Chapter 9
Errors in the Theory of Stellar Structure.
The Size of the Sun if A. Eddington's Theory of Stellar Structure Were Correct.

Calculations based on A. Eddington's scientific work "The Internal Constitution of the Stars" (1926).

According to Eddington's theory, thermonuclear fusion of hydrogen in a star occurs at its center, in the core. Under the influence of gravity, the hydrogen gas compresses, bringing atomic nuclei closer together and causing their fusion. The thermonuclear fusion of hydrogen nuclei leads to a thermonuclear explosion, which expands the star's matter. After the expansion, the next gravitational compression occurs, and the processes repeat.

This scheme is simple and borrowed from the internal combustion engine, a brilliant invention of the late 19th and early 20th centuries, as A. Eddington himself mentioned, admiring the design of these engines.

The first steps in nuclear physics were taken in 1896 when Henri Becquerel discovered natural radioactivity. In 1911, Rutherford proposed the model of the atomic nucleus. In 1926, A. Eddington published his scientific work "The Internal Constitution of the Stars." In this work, Eddington expressed the opinion that the source of energy in the interiors of stars is nuclear reactions—the fusion of hydrogen atomic nuclei into helium atomic nuclei.

Theoretical physicists, when explaining incomprehensible physical phenomena, processes, and objects, rely on the knowledge existing in that particular historical period. Knowledge from the future is unavailable to them. At the beginning of the 20th century, the laws of nuclear physics and the physics of nuclear reactors were unknown!!! The neutron was discovered in 1932, after the publication of Eddington's "The Internal Constitution of the Stars." The first nuclear reactor was built only in 1942, in the USA. In Europe, a nuclear reactor was built in 1946, in the USSR. The construction and all related research were classified. In 1945, the first tests of nuclear weapons were conducted. In 1951, the first tests of the "Hydrogen" bomb were conducted. For the first time, the fusion of light atomic nuclei—thermonuclear fusion, which A. Eddington wrote about in "The Internal Constitution of the Stars" in 1926—was achieved. That is, the physical processes that A. Eddington described were experimentally realized on Earth 25 years after he hypothesized their existence, and 7 years after the death of the hypothesis's author, A. Eddington, himself.

Table 9.1 presents, in chronological order, the scientific discoveries and events related to the physical processes occurring in stars as described by A. Eddington. As can be seen from Table 9.1, all events significant for understanding nuclear physics and stellar structure occurred after Eddington's death and the publication of his scientific works. All knowledge of nuclear physics during A. Eddington's lifetime was insufficient for understanding the processes occurring in stars. Based on this knowledge, it was impossible to predict either the processes occurring in a star or the star's structure itself. Consequently, in his scientific work, A. Eddington could not rely on research and the laws of nuclear physics. He could not know the laws of nuclear reactor physics. In his scientific work, A. Eddington put forward hypotheses about the structure of stars as nuclear reactors, hypotheses about the physical and nuclear processes occurring in stars. However, these hypotheses were based on the knowledge of the 19th and early 20th centuries, in which nuclear physics and the physics of nuclear reactors were absent.

The only active force was gravity. Based on the gravitational concept, all theories and hypotheses in the physics of space were invented. Consequently, these scientific works were inherently flawed with physical and conceptual errors. And today, in modern astrophysics, these erroneous theories dominate.

(58) Table 9.1

Conceptual and Constructive Errors of A. Eddington.

The scientific and theoretical works of A. Eddington, A. Einstein, and other theoretical researchers of space are based on the dominant concepts of the early 20th century. At the beginning of the 20th century, as today, the gravitational and thermal concepts are dominant. The gravitational concept has dominated astrophysics for 300 years. It asserts that all physical processes and events occurring in space happen under the influence of gravity. And the main task facing space researchers is to find the source of this gravity. And if this source cannot be found, because it does not exist, then it is invented. As in the cases with dark matter, with the black hole, and with cosmic objects possessing incredibly high density (white dwarf, neutron star, boson star, and others).

And one would like to ask: "Why are there no such objects in the solar system? What makes us worse?"

One would also like to ask another very important question: "Where is NUCLEAR PHYSICS in astrophysics?" All of nuclear physics in astrophysics is limited to the information that thermonuclear fusion of hydrogen occurs in stars. That is, the level of knowledge of nuclear physics in astrophysics has remained at the level of 1926. At the level of A. Eddington's hypotheses! And gravity dominates in theoretical astrophysics, just as it did 100, 200, and 300 years ago.

It is precisely the dominance of the gravitational concept that gives rise to most errors in astrophysics.

It is psychologically natural that A. Eddington identified a star's gravity as the source of its physical processes.

At the beginning of the 20th century, one of the most brilliant engineering inventions was the internal combustion engine. A. Eddington was fascinated by its design. And the design of this engine, combined with the gravitational concept, theoretically fit the structure of a star. There were no other known physical concepts suitable for explaining the internal structure of a star generating thermonuclear energy. At the beginning of the 20th century, neither nuclear physics nor nuclear reactors existed. The theory of the physics and structure of stars was crafted from the most advanced concepts available: the design of the internal combustion engine and the dominant gravitational concept.

The second concept was the thermal one. The release of energy and heat, high temperature generates the high velocities of atomic nuclei necessary for the thermonuclear fusion of hydrogen.

It was precisely these two concepts and the design of the internal combustion engine that were taken as the foundation for the theory of the internal structure of stars.

Let us consider the scheme of a star operating as a nuclear reactor, according to A. Eddington's theory in "The Internal Constitution of the Stars".

The nuclear reactor—the star—operates like an internal combustion engine. According to Eddington's assertion, the temperature in the star's core reaches 40 million Kelvin. Let us calculate the size of such a star. We will perform the calculations for a star with the parameters of the Sun.

Is such a combination of physical processes possible? And what dimensions would a star have to possess if A. Eddington were correct?

For the synthesis of atomic nuclei, it is necessary to bring these nuclei within the distance where nuclear forces interact. To achieve this approach, a force must be created that exceeds the Coulomb repulsion force of the nuclei. If this approach of nuclei is created by gravity, then the force of gravity must have a value exceeding the Coulomb forces.

                  FG > FQ

Where FG is the gravitational force of the star, and FQ is the Coulomb repulsion force of two nuclei.

To simplify the analysis, let us assume these forces are equal: FG = FQ.

In this analysis, we will consider a star with the parameters of the Sun.

Where:

G = 6.67413 × 10⁻¹¹ N·m²/kg² — gravitational constant.

M = 1.9 × 10³⁰ kg — mass of the Sun.

m — mass of the atomic nucleus.

R — distance from the center of the star to the atomic nucleus participating in thermonuclear fusion under the influence of gravity, m (meters).

Where:

k = 9 · 10⁹ · N·m²/C² — proportionality constant.

qᵢ = zᵢ · e — charge of the atomic nucleus.

zᵢ — number of protons in the atomic nucleus.

e — elementary charge equal to the charge of the electron (with a positive sign).

e = 1.6021892 · 10⁻¹⁹ C (Coulombs).

r — distance to which two atomic nuclei must be brought together for their fusion.

r = r₁ + r₂

r₁, r₂ (rᵢ) — radii of the atomic nuclei participating in fusion.

rᵢ = (1.2 ÷ 1.4) · Aᵢ1/3 fm (fermi)

Aᵢ — number of nucleons in nucleus i.

For a proton and a hydrogen atomic nucleus with Aᵢ = 2, rᵢ = 0.8 · Aᵢ1/3 fm (fermi)

r² = (0.8 · A1/3 + 0.8 · A1/3)²

For other atomic nuclei, we take rᵢ = 1.4 · Aᵢ1/3 fm (fermi)

r² = (1.4 · A1/3 + 1.4 · A1/3)²

1 fm (fermi) = 10⁻¹⁵ m (meters).

Let us set up the equality FG = FQ:

In this equality, we are interested in the value of the parameter R, the distance from the center of the star to the atomic nucleus participating in thermonuclear fusion. That is, the entire mass of the star must be contained within a sphere of radius R.

After transforming the equality, we obtain the formula for determining the distance R:

Let us calculate the value of the parameter R for the fusion of two protons:

·        Mass of a proton: 1.672 · 10⁻²⁷ kg,

·        Radius of a proton: 0.8 · 10⁻¹⁵ m; the distance to which two protons must be brought together for fusion will be 1.6 · 10⁻¹⁵ m,

·        Charge of the proton nucleus: 1.

Substitute the parameters of the protons into formula (9.1) and determine R — the radius of a star with the mass of the Sun.

The data for calculating the parameter R in the cases of the fusion of two protons, two hydrogen nuclei H (deuterium), and two helium nuclei He are entered in Table 9.2. The results of calculating the parameter R for the listed cases are also included.

(59) TABLE # 9.2

As can be seen from the calculations, the fusion of hydrogen and helium, according to the scheme proposed by A. Eddington in 1926, is impossible in stars! The calculations showed that for a star with the mass of the Sun, fusion is possible only if the entire mass of the star is contained within a sphere with a radius ranging from 4.9·10⁻⁵ m to 13.73·10⁻⁵ m.

That is, a star with the mass of the Sun would have to be contained within a sphere of radius less than 1 mm. This does not correspond to reality or the actual parameters of the Sun. With the calculated values of R, the density of such stars would have to be from 2·10⁴¹ to 4·10⁴² kg/m³. For comparison, the density of an atomic nucleus is 10¹⁶ – 10¹⁷ kg/m³. The density of a proton is 7.796·10¹⁷ kg/m³. According to the fantasies of theoretical physicists, in a black hole with a mass of 10 solar masses, the density of matter should be 2·10¹⁷ kg/m³. The hypothetical density of the universe before the Big Bang is 10⁹⁶ kg/m³.

As can be seen from the calculations, the sizes of stars refute A. Eddington's hypothesis that thermonuclear fusion occurs under the influence of gravitational compression of stellar matter. However, the refutation of the gravitational mechanism of thermonuclear fusion in stars does not disprove the thermonuclear fusion itself that occurs within them. The calculations disprove it, but thermonuclear fusion and other nuclear reactions do exist in stars. Consequently, a different scheme, not gravitational, for generating nuclear reactions and thermonuclear fusion is realized in stars.

Is it possible to generate nuclear reactions and thermonuclear fusion in a star through non-gravitational means?
Yes, it is possible!!!

Nuclear physicists found, developed, and tested such a scheme. In 1951-1952, a scheme for generating thermonuclear fusion that excludes gravity was tested. This is the scheme of the hydrogen bomb, the first tests of which took place in 1951 and 1952, seven years after A. Eddington's death. Eddington never learned of these tests.

From this physical-historical analysis, a conclusion can be drawn. A. Eddington's theories on the structure of stars and the physical processes within them are based on outdated concepts and an incorrect design. Due to the lack of necessary research information, Eddington's theories were built from the outset on incorrectly chosen laws.

However, 100 years ago, objective scientific information was unavailable; this scientific work was another important step in understanding the world around us. It gave impetus to the study of stars and the physics of space. It spurred the development of research programs and technological progress in space exploration.

Today, relying on modern scientific data and new methods of analytical research, an opportunity has arisen to evolve in our understanding of the physics of space. But, unfortunately, this evolution of cosmic knowledge is hindered by a psychological factor. Namely, the inertia of thinking associated with a psychological attachment to outdated, erroneous theories. Unfortunately, researchers in analytical astrophysics have to spend time, effort, and resources searching for errors, analyzing, calculating, and refuting outdated but still prevailing and dominant theories in astrophysics.

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