Law Of Universal Gravitation Research Articles

The Problem of Two Bodies with a Finite Velocity of Gravity

From the moment of Newton’s discoveryof the law of universal gravitation, ordinary differentialequations were used to study the motion of bodies,since it was assumed that the velocity of gravitationis infinite. However, in reality the velocity of gravityis finite, which is consistent with the theory of relativityof Einstein, which postulated that the velocity ofgravity matches the velocity of light, and the studiesconducted by S. Kopeikin and E. Fomalont on the fundamentallimit of the velocity of gravity. Due to thedelay of the gravitational field for studying the motionof bodies, the mathematical apparatus based on differentialequations with a delay argument is the mostacceptable one. These equations are used to constructand study the mathematical model of the motion of twobodies. It is shown that the motion of these bodies withidentical masses (with finite velocity of gravity!) is notcarried out in accordance with Kepler’s laws.

A novel shilling attack detection model based on particle filter and gravitation

With the rapid development of e-commerce, the security issues of collaborative filtering recommender systems have been widely investigated. Malicious users can benefit from injecting a great quantities of fake profiles into recommender systems to manipulate recommendation results. As one of the most important attack methods in recommender systems, the shilling attack has been paid considerable attention, especially to its model and the way to detect it. Among them, the loose version of Group Shilling Attack Generation Algorithm (GSAGen l ) has outstanding performance. It can be immune to some PCC (Pearson Correlation Coefficient)-based detectors due to the nature of anti-Pearson correlation. In order to overcome the vulnerabilities caused by GSAGen l a gravitation-based detection model (GBDM) is presented, integrated with a sophisticated gravitational detector and a decider. And meanwhile two new basic attributes and a particle filter algorithm are used for tracking prediction. And then, whether an attack occurs can be judged according to the law of universal gravitation in decision-making. The detection performances of GBDM, HHT-SVM, UnRAP, AP-UnRAP Semi-SAD, SVM-TIA and PCA-P are compared and evaluated. And simulation results show the effectiveness and availability of GBDM.

Improved FAST corner‐detection method

An improved features from accelerated segment test (FAST) corner-detection method for suppressing SAR image speckle noise is proposed here. The direction of the corner candidate is first computed by the law of universal gravitation and is introduced into corner detection to divide the 16 pixels around the corner candidate into two groups without repeatedly searching. Then, the similarity between the corner candidate and its surrounding pixels is computed to suppress the points affected by SAR speckle noise. Finally, the phenomenon of corner density is eliminated based on non-maximum suppression. The experimental results show that authors’ method has better suppressing effect compared with FAST-8 and SIFT corner-detection methods.

Calculation of the Precession of the Perihelion of Mercury’s Orbit Within the Framework of the Generalized Law of Universal Gravitation with Allowance for the Ellipticity of Planet Orbits

The precession of the perihelion of Mercury’s orbit is simulated numerically within the framework of the generalized law of universal gravitation in the field of the Sun and planets taking into account the ellipticity of the planet orbits and new data on the flattening, the mass of the Sun, and the gravitational constant. Calculations were carried out with increased accuracy (up to 19–20 decimal places) and iteration steps of 0.00005 s and 0.0001 s starting from the asteroid belt. It has been shown that the average precession of the perihelion of Mercury’s orbit in 100 years calculated within the framework of the generalized law of universal gravitation and averaged over long time periods from several hundred years to several thousand years taking into account the ellipticity of planet orbits is ~554.2”. This is less than the observed shift of the perihelion of Mercury’s orbit by ~19.9”. As is well known, the observed shift is ~574.1”. That is, the question on the adequacy of the generalized law of universal gravitation to the observances still remains open. However, it is possible that an object of small size (or several such objects) may be located inside Mercury’s orbit, and one more object, whose mass should not exceed at least ~0.2 of the Earth mass may be located at the diametrically opposite point of the Earth orbit behind the Sun. The results obtained are valid to within 1–2 decimal places.

An Equivalence for Both Coulombian and Gravitational Interactions

The main purpose of this article is to demonstrate that electromagnetic and gravitational phenomenology are two different expressions of the same interaction that we can call “universal interaction”. In order to reach the aim, it is therefore necessary to imagine the matter in a slightly different way, as well as equivalent, to what has been done until today by the literature everywhere accepted. Even if differently imagined, this proposed structure of matter cannot and must not escape from reflecting the measurements and phenomenologies widely experimented in laboratories all over the world. In the proposed model the proton radius; the electron mass; the Avogadro constant; the existence and the mass of neutron and the existence of neutrino are theoretically derived. The main consequence is therefore a more general rewriting of Newton’s law of universal gravitation. A definitive value for the universal gravitational constant is proposed.

Exponentially Changeable Quantities; An Attempt to Extend the Transition Time

As many physical changes and conversions are done by exponential mathematical forms during the time that concerns us, the problem rises when the phenomenon has finished, the conversion is completed and the saturation has come upon the changed quantity. Thus, after the saturation is obtained, time becomes unable to provide us with further information and data. The difficulty becomes substantial when those exponential chronicle changes are used on the chronologies and dating of materials which are under scrutiny. Especially when the duration of time is not extended, the results are limited. Those exponential conversions appear in Plasma Physics in the growth or the damping of the plasma waves, as well. With the present theoretical work a non constant coefficient of the conversion is suggested, whose result is the extension of the conversion time. Also, it is proved that the under-duplication time becomes much more extended than it was with the constant conversion coefficient. Furthermore, it is proved that the under-duplication time continually increases as the under-duplications are multiplied. It should be considered that the initial formulation of the basic physical laws (Coulomb law, Biot-Savart law, law of Universal Gravitation, e.t.c) has been done with the first order approach, taking the ratio coefficients as constants. The present study is an extension of the formulation of the well-known laws with the second order approach.

Calculating Newton’s Gravity (Big G) from Coulomb, Lorentz and Centripetal Force

The velocity of the Earth around the Sun and its corresponding mass are used in a standard centripetal force equation to match what Isaac Newton calculated with the Universal Law of Gravitation in 1687. Electromagnetic calculations are used to prove that electromagnetic forces are an insignificant contributor to the centripetal force or gravity, but do provide the bending force for the planets to maintain a circular orbit around the Sun. It is thus proven using classical physics that the force of gravity is a simple centripetal force with a very small electromagnetic force contribution.

Forces attributed to dark matter may originate from entangled particles as seen in the shape of galaxies formed by GRBs

Recently, it has been suggested that entangled particles may be connected by a wormhole. If that is right, what is the distance between them we have to take into account when applying Newton's law of universal gravitation to these particles? We propose the idea that these particles may attract each other regardless of distance, resulting in a force that behaves exactly the same way as the force derived from presumed dark matter. Traces of such a force seem to be present in galaxies due to gamma ray bursts (GRBs) that produce entangled particles which hit various objects. We can observe that in barred spiral galaxies the arms always pass through the nucleus of the galaxy so we believe that the very first GRB happened at the central supermassive black hole (SMBH) and the arms are the traces of this ancient GRB. If we see an unbarred spiral galaxy, we can be certain that the arms do not pass through the core and we think the very first GRB happened close to the core. Ring galaxies may also be considered as a type of spiral galaxies, since there is a section where the ring is broken, i.e. where the arms do not meet. So the very first GRB happened far from the core. Elliptical galaxies may have resulted from an ancient GRB which hit from outside. The arms rotating in opposite directions of the NGC4622 galaxy support our hypothesis. Finally in the silk threads of the spider web of the universe, the traces of GRBs can be seen.

Isaac Newton and Natural Philosophy

Isaac Newton is generally regarded as one of the greatest scientists in history, yet the spectrum of his interests was much broader than that of a contemporary scientist. He was deeply involved in alchemical, religious and biblical studies, and in the later part of his life he played a prominent role in British politics, economics and the promotion of scientific research. Newton's pivotal work Philosophiae naturalis principia mathematica, which sets out his laws of universal gravitation and motion, is regarded as one of the most important works in the history of science. Niccolo Guicciardini's enlightening biography offers an accessible introduction to Newton's celebrated work in mathematics, optics and astronomy and to how Newton viewed these scientific fields in relation to his quest for the deepest secrets of the universe, matter theory and religion. Guicciardini sets Newton the natural philosopher in the troubled context of the religious and political debates that took place during Newton's life, which spanned from the years of the Civil War to the Restoration, the Glorious Revolution and the Hanoverian succession. Taking into account the latest Newtonian scholarship, this fast-paced biography will appeal to all those with an interest in this iconic figure and the great scientific revolution of the early modern period.

Technological Applications of the Grand Unified Theory

This paper presents the fundamentals of quantum gravity, one of the two pillars of the grand unified theory (GUT) and its technological applications. GUT is a physical theory, i.e., a mathematical space where the basic premises or axioms are laws of nature. Therefore, GUT inherits the rigor of mathematics, its language, as a deductive system. Proposed by Albert Einstein in the 1920s to unify the four forces of nature – gravity, electromagnetism and the weak and strong forces of quantum physics, it did not materialize until the discovery of the superstring, fundamental building block of matter (1997). The discovery was needed to solve the 200-year old gravitational n-body problem that same year. The solution yielded 9 natural laws of GUT beyond the four laws of thermodynamics and Newton’s three laws of motion and his universal law of gravitation. True to its name, what started with the narrow objective of unifying the four forces of nature, GUT now unifies the natural sciences in the sense that every natural science field is an extension of GUT plus natural laws specific to that field. Moreover, every natural phenomenon (appearance of nature) is explained by natural laws. Most of all, GUT explains how nature works which makes it the basis for designing a class of technologies called GUT technologies. We focus on two of them: (1) Technology for massive generation of electricity using the clean, free, indestructible and inexhaustible dark matter that is abundant everywhere around us. This technology if used worldwide can do away with fossil, nuclear fuel and geothermal fuel. Then, it can reverse within limits the negative impact of climate change because nature heals itself when left alone. (2) Magnetic charger for battery cars and vehicles using the same clean, free and inexhaustible energy source. The paper also offers improvement of the magnetic train. Only China, Japan and South Korea own and operate magnetic trains.

Generalized gravity model for human migration

The gravity model (GM) analogous to Newton’s law of universal gravitation has successfully described the flow between different spatial regions, such as human migration, traffic flows, international economic trades, etc. This simple but powerful approach relies only on the ‘mass’ factor represented by the scale of the regions and the ‘geometrical’ factor represented by the geographical distance. However, when the population has a subpopulation structure distinguished by different attributes, the estimation of the flow solely from the coarse-grained geographical factors in the GM causes the loss of differential geographical information for each attribute. To exploit the full information contained in the geographical information of subpopulation structure, we generalize the GM for population flow by explicitly harnessing the subpopulation properties characterized by both attributes and geography. As a concrete example, we examine the marriage patterns between the bride and the groom clans of Korea in the past. By exploiting more refined geographical and clan information, our generalized GM properly describes the real data, a part of which could not be explained by the conventional GM. Therefore, we would like to emphasize the necessity of using our generalized version of the GM, when the information on such nongeographical subpopulation structures is available.

G complex mass theory

Zhou Yi said, “Wuji (No have) born Tai Chi (have), Tai Chi born two state of affairs”. Tai Chi is the smallest unit of substance. The two state of affairs are real (G particle) and imaginary (field). The real state is the particle state (g particle) formed by the accumulation of Tai Chi. The imaginary state is the field (wave) state formed by the evacuation of Tai Chi. The motion of g particles in complex space-time to form quarks and leptons, Neutrinos are magnetic monopole. The field state and the particle state are both opposite and unified, and they transform each other. The Chinese diagram of the universe best defines the qualitative description of this relationship. The complex in mathematics can quantitatively describe the contradiction-the insides of things are opposite and unified in mutual conversion. All the elementary particles (fermion and bosons) are different motions of the sample particle in complex space-time. The real part of physical quantity reflects the Feynman geometry of the particle (fermion) that is macroscopic and non-linear; the imaginary part represents the Lobachevsky geometry that is microscopic, linear and fluctuating (bosons). The real part of electromagnetic force satisfies Coulomb law, and its imaginary part meets Lorentz law. The real part of mass force satisfies Newton’s law of universal gravitation, and its imaginary part meets Coriolis law. The real part of energy constitutes the macroscopical mass-energy equation of Einstein, and the imaginary part forms the Planck equation of microscopical quantum. The rest mass of electron and the charge are not in the same space, but satisfy the relationship between real and imaginary parts. The theory can explain the tests by Hao Ji, Jinsong Feng, Qi Liu, et al. It also shows that the charges with the same nature repulse each other, but attract each other with the different natures; on the contrary, the masses with the same nature attract each other. The theory can fundamentally solve the divergence in quantum field.

An Improved Subpixel Mapping Algorithm Based on a Combination of the Spatial Attraction and Pixel Swapping Models for Multispectral Remote Sensing Imagery

To obtain spatial feature distributions from the mixed pixels of remote sensing images and increase the accuracy of land-cover classification and recognition, a double-calculated spatial attraction model (DSAM) based on the combination of spatial attraction model (SAM) and pixel swapping model (PSM) is presented and verified by introducing the law of universal gravitation to describe the attraction between pixels. In DSAM, SAM was used to improve the initialization algorithm of PSM, and the optimization algorithm of PSM was improved accordingly. Using a SPOT-5 remote sensing image, related subpixel mapping (SPM) experiments were performed to verify the SPM effect of DSAM and to test its accuracy. The experimental results indicated that the DSAM SPM results were superior to the SPM results of SAM and PSM. DSAM was proven effective and applicable for the SPM of remotely sensed images, and the model can improve the accuracy of SPM and landcover classification.

Central force fields and Kepler's laws

In this survey we give very simple proofs of Kepler's Laws and other facts about central force fields using only Newton's second law, Newton's law of universal gravitation, basic notions of vector calculus, and an elementary double integral.Hopefully, this article will help undergraduate students of mathematics and engineering who wish to understand these fundamental scientific discoveries.In many textbooks (see, for instance, [1, 2, 3, 4, 5]), Kepler's Laws are obtained using conservation of energy and angular momentum, differential equations, mobile reference systems, or notions not so well-defined such as differentials or ‘infinitesimal elements’. Some of the arguments appear to be rather involved if one is not accustomed to them, whereas the proof of Kepler's Laws may actually be obtained from quite simple facts.

What is gravity?

We review the historical pursuits and recent developments on the origin of gravity. We start with the Newtonian gravity and Einstein gravity to introduce the two major leaps of the historical pursuits on the origin of gravity. Then we introduce the recent developments on the origin of gravity from the point of view of modified gravity, quantum gravity and holographic gravity. For Newtonian gravity, we start with Keplers law on planetary motion to introduce the Newtons universal law of gravitation, and recent developments on the modified Newtonian dynamics and dark matter; for Einstein gravity, we explain the geometrization of gravity, and introduce the application of Einstein gravity on cosmology and gravitational waves; for modified gravity, we introduce it from the point of view of extra gravitational degrees of freedom, higher derivative gravity and higher dimensional gravity; for quantum gravity, we introduce it from the point of view of covariant quantum gravity, canonical quantum gravity and other scenarios of quantum gravity; for holographic gravity, we introduce its holographic picture, emergent properties and its connection with quantum information. However, the answer to the question of gravity origin still remains unknown. We point out here that three possible roads to approach the nature of gravity can be taken in future. The first one is the coming observations of gravitational waves from both ground-borne and space-borne gravitational-wave detectors. A system involving either black hole or neutron star has certainly run into the regime of strong gravity, which is quite different from previous tests for general relativity that is in the regime of weak gravity. The gravitational-wave observation will most likely provide us with clues on classical gravity with any possible deviations if Einstein gravity does modify itself at classical level. The second one is the understanding of the cosmic acceleration at both early-time and late-time. The cosmic acceleration at early-time is supposed to be driven by cosmic inflation, and the cosmic acceleration at late-time is supposed to be driven by the cosmological constant or alternatively dark energy. Future precise observations of radiation fluctuations and matter fluctuations will show us the way approach the nature of quantum gravity. The third one is the cognition of the relation of quantum gravity and quantum information. The past fifty years or so of pursuit on quantum gravity has leaded us to the path on the conjecture that quantum gravity might be emerged from quantum information. Although the perspective of this idea is not clear, it might be our best shot for now.

Jammer Localization in Multihop Wireless Networks Based on Gravitational Search

Multihop Wireless Networks (MHWNs) can be easily attacked by the jammer for their shared nature and open access to the wireless medium. The jamming attack may prevent the normal communication through occupying the same wireless channel of legal nodes. It is critical to locate the jammer accurately, which may provide necessary message for the implementation of antijamming mechanisms. However, current range-free methods are sensitive to the distribution of nodes and parameters of the jammer. In order to improve the localization accuracy, this article proposes a jammer localization method based on Gravitational Search Algorithm (GSA), which is a heuristic optimization evolutionary algorithm based on Newton’s law of universal gravitation and mass interactions. At first, the initial particles are selected randomly from the jammed area. Then, the fitness function is designed based on range-free method. At each iteration, the mass and position of the particles are updated. Finally, the position of particle with the maximum mass is considered as the estimated jammer’s position. A series of simulations are conducted to evaluate our proposed algorithms and the simulation results show that the GSA-based localization algorithm outperforms many state-of-the-art algorithms.

Finite element analysis of large body deformation induced by a catastrophic near impact event

Finite element simulations of near impacts of terrestrial bodies are presented to investigate possible deformation behavior induced by a massive body during the creation week and/or Genesis Flood. Using the universal law of gravitation, a gravitationally loaded objected is subjected to the ‘pull’ of a near passing fly-by object, and the resulting surface deformations are studied. An Internal State Variable (ISV) pressure dependent plasticity model for silicate rocks (Cho et al., 2018) is used to model the deformation behavior and to capture the history effects involved during the complex surface loading/unloading found in a near impact event. The model is used to simulate the earth and a “fly-by” object interaction and is able to accurately reproduce the internal pressure profiles of the earth and fly-by object. In this context, the fly-by object can be the original Moon, a meteor, or another type of large object that has moved through space to interact with the Earth. Due to the wide range of features that can drive surface deformations during a near impact event, a Design Of Experiments (DOE) methodology was used to independently investigate the influences of five parameters (stationary body size, core material, core/mantle thickness ratio, passing object mass, and passing object distance) concerning surface deformation. The results indicate that the passing body distance, stationary body size, and core/mantle ratio are the most dominant influence parameters on surface deformation. Examination of the ISV parameters of the mantle during deformation shows a complex relationship between the hardening and recovery terms of the model and the resulting plastic strain and surface deformation induced from the near pass event. Surface rise from the near passage of a Moon sized object could be as high as 800 m, in turn causing large tsunamis and possibly causing the Earth’s crust to crack. For this first of its kind study, the conclusions provide understanding of the possible ranges of deformations observed from a near pass event and provides insights into possible catastrophic deformation mechanisms relevant to the young Earth paradigm.

EGSA: a new enhanced gravitational search algorithm to resolve multiple sequence alignment problem

Multiple sequence alignment is a very important and useful tool for genomic analysis in many tasks in bioinformatics. However, finding an accurate alignment of DNA or protein sequences is very difficult since the computational effort required grows exponentially with the sequences number. In this paper, we propose a new sequence alignment algorithm based on gravitational search algorithm (GSA). The gravitational search algorithm (GSA) is a recent metaheuristic inspired from Newton's laws of universal gravitation and motion. Moreover, to avoid the convergence toward local optima, we enhance GSA behaviour by introducing a new mechanism based on simulated annealing concept. Such concept offers a good balance between the exploration and exploitation in GSA and can lead to good alignment quality for the MSA problem. The accuracy and efficiency of the proposed algorithm are compared with recent and well-known alignment methods using BAliBASE benchmark database. The analysis of the experimental results shows that the algorithm can achieve competitive solutions quality.

Law of universal gravitation with real magnetic charges and “dark energy”

The discovery by the author of real magnetic charges, as well as of true antielectrons in the structures of the Physical Mass (atoms, nucleons, substance etc.) assume the necessity of introducing substantial corrections to the interpretation of well–known effects and even of ingrained physical laws, when the formation of which these spinor particles were ignored. The joint orbital currents of electric and magnetic charges in atomic shells are the source of the gravitational field which is vortex electromagnetic field. The results of the study of magnetic charges have made author possible to discover such the entity as the world Physical Triad which is formed by three fundamental phases: Matter, Antimatter and Energo–phase (Energo–medium). The force derivative from of the Energo–phase referred to as “Dark energy” is determined by the nonequilibrium states in the form of local regions pressure created by own particles of Energo–medium which are called the Energions (denoted as e). The formation of “Dark energy” in the Energo–medium is induced by spinor fields, including the gravitational field. It is “Dark Energy” that determines the global energy of the real World and realizes all the so–called interactions between masses and charged particles. The need to amend the existing interpretation of the law of Universal gravitation is associated with the clarification of the real nature of the gravitational field, as well as with the definition of the status of “Dark energy” as real force factor affecting the masses (bodies) in their so–called interactions. The latter provision also assumes the obligatory replacement of the fictitious term “attraction” of bodies to “pressing” or “squeezing” them by the forces of “Dark Energy”. At the same time, the quantitative proportions corresponding to the physical processes observed in practice within the framework of the law of universal gravitation law remain unchanged.

EGSA: a new enhanced gravitational search algorithm to resolve multiple sequence alignment problem

Multiple sequence alignment is a very important and useful tool for genomic analysis in many tasks in bioinformatics. However, finding an accurate alignment of DNA or protein sequences is very difficult since the computational effort required grows exponentially with the sequences number. In this paper, we propose a new sequence alignment algorithm based on gravitational search algorithm (GSA). The gravitational search algorithm (GSA) is a recent metaheuristic inspired from Newton's laws of universal gravitation and motion. Moreover, to avoid the convergence toward local optima, we enhance GSA behaviour by introducing a new mechanism based on simulated annealing concept. Such concept offers a good balance between the exploration and exploitation in GSA and can lead to good alignment quality for the MSA problem. The accuracy and efficiency of the proposed algorithm are compared with recent and well-known alignment methods using BAliBASE benchmark database. The analysis of the experimental results shows that the algorithm can achieve competitive solutions quality.