Not Relying on the Newton Gravitational Constant Gives More Accurate Gravitational Predictions

The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the kilogram mass definition. We will claim that G is just a term needed to correct the incomplete kilogram definition so to be able to make gravity predictions. But there is another way;namely, to directly use a more complete mass definition, something that in recent years has been introduced as collision-time and a corresponding energy called collision-length. The collision-length is quantum gravitational energy. We will clearly demonstrate that by working with mass and energy based on these new concepts, rather than kilogram and the gravitational constant, one can significantly reduce the uncertainty in most gravity predictions.

Motion State Modification of Coulomb’s Law and Dynamic Gravitation

As we know, Coulomb’s law describes the interaction between static charges. In this paper, the modified formula of Coulomb’s law in the state of charge motion is given. Based on this formula, Ampere’s law and Lorentz’s law of force are derived by pure mathematics. According to the similarity between the formula of universal gravitation and Coulomb’s law, the correction of the formula of universal gravitation under the state of motion is assumed boldly, and some inferences are made on the motion law of celestial bodies.

New Interpretation of Newton’s Law of Universal Gravitation

Elliptical motions of orbital bodies are treated here using Fourier series, Fortescue sequence components and Clarke’s instantaneous space vectors, quantities largely employed on electrical power systems analyses. Using this methodology, which evidences the analogy between orbital systems and autonomous second-order electrical systems, a new theory is presented in this article, in which it is demonstrated that Newton’s gravitational fields can also be treated as a composition of Hook’s elastic type fields, using the superposition principle. In fact, there is an identity between the equations of both laws. Furthermore, an energy analysis is conducted, and new concepts of power are introduced, which can help a better understanding of the physical mechanism of these quantities on both mechanical and electrical systems. The author believes that, as a practical consequence, elastic type gravitational fields can be artificially produced with modern engineering technologies, leading to possible satellites navigation techniques, with less dependency of external sources of energy and, even, new forms of energy sources for general purposes. This reinterpretation of orbital mechanics may also be complementary to conventional study, with implications for other theories such as relativistic, quantum, string theory and others.

On the Physical Nature of Einstein’s Gravitational Lensing Effect

Gravitational lensing has become a powerful research tool for exploring the distribution of matter and energy in the universe nowadays, as glare phenomena around the Sun and massive galaxies are indeed observed on the Earth. What is the physical nature of gravitational lensing effect? Both Newton’s law of gravitation and Einstein’s theory of relativity are difficult to physically explain these glare phenomena. This study points out that the observed glare around the Sun and large galaxies is a result or product of the orthogonal interaction of high-energy particles emitted from different star light sources. It shows a new physical state associated with abnormal high mass-energy density.

Newton Did Not Invent or Use the So-Called Newton’s Gravitational Constant;G, It Has Mainly Caused Confusion

Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was and not . In this paper, we will show how a series of major gravity phenomena can be calculated and predicted without the gravitational constant. This is, to some degree, well known, at least for those that have studied a significant amount of the older literature on gravity. However, to understand gravity at a deeper level, still without G, one needs to trust Newton’s formula. It is when we first combine Newton’s assumptionn, that matter and light ultimately consist of hard indivisible particles, with new insight in atomism that we can truly begin to understand gravity at a deeper level. This leads to a quantum gravity theory that is unified with quantum mechanics and in which there is no need for G and not even a need for the Planck constant. We claim that two mistakes have been made in physics, which have held back progress towards a unified quantum gravity theory. First, it has been common practice to consider Newton’s gravitational constant as almost holy and untouchable. Thus, we have neglected to see an important aspect of mass;namely, the indivisible particle that Newton also held in high regard. Second, standard physics have built their quantum mechanics around the de Broglie wavelength, rather than the Compton wavelength. We claim the de Broglie wavelength is merely a mathematical derivative of the Compton wavelength, the true matter wavelength.

Connecting Newton’s G with the Rest of Physics—Modern Newtonian Gravitation Resolving the Problem of “Big G’s” Value

As a simplified, idealized understanding of a physical system the General Relativity model has been highly successful in its gravitational role. However, it fails to address the problem of sufficiently precise measurement of “Big G”, the Newtonian Gravitation Constant, and has failed to obtain connection of “Big G” to the rest of physics. Because “Big G” arises naturally from Newton’s treatment of gravitation, this paper elaborates the Modern Newtonian Model of Gravitation and through it resolves the problems of “Big G” at which General Relativity has failed. Specifically: The causes of the problems in measuring “Big G” are resolved, “Big G” is connected to the rest of physics, and a sufficiently precise value of “Big G” is obtained by calculation from other fundamental physical constants. The companion paper The Experimental Data Validation of Modern Newtonian Gravitation over General Relativity Gravitation, which is available in this journal, publishes the results of this paper’s “Part V—Testing the Hypothesis and the Derivation”.

The Experimental Data Validation of Modern Newtonian Gravitation over General Relativity Gravitation

The paper Connecting Newton’s G With the Rest of Physics-Modern Newtonian Gravitation Resolving the Problem of “Big G’s” Value derived the value of the gravitation constant “Big G”, G of Newton’s Law of Gravitation, directly from other physics fundamental constants but left it to a subsequent paper to experimentally validate the derived G. The present paper performs that validation by examining various past experiments intended to measure “Big G”, in each case determining the acceleration, ag, as found per Einstein’s General Theory of Relativity versus per Modern Newtonian Gravitation for that case. The ratio of those two times the reported measured “Big G” value yields a result identical to the G determined from the derived formulation for G, within the error range of the reported measured “Big G” measurement. That thus validates the correctness of the derived formulation for G. The next important issue, what causes gravitation, how does the effect take place, is addressed and resolved in the paper The Mechanics of Gravitation-What It Is;How It Operates, which is available in this journal.

The Research of the Flow of Bodies with Use of the Vector Form of the Newton’s Law for the Viscous Liquid

On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.

New Theory to Understand the Mechanism of Gravitation

Gravitation is still the least understood interaction among the fundamental forces of Nature. A new theory that explains the mechanism of gravitation and the origin Newton’s laws of gravitation and general relativity and distinguishes between two of the Newton’s laws has been proposed. It is shown that the vortex formation created during the Big Bang event is the origin of the gravitational force. The vortex curves the vacuum (space-time) around it, attract and condense energy and dust to its center to form the mass. The gradient pressure in the vortex creates a flow that upon interaction with an object transfers a part of its momentum to the object and pushes it toward the center. The force exercised on the object is equivalent to Newton’s second law. The force of attraction between two vortices is equivalent to Newton’s third law. The drag force between the energy flow of the vortex and the static vacuum diminishes the gravitational force and is equivalent to the G constant. The proposed theory could provide new interesting insights for a comprehensive understanding of gravitation and represents a theoretical starting point for the engineering of anti-gravitation technology.

Q-Theory: A Connection between Newton’s Law and Coulomb’s Law?

Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, qpl, was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, , where ζ(3) equals Apery’s constant, 1.202 …, and, n+(0)=n_(0), is the relaxed, i.e., , number density of the positive and negative mass planckions. In the present epoch, we estimate that, n+(0) equals, 7.848E54 m-3, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, l+(0)=l_(0)=5.032E-19 meters. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, , due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E-48 meters, within the vacuum made up of these particles. On the surface of the earth, where, g=9.81m/s2, the displacement amounts to, 7.824E-38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.

Adapted Metrics for a Modified Coulomb/Newton’s Potential

Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.

Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.

The Mechanics of Gravitation—What It Is;How It Operates

From a start of only the limitation on the speed of light, the necessity of conservation, and the impossibility of an infinity in material reality, the present paper presents a comprehensive development of the mechanics, the operation of gravitation. Experience shows that everything has a cause and that those causes are themselves the results of precedent causes, and ad infinitum. Defining and comprehending the causality or mechanism operating to produce any observed behavior is essential to understanding or explaining the behavior. The behavior of gravitation is well known, described by Newton’s Law of Gravitation. But what gravitational mass is, how gravitational behavior comes about, what in material reality produces the effects of gravitation, is little understood. The extant hypotheses include Einstein’s General Relativity’s bending of space, efforts to develop “quantum gravitation”, and attempts to detect “gravitons”. None of those addresses the cause, the mechanism of gravitation. As demonstrated in the present and its prior papers, gravitation is an outward flow from gravitating masses. That means that by manipulating that flow gravitation can be controlled. The procedure for obtaining such control and the design for several various applications are presented in the paper Gravitational and Anti-gravitational Applications which is available in this journal.

Gravitational Model of the Three Elements Theory: Mathematical Explanations

The aim is to parse the mathematical details related to the gravitational model of the three elements theory [1]. This model is proven to be coherent and really compatible with relativity. The Riemannian representation of space-time which is used in this model is proven to be legal. It allows to understand relativity in a more human sensitive manner than Minkowskian usual representation.

Derivation of Maxwell’s Equations via the Covariance Requirements of the Special Theory of Relativity, Starting with Newton’s Laws

The purpose of this paper is to establish a connection between Maxwell’s equations, Newton’s laws, and the special theory of relativity. This is done with a derivation that begins with Newton’s verbal enunciation of his first two laws. Derived equations are required to be covariant, and a simplicity criterion requires that the four-vector force on a charged particle be linearly related to the four-vector velocity. The connecting tensor has derivable symmetry properties and contains the electric and magnetic field vectors. The Lorentz force law emerges, and Maxwell’s equations for free space emerge with the assumption that the tensor and its dual must both satisfy first-order partial differential equations. The inhomogeneous extension yields a charge density and a current density as being the source of the field, and yields the law of conservation of charge. Newton’s third law is reinterpreted as a reciprocity statement, which requires that the charge in the source term can be taken as the same physical entity as that of the test particle and that both can be assigned the same units. Requiring covariance under either spatial inversions or time reversals precludes magnetic charge being a source of electromagnetic fields that exert forces on electric charges.

Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations

Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.

Analysis of Electrical Dipoles Interaction Forces as a Function of the Distance and of the Form of Electrical Force Law

Here, we initially introduced and demonstrated two principles: orientation OR principle and attraction AT principle of electrical dipoles. The OR principle stipulates that any two electrical dipoles P1A, P1B, from two bodies A and B, at any distance in the free state each, will be reciprocally oriented parallel and in the same sense if the electrical interaction forces F between them are of decreasing type with distance r. If the electrical interaction forces F are of increasing type with distance, the two dipoles will be reciprocally oriented parallel but on the opposite sense. The AT principle stipulate that any two electrical dipoles P1A, P1B, at any distance in the free state each, will present always a reciprocal force of attraction FD in both cases of orientation accordingly to OR principle in case of any type of electrical force F decreasing or increasing with distance. These findings may complete our previous work where we found that FD force, between two electrical dipoles P1A, P1B considered at atomic and nuclear level, is in fact the actual gravitation Newton force FN. The paper must be considered together with this work for more consistency.

Computational Solution to the Problems of Projectile Motion under Significant Linear Drag Effect

This paper investigates the computational solution to the problem of projectile motion under a significant linear drag effect. The drag force acting on the particle within the medium of propagation is proportional to the cross-section area of the projectile, the velocity of the particle, and the medium’s density. From zero air resistance force (vacuum) the problems are well known with solutions, but with air resistance (drag force) the problems have no exact analytical solutions which lead to most of the significant scientific research works using numerical methods. Therefore, this study aims to present the analysis of the computational modelling of drag force exerted by the surrounding medium on the linear motion. However, the horizontal and vertical components of differential equations of motion were derived and characterized from the solutions governed by Newton’s 2nd law of motion. The baseball features were presented as the projectile (object) in this work. In addition, the numerical computational results were received from FreeMat. The results were discussed and compared with those from the vacuum. Moreover, the displacements, velocities, range, and trajectories of the projectile were all discussed and a conclusion was made.

The Quantization of Space

In the present work, it will be shown that the dimensionless number 137 of the fine-structure constant α demands a quantization of space. For this purpose, we refer to a volume constant of electromagnetic processes, which takes effect as a volume quantum. This involves not only a re-evaluation of the Dirac equation but also, and above all, a determination of Einstein’s velocity vector as the fundamental property of these processes. A prerequisite is the linking of the hydrogen spectrum with the hydrogen nucleus.