![]() ![]() At the big bang, there was only one sphere. The smallest one is the “material universe” and the largest is the “luminous universe”. The universe is made of two 4-D expanding spheres, one imbricated in the other. Our cosmological model is used to get all the equations. To compare the results of our new equations with the articles published in 2019, we will use the CODATA 2014. We use the compact form of notation to display tolerances (i.e. In the third step, we will show that G is not constant and why it varies according to time as well as to the location in the universe where it is measured. It is an exercise which is useful, among other things, to get certain equations which overcome the difficulties to do experimental measurements as well as to show that G is intimately linked to the other parameters of the universe. We will enumerate, in a second step, 33 different equations giving G. It will be shown that there is a slight difference between the CODATA (Committee on Data for Science and Technology) value and the theoretical value of G, and we will explain why. Using mathematical tools and software, the data will be processed to determine an estimate of G. To validate the theoretical value of G found in the past, we wish, in a first step, to list the results of all the recent experiments aimed at measuring it. To help the reader, we will summarize the theory that is behind this equation. With a new cosmological model, G is obtained (see Equation (31) further) as a function of the speed of light in a vacuum c, the fine-structure constant α, and the parameters of the electron (mass m e and classical radius r e). Our article will also show that G could evolve over time and not be a real constant. As early as 1995, physicists suggested that certain measures of G may be tainted with systematic errors. Even if the recent measurements show small margins of error, they do not always overlap. Several attempts to measure G have been made over time. ![]() In Einstein’s equation of general relativity, R μv is the Ricci curvature tensor, R is the scalar curvature, g μv is the metric tensor, L is the cosmological constant, G is Newton’s gravitational constant, c is the speed of light in a vacuum, and T μv is the stress-energy tensor. In Newton’s equation of gravity, the attractive force F between two masses m 1 and m 2, separated by a distance r, depends on G that acts as a coupling coefficient. It is one of the least well-known constants despite all current technological means. Its value is used in Newton’s equation and that of Einstein’s general relativity. The universal gravitational constant G (also called Newton’s gravitational constant) has a special character because it is considered to be one of the 3 most fundamental constants in physics since no model allows its value to be deduced from other known constants. However, at our location in the universe and for a relatively short period, this parameter may seem constant. It’s value probably slowly varies in time and space. Since we have been able to link G with Hubble parameter H 0 (which evolve since its reverse gives the apparent age of the universe), we deduce that G is likely not truly constant. These equations may be useful for astrophysicists who work in this domain. Knowing that our theoretical value of G is in agreement with the measured value, we want to establish a direct link between G and as many other constants as possible to show, with 33 equations, that G is probably linked with most constants in the universe. We make the hypothesis that most G measurements are affected by an unknown systematic error which creates two main groups of data. Here, we want to show that our theoretical value of G is the right one by interpreting measurements of G with the help of a new technique using cubic splines. ![]() However, in a 2019 article, with a new cosmological model, we showed that G seams related to other constants, and we obtained a theoretical value of. Modern physics is unable to link G with other constants. Due to the low intensity of gravitation, it is difficult to obtain reliable results because they are disturbed by surrounding masses and environmental phenomena. In 1798, with a torsion balance, Cavendish measured. ![]() In 1686, Newton discovered the laws of gravitation and predicted the universal gravitational constant. ![]()
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