penetration rate of horizontal kick-off section.