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NUCLEARGRAVITATION
FIELD THEORY
Chapter IX:Comparison of the Nuclear Gravitational Field to theGravitational Field of the Sunand the Gravitational Field of a Neutron Star
The one characteristic that physicists observe regarding the "Strong Nuclear Force" is that it appears to be a very "short ranged" force. To the best of my knowledge, no empirical equation has ever been established for mathematically describing the characteristics of the "Strong Nuclear Force." The Physics Community has assumed that the "Strong Nuclear Force" is inversely proportional to the radial distance from the nucleus to at least the seventh power. The following equation is a representation of that assumed relationship where "F" represents the "Strong Nuclear Force," "K" represents a constant of proportionality, and "r" represents the distance between the center of gravity of the nucleus of interest and a proton or neutron at a specific point in space outside the nucleus.

The field of the "Strong Nuclear Force" appears to drop off almost immediately outside the nucleus of the atom. The "Strong Nuclear Force" holding the nucleus together has always been assumed to be a short ranged "super-force" much stronger force than the Electrostatic Force of Repulsion of the protons. Physicists and engineers are still trying to develop a reactor design to sustain a controlled Nuclear Fusion Reaction where the usable energy for work coming out of the reactor is greater than the energy required to initiate and maintain the fusion reaction. Initiating and maintaining a sustained, controlled, fusion reaction requires extreme temperatures (millions of degrees Kelvin) and pressures (millions of pounds per square inch). The extreme temperatures ensure the Deuterium and Tritium nuclei have sufficient kinetic energy to overcome the Electrostatic Repulsion Force of the protons in the Deuterium and Tritium nuclei. The extreme pressures ensure a high enough density of the nuclei to raise the probability of particle interaction. A stable "plasma" with the required temperature and pressure to sustain a fusion reaction is extremely difficult to maintain. The plasma must be "pinched" within a magnetic field of a reactor to provide the required temperature and pressure to support fusion. Figure 9-1 and Figure 9-2 demonstrate how the Tokamak Fusion Reactor establishes the "pinched" plasma to support fusion.

Figure 9-1:Cutaway Diagram of the Tokamak Fusion Reactor at Princeton UniversityIndicating Location of the Plasma in the Magnetic Field

Figure 9-2:Internal View of the Tokamak Fusion Reactorat Princeton University
What is a Tokamak?
The most successful and promising fusion confinement device is known as a Tokamak. The word Tokamak is actually an acronym derived from the Russian words toroid-kamera-magnit-katushka, meaning "the toroidal chamber and magnetic coil." This donut-shaped configuration is principally characterized by a large current, up to several million amperes, which flows through the plasma. The plasma is heated to temperatures more than a hundred million degrees centigrade (much hotter than the core of the sun) by high-energy particle beams or radio-frequency waves.
Reference: http://ippex.pppl.gov/fusion/fusion4.htm
Maintaining a stable "pinched" plasma in a magnetic field is very difficult at best. If a solid vessel is used to maintain the plasma and the plasma comes into contact with the vessel wall, then the plasma will immediately transfer heat to the vessel and cool off to below the required fusion temperatures. Likewise, the chance of the solid vessel vaporizing when coming into physical contact with the plasma is extremely high.

NOTE:
There are four states of matter: solid, liquid, gas, and plasma. Examples of the first three states of matter are water in the form of ice, a solid, water in the form of a liquid as is found in a lake or swimming pool during the Summer, and steam (gas or vapor) as what emanates from a teapot on a stove. The fourth state, the plasma state, can only exist at a extremely high temperatures where the kinetic energy of the subatomic particles, the nuclei and their electrons, is such that the electrons are no longer bound to their respective nuclei.
If the Nuclear Gravitation Field Theory is to demonstrate that the "Strong Nuclear Force" is the same force as that of Gravity, a reasonable explanation must be provided to explain why the "Strong Nuclear Force" does not follow Newton's Law of Gravity and provide an expected field strength reduction proportional to the square of the distance from the center of the nucleus. Recall Newton's Law of Gravity states:
As mentioned earlier, the field intensity of the "Strong Nuclear Force" drops off much more rapidly than predicted by Newton's Law of Gravity leading one to believe the Nuclear Gravitation Field cannot be the same as the "Strong Nuclear Force." The field intensity of the "Strong Nuclear Force" appears to drop off proportional to the inverse of the distance from the nucleus to the seventh power or greater. If the "Strong Nuclear Force" and the Nuclear Gravitation Field are the same, then the "Strong Nuclear Force" should drop off proportional to the inverse of the distance squared from the nucleus as predicted by Newton's Law of Gravity. However, what if the Nuclear Gravitation Field intensity, in close proximity to the nucleus, is on the same order of intensity of the gravitational field of a star? If that is the case, then the General Relativistic effects of strong gravitational fields may be affecting the Nuclear Gravitation Field as a function of distance from the nucleus. The intent of the methodology of the following evaluation is to determine whether or not the Nuclear Gravitation Field in the vicinity of the nucleus has the intensity to result in measurable "
Space-Time Compression."
Evaluate the "Pure Classical Physics" approach to calculating the Nuclear Gravitation Field at the surface of the nucleus of the atom using Newton's Law of Gravity.
Compare the "Pure Classical Physics" calculated Nuclear Gravitation Field intensity assuming fields of force, energy, and matter are continuous functions versus the estimated Nuclear Gravitation Field intensity using the principles of Quantum Mechanics assuming fields of force, energy, and matter are discrete functions.
In order to determine whether or not the Nuclear Gravitation Field at the surface of the nucleus has an intensity great enough to result in observable General Relativistic effects, one must compare the Nuclear Gravitation Field at the surface of the nucleus to the gravitational field in the vicinity of the Sun's surface and in the vicinity of the surface of a Neutron Star. Gravitational fields in the vicinity of stars are more than intense enough for significant General Relativistic effects to be observed. The Neutron Star was selected as one of the cases to study because the density of the nucleus, which is made up of protons and neutrons, is very close to the density of a Neutron Star. A Neutron Star typically contains the mass approximately that of our Sun, however, the matter is concentrated into a spherical volume with a diameter of about 10 miles or 16 kilometers. The radius of a Neutron star is about 5 miles or 8 kilometers. Figure 9-3 illustrates the relative size of the Earth to the size of a White Dwarf star and a Neutron star.


Figure 9-3:Comparative Sizes of the Earth,a Typical White Dwarf Star,and a Typical Neutron Star
Reference: "The Life and Death of Stars," by Donald A. Cooke, Page 131, Figure 8.12
This calculation will assume one solar mass for both the mass of the Sun and the Neutron Star. In this analysis, no General Relativistic effects will be considered in the calculations because the calculations are too cumbersome and not required to obtain the "ballpark values" needed to determine gravitational field intensities. Qualitative analyses are sufficient to satisfy the purposes for this evaluation. If the intensity of the Nuclear Gravitation Field at the surface of the nucleus is approximately equal to or greater than the gravitational field at the surface of our Sun, then it can be reasonably assumed that General Relativistic effects are present in the vicinity of the nucleus and must be considered when evaluating the "Strong Nuclear Force." Recall Newton's Law of Gravity and Newton's Second Law of Motion states:
Therefore:

The rearranging of Newton's Law of Gravity and Newton's Second Law of Motion can be used to determine the gravitational acceleration at any given distance from a gravitational source such as a planet or star. The acceleration of gravity is analogous to the gravitational field established by the mass of that planet or star.
First, the gravitational field at the Sun's surface will be determined. The Sun's mass, MSun, is 1.99×1030 kg. The Sun's diameter is 864,000 miles, therefore, the Sun's radius, RSun, is equal to 432,000 miles. In MKS units, the Sun's radius, RSun, is equal to 6.96×105 km equal to 6.96×108 meters. The Universal Gravitation Constant, "G," is equal to 6.67×10-11Newton-meters2/kg2. The gravitational field of the Sun's surface, which is represented by the gravitational acceleration at the Sun's surface, is calculated below:
aSun = 2.74×102 Newtons/kg = 2.74×102 meters/second2
Earth's gravitational field at sea level, which is represented by Earth's gravitational acceleration at sea level is about 9.87 meters/second2. The "g-force" at the Sun's surface can be determined by normalizing the Sun's gravitational field relative to Earth's gravitational field at sea level. Earth's gravitational field at sea level is assumed to be 1g. The ratio of the acceleration of gravity on the Sun's surface to the acceleration of gravity on the Earth's surface represents the g-force on the Sun's surface. The g-force on the Sun's surface is calculated as follows:

The Sun's gravitational field is strong enough to affect planet Mercury's orbit such that it deviates from the classical Newton's Law of Gravity and Kepler's Laws of Orbital Motion (see "Tests of Einstein's General Theory of Relativity," in Chapter V). Mercury orbits the Sun at an average distance of 36,000,000 miles from the Sun's surface. It was also previously presented that the Sun's gravitational field is strong enough to bend light. During a "Total Solar Eclipse," the background stars in the vicinity of the Sun will appear to be displaced because of the Sun's gravity bending their light. This bending of light is occurring in a gravitational field equal to or less than 27.8 g. Any gravitational field intensity equal to or greater than the Sun's gravitational field will require consideration of the effects of General Relativity.
Next, the gravitational field at the surface of a Neutron Starwill be analyzed. The Neutron Star is assumed to contain the same mass as the Sun, therefore, the mass of the Neutron Star, "MNeutron Star," is equal to 1.99×1030 kg. As presented previously, the Neutron Star's radius, which will be defined as "RNeutron Star," is about 5 miles equal to about 8 km or 8×103 meters. The gravitational field of a Neutron Star, which is represented by the gravitational acceleration at the star's surface, is calculated below:

aNeutron Star = 2.07×1012N-kg-1 = 2.07×1012 meters/second2
To determine the "g-force" at the Neutron Star's surface, the gravitational field of the Neutron Star must be normalized relative to Earth's gravitational field in the same manner used to calculate the g-force at the Sun's surface. Earth's gravitational field is 1g. The ratio of the acceleration of gravity on the Neutron Star's surface to the acceleration of gravity on the Earth's surface represents the g-force on the Neutron Star's surface. The g-force on the Neutron Star's surface is calculated as follows:
It has been previously demonstrated that the Sun's gravitational field of 27.8g can warp or bend Space-Time (see "Tests of Einstein's General Theory of Relativity," in Chapter V). The gravitational field of a Neutron Star, at 2.10×1010g, has an intensity of nearly a billion times greater than the Sun's gravitational field. The Neutron Star's gravitational field will result in substantial "Space-Time Compression." The mass of the Black Hole is about three times the Sun's mass and its mass is concentrated at a pinhead size singularity. The gravitational field and the warping of Space-Time associated with a Black Hole very well may approach infinity.
The next step is to calculate the gravitational field at the surface of a Uranium-238 nucleus, the most naturally occurring isotope of Uranium. This calculation will use Newton's Law of Gravity assuming purely Classical Physics so the Nuclear Gravitation Field for the Uranium-238 nucleus is assumed to be a continuous function. Hence, Quantum Mechanics will not be initially considered. Uranium, or Element Number 92, is the highest number element naturally occurring on Earth. The atomic mass of the Uranium nucleus is
238.050785 Atomic Mass Units (AMU) which is equal to 3.953×10-25 kg. The Uranium nucleus contains 92 protons and 146 neutrons for a total of 238 nucleons. The classical diameter of a neutron or proton is 1.0×10-15 meter. It is desired to determine the approximate diameter of the Uranium-238 nucleus. Protons and neutrons are assumed to be spherical in shape. However, because they are spheres, they do not pack together without having spatial gaps between them. Therefore, the actual space, both usable and unusable, in the nucleus that each proton and neutron takes up is assumed to be the smallest cube that either the sphere of a proton or neutron would fit into. If the diameter of a proton or neutron is 1.0×10-15 meter, then the smallest cube that can hold that proton or neutron will dimensionally have length, width, and height of 1.0×10-15 meter. The volume of such a cube would be equal the length of the side of the cube to the third power. The volume of the cube is equal to 1.0×10-45 meter3. Assuming all the protons and neutrons in a Uranium-238 nucleus were cubes, the number of cubes in the nucleus would be 238 and the volume of the cubes would be 2.38×10-43 meter3. To determine the approximate diameter of the sphere of the Uranium-238 nucleus, it must be assumed that all 238 cubes must fit inside the volume of the sphere of the nucleus. First, one must find the radius and diameter of a sphere that has a volume of 2.38×10-43 meter3. The equation for the volume of a sphere is provided below:
Where "V" represents the volume of the sphere and "R" represents the radius of the sphere. The next step is to assume the volume of the sphere is that of the volume of a Uranium-238 (
92U238) nucleus, "VU-238," calculated to be 2.38×10-43 meter3, above, and solve for the radius, "RU-238," of the 92U238 nucleus:
The diameter of the nucleus is twice the radius, hence, the diameter = 7.689×10-15 meter. The diameter of a single nucleon is about 1.0×10-15 meter. In order to have "whole nucleons" lined up across the diameter of the 92U238 nucleus, the calculated diameter will be rounded up to 8.00×10-15 meter. The rounded nuclear diameter is conservative because the density of the 92U238 nucleus used in the calculation is smaller than the actual density. This will also ensure that all the protons and neutrons that make up the 92U238 nucleus exist within the imaginary sphere of interest assumed to be the 92U238 nucleus. The original assumption of the sphere radius did not prevent partial cubes from being placed in different locations within the 92U238 nuclear sphere to allow 238 cubes to fit within the 92U238 nuclear sphere. It is not reasonable to assume protons and neutrons be cut up into fractions in order to fit within the total sphere of the 92U238 nucleus. A diameter of 8.0×10-15 meter for the 92U238 nucleus is a reasonable value to ensure whole cubes fit within the nuclear sphere. The radius of the 92U238 nucleus is half the diameter of the 92U238 nucleus or 4.0×10-15 meter. Now that the dimensions of the 92U238
nucleus are known, the gravitational field at the surface of the 92U238 nucleus can be determined. As noted previously, acceleration of gravity represents the gravitational field intensity. The mass of the 92U238 nucleus, "MU-238," was determined to be 3.953×10-25 kg and the radius of the 92U238 nucleus, "RU-238," was determined to be 4.0×10-15 meter. Using Newton's Law of Gravity, the acceleration, or gravity field, at the surface of the 92U238 nucleus is calculated below:

aU-238 = 1.648×10-6 Newtons/kg = 1.648×10-6 meter/second2
To determine the "g-force" at the surface of the 92U238 nucleus, the gravitational field of the 92U238 nucleus must be normalized relative to Earth's gravitational field in the same manner used to calculate the g-force at the Sun's surface. Earth's gravitational field is 1g. The ratio of the acceleration of gravity on the surface of the 92U238 nucleus to the acceleration of gravity on the Earth's surface represents the g-force on the surface of the 92U238 nucleus. The g-force on the surface of the 92U238 nucleus is calculated as follows:

Using the "Classical Newtonian Physics" analysis for this calculation, it appears that the acceleration of gravity in the vicinity of the 92U238 nucleus is very insignificant and feeble. This analysis assumes the purely Classical Physics approach in the calculation, disregarding any Quantum Mechanical effects. Therefore, the calculated Nuclear Gravitation Field is assumed to be a continuous function at the surface of the 92U238 nucleus. Assuming Classical Physics, only, the gravitational field of the 92U238 nucleus is too feeble to have any measurable amount of "Space-Time Compression" occur. The rapid "drop off" of the "Strong Nuclear Force" as it propagates outward from the nucleus would indicate that the "Strong Nuclear Force" is not a gravitational field if the "Classical Newtonian Physics" analysis is accepted as the final evaluation. Without "Space-Time Compression" taking place, the "Strong Nuclear Force" and Gravity could only be the same if the intensity of the "Strong Nuclear Force" drops off proportionally to the inverse of the square of the distance from the center of the nucleus as observed.
What if the effects of Quantum Mechanics are considered? The protons and neutrons exist in discrete energy levels within the nucleus just as the electrons "orbit" about the nucleus within discrete energy levels. The electron energy levels were determined by solving the Schrodinger Wave Equation used in Quantum Mechanics for the Nuclear Electric Field. If Classical Electrostatics and Classical Physics are applied to the electron orbits about the nucleus, then the electrons should spiral into the nucleus and neutralize the protons by changing them to neutrons and the atom would not continue to exist as observed. Quantum Mechanics must also be applied to the analyses when analyzing the forces in the atomic or nuclear realm. The discrete energy levels of the protons and neutrons in the nucleus can be determined by using the Schrodinger Wave Equation for the Nuclear Gravitation Field. The probability of absorption of a proton or neutron by a nucleus is related to the kinetic energy of the proton or neutron. Protons or neutrons must have discrete energies in order to be absorbed by the nucleus. Since the energy levels within the nucleus are known to be discrete energy levels, then it would be reasonable to assume that the fields associated with those energy levels would also be discrete rather than continuous. If the "Strong Nuclear Force" and Gravity are the same force, then the Nuclear Gravitation Field must be made up by quantized, or discrete, fields to be consistent with the discrete energy levels that exist for the protons and neutrons in the nucleus. If Gravity is quantized, then the intensity of the Nuclear Gravitation Field in the vicinity of the nucleus may very well be equal to or greater than the gravitational field intensity of the Sun at its surface.

Index and Direct Links to Other Chapters of Nuclear Gravitation Field Theoryand Nuclear Gravitation Field Theory Home Page/Table of Contents:
Nuclear Gravitation Field Theory
Purpose for Evaluation of the Strong Nuclear Force and the Force of Gravity
Executive Summary
The Classical Physics Evaluation of Electrostatics and Gravity
The Electrostatic Repulsion Force
Newton's Law of Gravity - The Attractive Force of Masses
Comparison of Electrostatic Repulsion and Gravitational Attraction
Nuclear Gravitation Field Theory: Major Stumbling Blocks to Overcome

New Theory Results Must Equal Old Theory Results When and Where Applicable
Newton's Law of Gravity as It Applies to Large Masses and Nuclear Gravitation Field Theory
Kepler's Laws, Gravity, and Nuclear Gravitation Field Theory
Structure of the Nucleus of the Atom
The Schrodinger Wave Equation and Quantum Mechanics - The Particle and Wave Characteristics of Matter
Nuclear Gravitation Field Theory Versus Accepted Strong Nuclear Force Overcoming Electrostatic Repulsion
Comparison of the Nuclear Gravitation Field to the Gravitational Field of the Sun and the Gravitational Field of a Neutron Star
Quantum Mechanics, General Relativity, and the Nuclear Gravitation Field Theory
Properties of the Strong Nuclear Force, Nuclear Properties of Bismuth, and the Nuclear Gravitation Field Theory

Conclusion
Appendix A: References
Appendix B: Background of the Author
Index and Direct Hyperlinks to the Other Web Pages on this Website:
Gravity Warp Drive Home Page
Nuclear Gravitation Field Theory (Specific Chapter Links are Provided on this Web Page)
Purchase e-Books
History of My Research and Development of the Nuclear Gravitation Field Theory
"The Zeta Reticuli Incident" by Terence Dickinson
Supporting Information for the Nuclear Gravitation Field Theory

Government Scientist Goes Public
"Sport Model" Flying Disc Operational Specifications
Design and Operation of the "Sport Model" Flying Disc Anti-Matter Reactor
Element 115
Bob Lazar's Gravity Generator
United States Patent Number 3,626,605: "Method and Apparatus for Generating a Secondary Gravitational Force Field"
United States Patent Number 3,626,606: "Method and Apparatus for Generating a Dynamic Force Field"
V. V. Roschin and S. M. Godin: "Verification of the Searl Effect"
The Physics of Star Trek and Subspace Communication: Science Fiction or Science Fact?
Constellation: Reticulum

Reticulan Extraterrestrial Biological Entity
Zeta 2 Reticuli: Home System of the Greys?
UFO Encounter and Time Backs Up
UFO Testimonies by Astronauts and Cosmonauts and UFO Comments by Presidents and Top U.S. Government Officials
Pushing the Limits of the Periodic Table
General Relativity
Rethinking Relativity
The Speed of Gravity - What the Experiments Say
Negative Gravity
The Bermuda Triangle: Space-Time Warps

The Wright Brothers
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