Calculations – Force Equation
The results of forces using the Force Equation were calculated at various distances and compared to known results that have been verified with classical equations: Newton’s law of gravity and Coulomb’s law for electromagnetism. The findings are identical and are shown the table below.
The strong force only applies to objects at small distances, so the third and fourth columns contain calculations at distances of 8.45E-16 m (0.845 fm) and 1.13E-15 m (1.13 fm), calculating these forces to be 44.2K and 24.9K newtons respectively. Similarly, the gravity of planets is measured over large distances, so the last and second to last columns contain distances between the Earth and the Sun and Moon. In the last column, the gravitational force between the Sun and Earth is calculated at 3.542E+22 newtons, which is a variation of 0.00% when using Newton’s law. In the second to the last column, the gravitational force between the Earth and Moon is calculated at 1.976E+20 newtons, also a variation of 0.00% from the traditional calculation. Also, a test of different electron and positron combinations across various distances, from the distance between two quarks to the distance between the Earth and Sun, were used to calculate the electromagnetic force. All calculations agree with the traditional calculation using Coulomb’s law with no difference (0.00%).
Force Distance (m) | Count (Q1, Q2) | 8.45E-16 | 1.13E-15 | 1.40E-10 | 1.00E+00 | 3.85E+08 | 1.50E+11 |
Electromagnetism |
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Two Electrons (Calculated) | -1, -1 | 3.228E+02 | 1.816E+02 | 1.177E-08 | 2.307E-28 | 1.556E-45 | 1.031E-50 |
Two Electrons (Coulomb’s Law) | 3.228E+02 | 1.816E+02 | 1.177E-08 | 2.307E-28 | 1.556E-45 | 1.031E-50 | |
% Difference | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | |
Multiple Electrons (Calculated) | -5, -10 | 1.614E+04 | 9.079E+03 | 5.885E-07 | 1.154E-26 | 7.782E-44 | 5.154E-49 |
Mult. Electrons (Coulomb’s Law) | 1.614E+04 | 9.079E+03 | 5.885E-07 | 1.154E-26 | 7.782E-44 | 5.154E-49 | |
% Difference | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | |
Electron/Positron (Calculated) | -1, 1 | -3.228E+02 | -1.816E+02 | -1.177E-08 | -2.307E-28 | -1.556E-45 | -1.031E-50 |
Elect. / Posit. (Coulomb’s Law) | -3.228E+02 | -1.816E+02 | -1.177E-08 | -2.307E-28 | -1.556E-45 | -1.031E-50 | |
% Difference | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | |
Gravity | |||||||
Two Electrons (Calculated) | -1, -1 | 7.749E-41 | 4.359E-41 | 2.826E-51 | 5.538E-71 | 3.736E-88 | 2.475E-93 |
Two Electrons (Newton’s Law) | 7.749E-41 | 4.359E-41 | 2.826E-51 | 5.538E-71 | 3.736E-88 | 2.475E-93 | |
% Difference | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | |
Two Protons (Calculated) | 1, 1 | 2.613E-34 | 1.470E-34 | 9.526E-45 | 1.867E-64 | 1.260E-81 | 8.343E-87 |
Two Protons (Newton’s Law) | 2.613E-34 | 1.470E-34 | 9.526E-45 | 1.867E-64 | 1.260E-81 | 8.343E-87 | |
% Difference | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | 0.000% | |
Earth / Moon (Calculated) | 3.57E51, 4.39E49 | 1.976E+20 | |||||
Earth / Moon (Newton’s Law) | 1.976E+20 | ||||||
% Difference | 0.000% | ||||||
Earth / Sun (Calculated) | 3.57E51, 1.19E57 | 3.542E+22 | |||||
Earth / Sun (Newton’s Law) | 3.542E+22 | ||||||
% Difference | 0.000% | ||||||
Strong Force | |||||||
Strong Force (Calculated) | -1, -1 | 4.424E+04 | 2.488E+04 | ||||
Strong Force (Measured) | ~ | 2.500E+04 | |||||
% Difference | 0.468% | ||||||
Summary of Calculations using Force Equation (force calculated in newtons)
Calculations – Acceleration Equation
Acceleration and force are related from Newton’s Second Law, and later it is shown with a new acceleration equation that surface gravity (g), which is acceleration due to gravitation, can be calculated accurately with the same method for counting particles as was performed using the Force Equation in the calculations in the table above. The known surface gravity values for the Sun, Earth, Moon and the remaining planets in the solar system are found in the table below. They are compared to the calculated versions using the Acceleration Equation for Gravity in the “Calculated” column.
The source values of g are available to two decimal places. However, the calculated values extend beyond two decimal places, resulting in a difference in the known values and calculated values. Upon closer inspection, rounding up or down to the nearest decimal would result in a match against the known values for each of the calculations.
Surface Gravity (g) | Radius | Mass | Nucleon Count | Value | Calculated | % Diff |
Sun | 695,700,000 | 1.98855E+30 | 1.18888E+57 | 274.00 | 274.21 | -0.08% |
Jupiter | 71,492,000 | 1.8986E+27 | 1.1351E+54 | 24.79 | 24.79 | -0.01% |
Saturn | 60,268,000 | 5.6836E+26 | 3.39802E+53 | 10.44 | 10.44 | -0.03% |
Uranus | 25,559,000 | 8.681E+25 | 5.19006E+52 | 8.87 | 8.87 | 0.01% |
Neptune | 24,764,000 | 1.0243E+26 | 6.12392E+52 | 11.15 | 11.15 | 0.02% |
Earth | 6,375,223 | 5.972E+24 | 3.57044E+51 | 9.81 | 9.81 | 0.00% |
Venus | 6,051,800 | 4.8675E+24 | 2.9101E+51 | 8.87 | 8.87 | 0.00% |
Mars | 3,396,200 | 6.4171E+23 | 3.83655E+50 | 3.71 | 3.71 | -0.06% |
Mercury | 2,439,700 | 3.3011E+23 | 1.97361E+50 | 3.70 | 3.70 | -0.04% |
Moon | 1,738,100 | 7.34767E+22 | 4.39291E+49 | 1.62 | 1.62 | -0.20% |
Pluto | 1,187,000 | 1.303E+22 | 7.79016E+48 | 0.62 | 0.62 | 0.45% |
Surface Gravity using Acceleration Equation for Gravity (force calculated in m/s^{2})
Notes about references for values in Acceleration Table:
- Values for radius, mass and the surface gravity value (g) were obtained from Wikipedia pages for each of the planets.
- Equatorial radius was used as the radius for planets unless it was not present, in which case the mean radius was used. Earth is the only exception for radius. The radius used for the Earth is 6,375,223 meters to be consistent with Newton’s calculation to arrive at the known surface gravity of Earth.
- The NASA fact sheet on Uranus was used for its surface gravity value since the Wikipedia value was incorrect at the time of calculation.
Calculations – Velocity Equation
In the table below, velocity was calculated for gravitational acceleration based on time, using the Velocity Equation for Gravity and compared to a non-relativistic value (velocity = acceleration * time).
Velocity (t) | Time (t) | Wavelength | Value (v=at) | Calculated | % Diff |
Earth | 1 | 2.81794E-17 | 9.81 | 9.81 | 0.00% |
Earth | 50 | 2.81794E-17 | 490.33 | 490.33 | 0.00% |
Earth | 1000 | 2.81785E-17 | 9806.65 | 9806.33 | 0.00% |
Jupiter | 1 | 2.81794E-17 | 24.79 | 24.79 | -0.01% |
Jupiter | 50 | 2.81793E-17 | 1239.50 | 1239.59 | -0.01% |
Jupiter | 1000 | 2.81771E-17 | 24790.00 | 24789.87 | 0.00% |
Sun | 1 | 2.81794E-17 | 274.00 | 274.21 | -0.08% |
Sun | 50 | 2.81781E-17 | 13700.00 | 13709.90 | -0.07% |
Sun | 1000 | 2.81537E-17 | 274000.00 | 273959.94 | 0.01% |
Relativistic Velocity | |||||
Sun | 1.00E+14 | 3.08082E-25 | N/A | 299,792,455 | |
Sun | 1.00E+15 | 3.08082E-26 | N/A | 299,792,458 | |
Sun | 1.00E+16 | 3.08082E-27 | N/A | 299,792,458 |
Velocity due to Gravity Using Velocity Equation
Notes about references for values in Velocity Table:
- Time is in seconds (s) and wavelength in meters (m). Therefore the value and calculated columns are velocity expressed in meters per second (m/s).
- Calculations assume constant acceleration and zero initial velocity for simple comparison.
- The value column uses a non-relativistic calculation (v << c) of velocity where v=at.
- The difference between the traditional calculation (value column) and the energy wave theory calculation (calculated column) becomes larger as velocity increases, due to relativity. In the final three rows, the relativistic velocity of Sun’s gravity at 1.00E14 seconds approaches the speed of light. At 1.00E15 and 1.00E16 seconds, velocity remains constant at the speed of light: 299,792,458 meters per second.
Source Data: All tables shown here for force calculations can be found in the downloadable spreadsheet. Further information on the derivation of the equations and how to replicate them is in the Forces paper.