Law Of Universal Gravitation Research Articles

Basic Mathematical form Of Nature of Space And Dimension of Observable Universe and Beyond

In this innovative research I have advanced the theory of space with definition of space, definition of types of space, and introduced energy-mass transformation, gravity and gravitation force. With this advance research, finally I have defined basic mathematical form of “Nature of space and Dimension of Observable Universe and beyond”.As we know the universe is defined as all space-time and their contents. However, several questions still remain open regarding higher dimension, singularity, gravity collapse at horizon of black hole, unified gravity, theory of everything, dark matter, dark energy, existence of observable universe and beyond, question for mathematical form of everything, question for matter itself, and question for the space itself. These open questions have driven this scientific research of “Basic Mathematical form Of Nature of Space and Dimension of Observable Universe and beyond”. My research findings indicate that the space itself is the entity with having physical properties. The space can be described by physical structure and its transformation. The space has two fundamental properties of energy and mass, and space can be described by energy- mass transformation. From these energy-mass transformation and physical structure transformation, I have defined the gravity, gravitation force and basicmathematical form of“Nature of space and Dimension of Observable Universe and beyond”. This basic mathematical form covers scope of higher dimension, unified gravity, singularity, horizon of black hole, and nature of space of observable universe and beyond. Several research have been conductedfor look into nature of space,space-time, gravity, unified gravity, higher dimensions, unified mathematical formof everything by Minkowski space,Higgs field, Aether medium, Newton’s law of universal gravitation, Electromagnetism, Planck constant,General relativity,Standard Model,Loop Quantum Gravity, Super symmetry, Super gravity, String theory and M-Theory. Despite these research, the questions still remain open for unified nature and for unified mathematical form of “Nature of space and Dimension of Observable Universe and beyond”. By researching the existence of matter, I found the existence of space was just accepted as the void, empty, and space-time background framework. My research reflects “Dimension of Observable Universe and beyond”encompasses all existence of observable universe and beyond it. The advance definition of space, definition of type of space, space transformation and energy-mass transformation perfectly describe existence of entire space & universe and its nature at very fundamental level. This very fundamental nature is presented in basic mathematical form. It is the most accurate foundation to answer those open questions. It is the novelty in astrophysics and foundation of entire existence.

Background gravitational waves as signature of the accelerated cosmic expansion

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature T in thermal equilibrium with a black-body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy. So, each dark particle occupies a very small area of space so-called Planck area [Formula: see text], which represents the minimum area of the whole space-time given by the spherical surface with area [Formula: see text], where [Formula: see text] is the Hubble radius. We realize that such spherical surface is the surface of the black-body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of [Formula: see text] due to the slight stretching of the fabric of space-time.

Learning Effective Good Variables from Physical Data

We assume that a sufficiently large database is available, where a physical property of interest and a number of associated ruling primitive variables or observables are stored. We introduce and test two machine learning approaches to discover possible groups or combinations of primitive variables, regardless of data origin, being it numerical or experimental: the first approach is based on regression models, whereas the second on classification models. The variable group (here referred to as the new effective good variable) can be considered as successfully found when the physical property of interest is characterized by the following effective invariant behavior: in the first method, invariance of the group implies invariance of the property up to a given accuracy; in the other method, upon partition of the physical property values into two or more classes, invariance of the group implies invariance of the class. For the sake of illustration, the two methods are successfully applied to two popular empirical correlations describing the convective heat transfer phenomenon and to the Newton’s law of universal gravitation.

Background gravitational waves as signature of the adiabatic expansion of a black body that represents the dark universe

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature T in thermal equilibrium with a black body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy represented by the vacuum energy, being quantized into virtual particles with extremely small masses that form such gas representing the own tissue of the expanding space–time governed by a negative pressure whose origin is the equation of state of vacuum, i.e., p = −ρ, where ρ is the vacuum energy density. So, each vacuum particle occupies a tiny area of space so-called Planck area [Formula: see text], which represents the minimum area of the whole space–time given by the spherical surface with area [Formula: see text], where RH is the Hubble radius. We realize that such spherical surface is the surface of the black body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the very small order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of 10−17Hz due to the slight stretching of the fabric of space–time.

Matrix methods and teaching the fundamentals of fluid and gas mechanics in higher education institutions

Problem. The instruction of physical and mathematical disciplines in higher education institutions employing cutting-edge methods and universal approaches, which seamlessly integrate scientific and engineering activities of future specialists, remains one of the pertinent and priority tasks. The utilization of multidimensional or even infinite-dimensional spaces has become an effective and nearly indispensable tool in mathematical modeling of physical phenomena. This circumstance is directly linked to the increasing level of abstraction and the refinement of mathematical methods. The use of geometric methods inherent in vector algebra and vector analysis as the foundation for studying mechanics, despite their illustrative nature, is losing its relevance. Methods built upon matrix formalism are evolving as substitutes. The matrix framework enables the exploitation of phase space advantages to derive canonical equations of motion for continuous media and electromagnetic field equations in covariant forms. The electromagnetic potential acquires mechanical significance, allowing the utilization of electromechanical analogies at a fundamental level rather than on a merely formal basis, as done in classical electrodynamics. Goal. The aim of this research is to study and justify the advantages of matrix methods for deriving equations of motion for fluids and gases from the canonical equations of mechanics by utilizing a continuum model in phase and physical space. The research is directed towards demonstrating the connection between the internal microscopic and macroscopic motion of fluids and gases, as well as highlighting the potential of matrix formalism both in terms of modeling and the utilization of computational tools. Methodology. The methodological basis for selecting matrix methods lies in the application of tensor analysis and its generalizations for modeling the motion of fluids and gases in physical and phase space. Results. It has been demonstrated that the matrix method, previously applied to classical and relativistic mechanics, allows for the consideration of the molecular structure of the environment by folding the multidimensional phase space of the mechanical system, represented by a particle of the medium, and thereby deriving equations of motion for fluids and gases from the canonical equations of classical mechanics and the equations of momentum balance of the medium. Originality. The combination of canonical equations as a result of applying the conservation law of matter in the form of balance equations in phase space and momentum balance equations in physical space allows for elucidating the relationship between macroscopic and microscopic motions of the medium, as well as the mathematical structure of the equations of motion for fluids and gases. Practical value. The proposed method allows, while remaining within the standard mathematical training offered by technical educational institutions, to effectively formalize the equations of motion for fluids and gases and provide them with an invariant form. By guiding oneself through invariance, both fundamental laws (such as the law of universal gravitation) and partial laws (the generalized Newton's law) can be obtained.

Effects of Multiple Representation in Student's Conceptual Understanding and Metacognitive Awareness in Mechanics

Using a mixed-method design, the study investigated the effect of the use of multiple representations on 207 (106 male and 101 female) Grade 11 students’ conceptual understanding and metacognitive awareness in learning concepts in physics (mechanics). There were five multiple representations (MRs) used in this study namely: (a) drawing/sketch, (b) free-body diagram/FBD, (c) description, (d) mathematical equation, and (e) concept map (Know - Want to know - Learn). These MRs were embedded in the teacher’s lesson plan as a strategy for teaching and learning selected topics in Mechanics. All these MRs were used by the teacher to discuss each lesson, and by the students to understand and do the tasks given to them. The conceptual understanding of the students was measured by obtaining the mean scores from the formative test scores in the form of a 10-item quiz for the following topics - Kinematics, Laws of Motion, and Universal Law of Gravitation. The students’ metacognitive awareness was measured using the 52-item metacognitive awareness inventory (MAI) questionnaire, given before and after the implementation of the teaching-learning intervention. Students’ perceptions on the use of MRs were also gathered in the form of short responses to a 5-item questionnaire. Their responses to these questions were used to elaborate and explain the results in the subcategories of the MAI. Mean scores in the formative tests revealed that students obtained passing grades in all three quizzes. Results also showed that there was an increasing trend in the students’ mean scores from Quiz 1 to Quiz 3. Paired t-test also showed that the increase in the students’ scores moving from Quiz 1, Quiz 2, to Quiz 3 were significant at p < 0.05. The results of the Metacognitive Awareness Inventory (MAI) questionnaire revealed that a significant difference was observed, when comparing the students’ profile scores before and after the implementation of the teaching-learning intervention. The use of multiple representations (MRs) made the students more aware of how they think about learn the physics concepts. Keywords: multiple representation, conceptual understanding, metacognitive awareness

Secular evolution of circumbinary 2-planet systems with isotropically varying masses

ABSTRACT We investigate the secular evolution of a four-body planetary system, where two planets move around a binary star configuration on quasi-elliptic orbits. It is assumed that the masses of all bodies can change isotropically at different rates and the bodies attract each other according to Newton’s law of universal gravitation. The purpose of this work is to investigate an influence of variability of the masses of the binary stars and their planets on the dynamical evolution of the planetary system. We consider the case of small eccentricities and inclinations of the bodies orbits and assume that their orbits do not intersect during evolution. Differential equations of the perturbed motion in the osculating analogues of canonical Poincaré elements were obtained in a general case of the many-body problem with variable masses in our previous work. Here we solve these equations numerically and investigate the secular evolution of some fictitious circumbinary 2-planet system under assumption that the two stars of the binary system lose their masses independently at different rates. In order to demonstrate the dynamical features of the equations we use the known parameters of the TOI-1338 system. Comparing the results of calculations in the cases of constant and variable masses, we show that the isotropic variability of the masses of bodies can influence substantially the secular perturbation of the orbital elements.

Principles and Equations of Physics: a multidisciplinary laboratory

In the last two academical years, as part of the Italian Ministry plan PLS – “Piano Lauree Scientifiche” (Scientific Degree Plan), two courses for high school students and teachers consisting in some interdisciplinary and transversal online meetings have been proposed. They regarded the three principles of dynamics, the law of universal gravitation and Maxwell’s equations. “Variations” around these topics were also presented – of historical, philosophical and also of musical nature – to make the cultural setting of what has been discussed deeper and make it meaningful in the present. At the end of each course, students produced a video of few minutes with a personal reworking and rethinking of the meaning of one of the topics discussed.

A Manifold‐Guided Gravitational Search Algorithm for High‐Dimensional Global Optimization Problems

Gravitational Search Algorithm (GSA) is a well‐known physics‐based meta‐heuristic algorithm inspired by Newton’s law of universal gravitation and performs well in solving optimization problems. However, when solving high‐dimensional optimization problems, the performance of GSA may deteriorate dramatically due to severe interference of redundant dimensional information in the high‐dimensional space. To solve this problem, this paper proposes a Manifold‐Guided Gravitation Search Algorithm, called MGGSA. First, based on the Isomap, an effective dimension extraction method is designed. In this mechanism, the effective dimension is extracted by comparing the dimension differences of the particles located in the same sorting position both in the original space and the corresponding low‐dimensional manifold space. Then, the gravitational adjustment coefficient is designed, so that the particles can be guided to move in a more appropriate direction by increasing the effect of effective dimension, reducing the interference of redundant dimension on particle motion. The performance of the proposed algorithm is tested on 35 high‐dimensional (dimension is 1000) benchmark functions from CEC2010 and CEC2013, and compared with eleven state‐of‐art meta‐heuristic algorithms, the original GSA and four latest GSA’s variants, as well as three well‐known large‐scale global optimization algorithms. The experimental results demonstrate that MGGSA not only has a fast convergence rate but also has high solution accuracy. Besides, MGGSA is applied to three real‐world application problems, which verifies the effectiveness of MGGSA on practical applications.

Isaac Newton vs. Robert Hooke on the Law of Universal Gravitation

Isaac Newton vs. Robert Hooke on the Law of Universal Gravitation

SUBSTANTIATION OF THE RESULTS OF THE LASER LOCATION OF THE TRAJECTORY OF THE MOON MOVING AWAY FROM THE EARTH

Progress in astronomical measurements of the trajectories of the movement of celestial bodies reveals new effects that require justification. In particular, it refers to the slight drift of the Moon from the Earth. A solution to this problem is possible only based on an adequate mathematical model. To perform this, it was adapted Newton's law of universal gravitation to the case of moving masses in flat space and physical time. At the same time, the final speed of propagation of the gravitational field can be considered. The differential equations of motion of the three-mass Sun-Earth-Moon cosmic system are obtained. In the heliocentric coordinate system, transient processes of the movement of the named celestial bodies are simulated, which testify to the presence of the Moon moving away from the Earth and the influence of the effects of movement on its course. The significant dependence of the final result on numerical methods of integration, computer calculation tools, and the values of space-velocity initial conditions is shown. The results of the simulation of transient processes are attached.

Newton’s Law of Universal Gravitation Explained by the Theory of Informatons

Newton’s Law of Universal Gravitation Explained by the Theory of Informatons

SUBSTANTIATION OF THE ANOMALIES OF THE MEASUREMENT RESULTS FOR TRAJECTORIES OF GRAVITATIONAL MANEUVER OF SPACE VEHICLES

In astronomical research, the problem of measuring the trajectories of the gravitational maneuver of space vehi- cles in the gravitational field of large celestial bodies arises. The known measurement results differ from those predicted by classi- cal celestial mechanics. A practical solution to this anomaly is possible only based on an adequate mathematical model. For this purpose, we have adapted Newton’s law of universal gravitation to the case of moving masses in a possible range of speeds in flat space and physical time. At the same time, the finite speed of propagation of the gravitational field is taken into account. The dif- ferential equations of motion of cosmic bodies have been obtained. In the heliocentric and planetocentric coordinate systems, tran- sient processes in the cosmic three-mass system are simulated – star, planet, and man-made spacecraft (Sun-Mercury-space probe). To more deeply identify the essence of gravitational interaction, transient processes of both acceleration and deceleration of the space vehicle were simulated depending on the specified space-velocity initial conditions for the differential equations of motion. The results of the simulation of transient processes are attached.

Inertia, gravity and the meaning of mass

Our concept of mass has evolved considerably over the centuries, most notably from Newton to Einstein, and then even more vigorously with the establishment of the standard model and the subsequent discovery of the Higgs boson. Mass is now invoked in various guises depending on the circumstance: it is used to represent inertia, or as a coupling constant in Newton’s law of universal gravitation, and even as a repository of a mysterious form of energy associated with a particle at rest. But recent developments in cosmology have demonstrated that rest-mass energy is most likely the gravitational binding energy of a particle in causal contact with that portion of the Universe within our gravitational horizon. In this paper, we examine how all these variations on the concept of mass are actually interrelated via this new development and the recognition that the source of gravity in general relativity is ultimately the total energy in the system.

Teoría relativista de gravitación para la dinámica Newtoniana modificada

Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. This theory is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics. In this work, we present a relativistic theory of gravitation for MOND.

GNaN: A natural neighbor search algorithm based on universal gravitation

The natural neighbor (NaN) method and its search algorithm (NaN-Searching) are widely used in many fields, including pattern recognition and image processing. NaN-Searching fundamentally overcomes the problem of the conventional nearest neighbor algorithm in selecting parameters for datasets with arbitrary shapes and achieves good results. However, this algorithm uses the conventional distance metric as the neighbor judgment criterion, which cannot accurately reflect the overall structure of the dataset in the process of neighbor search. Inspired by Newton’s law of universal gravitation, we propose a NaN search algorithm based on universal gravitation (GNaN-Searching). Our algorithm calculates gravitation using the structural features of data points in the dataset, it utilizes the gravitation between data as the neighbor judgment criterion, and inherits the no-parameter and dynamic neighborhood characteristics of the NaN search algorithm. Experimental results show that the natural neighborhood graph obtained by our method has a high performance in the representation of manifold data. We also applied the new method to clustering and outlier detection and achieved satisfactory results.

New label propagation algorithms based on the law of universal gravitation for community detection

New label propagation algorithms based on the law of universal gravitation for community detection

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

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

Estimating the relative importance of nodes in complex networks based on network embedding and gravity model

Identifying nodes that hold relative importance in complex networks is a burgeoning research area. Previous studies have demonstrated the effectiveness of the gravity model in capturing interactions among nodes in high-dimensional network space. Traditional algorithms predominantly concentrate on structural characteristics and node random walks in high-dimensional network space, overlooking substantial computational overhead and intricacies within the high-dimensional space. Simultaneously, the rapid evolution of the Internet has given rise to a series of emerging technologies, such as embedding models that can map high-dimensional network nodes to low-dimensional vector space. To address this issue, we introduce a novel algorithm for quantifying node relative importance, denoted as the Network Embedding and Gravity Model (NEGM). First, the network embedding method transforms nodes into low-dimensional, real-valued, dense vectors in Euclidean space. Then, drawing inspiration from Newton's law of universal gravitation, it proposes a novel gravity model. Finally, utilizing the novel gravity model, it calculates the aggregate attractive force of all nodes within the target node set. Experimental results show that NEGM excels in measuring the relative importance of nodes in various types of networks, demonstrating its significant potential for mining deep-seated information within authentic networks like protein networks and criminal networks.

Trajectory of a Spacecraft When It Passes by a Gravitational Body During Interstellar Travel

Interstellar space missions will require spacecraft that travel at relativistic speeds. Furthermore, their trajectories will be influenced by gravitational sources. Accordingly, this paper applies to interstellar missions a recently developed formulation of relativistic mechanics that predicts a spacecraft’s trajectory when it passes by a gravitational source at a relativistic speed. The formulation, called spacetime impetus, is unique in that it employs a relativistic universal law of gravitation that does not explicitly require general relativity while producing precisely the same results. Based on these developments, an analyst can now update nonrelativistic mission planning codes to give them general relativistic capabilities. It requires augmenting the code with relativistic velocities and relativistic accelerations, the replacement of the universal law of gravitation with a relativistic universal law of gravitation, and setting up Lorentz transformations between frames.