# 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)

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

## Constants & Formulas

Centripetal force: Fc

Newton’s gravitational force: Fg

Newton’s gravitational constant: G

Force-centre mass: m₁

Orbiting mass: m₂

Separation distance: R

Coulomb’s gravitational force: Fₑ

Coulomb’s constant: k

Force-centre elecrical charge: Q₁

Orbiting elecrical charge: Q₂

Velocity of orbiting mass: v

This paper should be read in conjunction with:

Constants

Laws of Motion

Planetary Spin

Rydberg Atom

Planck Atom

G

## 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

## Calculations

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 = G.m₁.m₂ / R² ÷ k.Q₁.Q₂ / R² = G.m₁.m₂ / k.Q₁.Q₂ = 4.40742111792333E-40

## 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.

Newton's motion constant; (*h*) can be used to calculate atomic shell number

h per electron shell | Newton's shell numbers | |||

h₁ = 1.15767587750606E-04 m²/s | h₁/h₁ = 1 | |||

h₂ = 2.31535175501211E-04 m²/s | h₂/h₁ = 2 | |||

h₃ = 3.47302763251817E-04 m²/s | h₃/h₁ = 3 | |||

h₄ = 4.63070351002422E-04 m²/s | h₄/h₁ = 4 | |||

h₅ = 5.78837938753028E-04 m²/s | h₅/h₁ = 5 | |||

h₆ = 6.94605526503633E-04 m²/s | h₆/h₁ = 6 | |||

h₇ = 8.10373114254239E-04 m²/s | h₇/h₁ = 7 | |||

Table 4: Newton's 'h' applied to electron shells |

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.

### Further Reading

You will find further reading on this subject in reference publications^{(55, 60, 61, 62, 63 & 64)}

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