• EXACT VALUE & FORMULA
• THE MATHEMATICAL LAW
• EARTH'S CORE PRESSURE (calculation procedure)
• DOES NOT EXIST
• NO NEED FOR A UNIFICATION THEORY

# Newton's Atom {© 28/10/2017}

This paper, which was released by Keith Dixon-Roche (one of CalQlata's Contributors) on the 28th of October 2017, describes the atom according to Isaac Newton.

Note: All the input data in these calculations has been provided by CalQlata's Constants page.
All calculations are the sole copyright priority of Keith Dixon-Roche © 2017
Keith Dixon-Roche is also responsible for all the other web pages on this site related to atomic theory
A 'pdf' version of this paper can be found at: Newton - The Paper

## Newton's Atom (a summary)

Fig 1. A Beryllium Atom

The above mentioned paper describes a procedure whereby sub-atomic particles may be described and defined using Newtonian mechanics, thereby unifying atomic and sub-atomic theories

It would also appear to prove that, along with the author's own spin theory, Newton's laws of motion describes the behaviour of electrons in an atom far more accurately and consistently than classical theory and thereby disproves the need for a unification theory.

Moreover, the atom is not nearly as complicated as has been claimed. It comprises only three sub-atomic particles; electrons following evenly spaced circular orbits around a nucleus of protons and neutrons
a very simple system!

## Calculations

In these calculations, the electron and proton in an hydrogen atom have been treated as a planet orbiting a force-centre (a star).
The purpose of these calculations is to see if Newton's laws of motion can be applied to atoms.

The following Table compares the calculation results from Newton's laws of motion and the author's spin theory when applied to the earth and a hydrogen atom for both gravitational and electrostatic forces.

 Earth Gravitational Force Electrostatic Force Units G:k 6.67359232E-11 6.67359232E-11 8.98755185E+09 m³/kg/s² m₁:Q₁ 1.9885E+30 1.67262164E-27 1.60217649E-19 kg:C m₂:Q₂ 5.96451977E+24 9.1093897E-31 1.60217649E-19 kg:C R₁ 6.9571E+08 1.77613270E-15 1.77613270E-15 m R₂ 6371000.685 1.45046059E-16 1.45046059E-16 m Δ⁽¹⁾ 0.154897828 1 5.013199118078 t 86164.1 4.656358032 7.58368E-15 s J₁ 9.23703809E+45 2.11061259E-57 1.27025550E-47 kg.m² J₂ 2.32349335E+36 7.66586456E-63 8.47134038E-50 kg.m² ω₁ 2.86533E-06 1.349377617 8.28514E+14 ᶜ/s Orbit T 3.1558118E+07 4.656358032 7.58368E-15 s a 1.4959460E+11 5.2917721E-11 5.2917721E-11 m b 1.4957371E+11 5.2917721E-11 5.2917721E-11 m e⁽²⁾ 0.01670914665 0 0 p 1.49552832E+11 5.29177211E-11 5.29177211E-11 m ƒ 1.47095E+11 5.29177211E-11 5.29177211E-11 m x' 2.49959808E+09 0 0 m L 9.39864971E+11 3.32491847E-10 3.32491847E-10 m K 2.97491436E-19 3.53673364E+38 2.74162451E+10 s²/m³ A 7.02944537E+22 8.79735542E-21 8.79735542E-21 m² Perigee R̂ 1.47095E+11 5.291772107E-11 5.291772107E-11 m F̌ 3.658178805E+22 3.631151755E-47 8.238722050E-08 N g -6.133232761E-03 -3.986163590E-17 -5.142206314E+11 m/s² v̌ 3.028600879E+04 4.592806255E-14 5.216453195E+00 m/s h 4.454920463E+15 2.430408403E-24 2.760428151E-10 m²/s PE -5.380998113E+33 -1.921522757E-57 -4.359743954E-18 N.m KE 2.735455000E+33 9.607707959E-58 2.179871977E-18 N.m E -2.645543113E+33 -9.607519611E-58 -2.179871977E-18 N.m Apogee Ř⁽³⁾ 1.520941962E+11 5.291772107E-11 5.291772107E-11 m Ř⁽³⁾ 1.520941962E+11 5.308391724E-11 5.291772497E-11 m F̂ 3.421649078E+22 3.631151755E-47 8.238722050E-08 N g -5.736671536E-03 -3.986163590E-17 -5.142206314E+11 m/s² v̂ 2.929053557E+04 4.592806255E-14 5.216453195E+00 m/s h 4.454920463E+15 2.430408403E-24 2.760428151E-10 m²/s PE -5.204129660E+33 -1.921522757E-57 -4.359743954E-18 N.m KE 2.558586547E+33 9.607707959E-58 2.179871977E-18 N.m E -2.645543113E+33 -9.607519611E-58 -2.179871977E-18 N.m A 5.918687303E+55 2.690405872E-78 6.104263241E-39 B 2.045888559E+76 4.775797602E-137 8.782651744E-68 C 7.915179174E+44 1.016826053E-67 2.307077145E-28 a -2.645543113E+33 -9.607519611E-58 -2.179871977E-18 b 7.915179174E+44 1.016826053E-67 2.307077145E-28 c -5.918687303E+55 -2.690405872E-78 -6.104263241E-39 Centripetal Force Calculations at Perigee and Apogee: (Fc = m₂.v/R = 1)⁽²⁾ FcP 3.7193039E+22 3.631151755E-47 8.238722050E-08 N fP 1.0167091 1 1 FcA 3.36447624166E+22 3.631151755E-47 8.238722050E-08 N fA 0.983290853349 1 1 fP.fA 0.99972080441818 1 1 Newton's Laws of Motion Applied to the Hydrogen Atom

The above results reveal the following:
1) These calculations only work for the electrostatic charge scenario if Δ ≈ 5, which means that the halo-effect of electrostatic charge in elementary particles is larger than the particle itself.
2) Centrifugal force calculations are correct only if the eccentricity is zero (the orbit is circular)
3) Ř = Ř for all three subjects (the earth, the hydrogen atom's gravitational forces and the hydrogen atom's electrostatic forces), which means that all three orbits are correct according to Newton's laws and the author's spin theory.

That the above calculation technique is exactly the same in all three scenarios proves that Newton's laws of motion do apply to atoms as long as spin theory is included.

## Comparison Between Planetary and Atomic Orbits

In addition to the above proof of Newton's laws when applied to the atom, comparison calculations were carried out between planetary and electron orbits, all of which use identical theories and therefore strengthen the claim that Newton's laws apply to atomic structures.

### The Systems

Rydberg: A standard atom of protons and orbiting electrons

Planck: A Planck mass orbiting a Planck mass force centre

Two known planetary force-centres each with a single orbiting planetary body

## Constants & Formulas

Newton’s gravitational coupling force: Fg = G.m₁.m₂ / R²
Coulomb’s electrostatic coupling force: Fₑ = k.Q₁.Q₂ / R²
Centripetal force: Fc = m₂.v² / R
Universal force coupling factor: φ = Fg/Fₑ = 4.40742111792333E-40
Newton’s gravitational constant: G
Coulomb’s constant: k
Force-centre mass: m₁
Orbiting mass: m₂
Force-centre elecrical charge: Q₁
Orbiting elecrical charge: Q₂
Separation distance: R
Velocity of orbiting mass: v

### Calculation Results

The following Table of results show that the same calculation rules apply to Planck’s Atom and planetary systems which are both coupled together with gravitational force only (K=1)

 Moon-Earth ⁽¹⁾ Sun-Earth ⁽¹⁾ Planck Atom Std. Atom Perigee Apogee Perigee Apogee v (m/s) 299792459 2187690.351 1084.034166 958.7083173 30279.07556 29287.2 R (m) 1.61617E-35 5.29177E-11 3.59508E+08 4.06504E+08 1.47095E+11 1.5206E+11 m₁ (kg) 2.17655E-08 1.67262E-27 5.96659E+24 5.96659E+24 1.9885E+30 1.9885E+30 m₂ (kg) 2.17655E-08 9.10939E-31 7.34892E+22 7.34892E+22 5.96659E+24 5.96659E+24 φ 1 4.40742E-40 1 1 1 1 Fg (N) 1.21038E+44 3.63115E-47 2.26408E+20 1.77084E+20 3.65945E+22 3.42437E+22 Fc (N) 1.21038E+44 3.63115E-47 2.40215E+20 1.66162E+20 3.71889E+22 3.36563E+22 Fg:Fc 1 1 1.00412615 1.000734727 Table 1: Forces ⁽¹⁾ some of these properties have been obtained from planetary systems not yet corrected with the final/actual value for Newton’s gravitational constant 'G' and therefore are not expected to provide and exact value of 1.0 for Fg:Fc

As can be seen from the above table, applying universal factor; 'φ' to Rydberg’s atom allows us to use Newtonian mechanics to define the properties and behaviour of sub-atomic particles.

Using Henri Poincaré’s formula EN = m.v² to convert the above properties to energies:

 Moon-Earth ⁽¹⁾ Sun-Earth ⁽¹⁾ Planck Atom Std. Atom Perigee Apogee Perigee Apogee φ 4.4074E-40 1 1 1 1 1 EN (J) 4.4384E+48 4.35974E-18 8.6359E+28 6.7546E+28 5.4703E+33 5.1178E+33 PEₐ (J) ⁽²ꞌ³⁾ -4.4384E+48 -4.3597E-18 -8.1367E+28 -7.196E+28 -5.381E+33 -5.2047E+33 KEₐ (J) ⁽²⁾ 2.2192E+48 2.1799E-18 4.318E+28 3.3768E+28 2.7352E+33 2.5589E+33 Table 2: Energies ⁽¹⁾ some of these properties have been obtained from planetary systems not yet corrected with the final/actual value for Newton’s gravitational constant 'G' and therefore are not expected to provide and exact value of 1.0 for Fg:Fc ⁽²⁾ whilst these values have been calculated using Rydberg’s formulas, the planetary energies can be seen to exactly replicate those for Newton's orbits for the earth and its moon) ⁽³⁾ these properties include spin induced energy and therefore vary slightly with Poincaré’s formula alone for planets. Planck’s and standard atoms do not include the effects of spin

As can be seen from the above Table the energies calculated using Newton’s formulas replicate the results from Rydberg’s, noting that the universal factor 'φ' is required for the Planck atom.

 Quantity Formula Planck (A) Newton (B) Ratio A/B t (s) = aₒ/c 5.39096122598358E-44 1.76514516887831E-19 3.05411776948031E-25 λ (m) = aₒ 1.61616952231127E-35 5.29177210670000E-11 3.05411776948031E-25 m (kg) = mN 2.17655000174590E-08 7.12660796350449E+16 3.05411776948031E-25 E (J) = m.c² 1.95618559889903E+09 6.40507585675677E+33 3.05411776948031E-25 F (N) = E/λ 1.21038391820525E+44 1.21038391820525E+44 1.0 Table 3: A Comparison of Newton’s and Planck's Atomic Values

If Newton's G were incorrect (i.e. not 6.67359232004332E-11 m³/kg/s²), variations would appear between the Ratios in the above table.

## Conclusions

Newton’s laws are universal, i.e. they apply to all orbiting systems irrespective of size, Rydberg’s formula only applies to particles coupled together by electrostatic force. However, whilst you can apply Rydberg’s rules to planetary systems (by multiplying the gravitational coupling force by 'φ'), you must first assume that they both carry a charge. You must also assume that the charge held by the sun is equal to the combined charge held by all of its orbiting bodies. To the author's knowledge, no such charge has been identified in the earth.

As the above theories are universal, i.e. they also apply to the electron, which is an elementary particle, the author considers it highly likely that Newtonian theory may be applied to all elementary particles and therefore also considers it unlikely that there is a need for the elusive Unification Theory.