go to the calculator page

The Mathematical Laws of Natural Science

Science took a wrong turn in the early 20th century, that spawned an ever-increasing number of fantastic theories; dark matter, photons, uncertainty, string-theories, sub-atomic particles, cosmic eggs, black-holes, anti-matter, event-horizons, etc. none of which could be verified either with the known laws of physics or even with each other. Over the following 120 years, the scientific community simply continued to create weird and wonderful theories that tried �€“ and failed �€“ to make sense of them. We have now reached a point where none of today's scientific theories bear any relationship to reality.

However, after starting all over again (returning to pre-20th century science), Keith Dixon-Roche has managed to generate a single scientific theory that can predict the behaviour and properties of the entire universe, from the electron to the 'Big-Bang' that reflects exactly what we see around us. His latest book; The Mathematical Laws of Natural Science, explains this theory and this calculator proves that it works.

It is important to understand that all genuine scientific laws of nature are invariable. Statistics only apply to the consequences of these laws, never the laws themselves. The mathematical laws of science are simple, just as you would expect. They can be understood by anybody with a slight mathematical and technical bent.

The creation of a neutron
Fig 1. A proton unites with its orbiting electron create a neutron @ 'Rn'


Physics begins with a complete rewrite of all the scientific constants generated by the pre-20th century scientists and the discovery of a number of new constants, all of which can be generated from just 4-Primary constants (m, e, Rn & tn), two ratios (ξm & ξv) and a bizarre constant (Σ) that either has no units or volume-squared. In fact, every scientific field (electricity, atomic, mechanical, energy, chemistry, etc.) can now be expressed using these same four units.

There are no approximates, estimates or uncertainties in their values, they are fixed and solid, just as nature intended. Accurate values (up to 15 decimal places) for all of these constants (>70) are listed, together with their formulas, in a help page via the calculator's menu item; 'Data Listing>Constants'.

Proton-Electron Pairs

Proton-electron pair
Fig 2. Proton-Electron Pair

Physics then goes on to explain the most basic natural structure, the proton-electron pair; a single proton orbited by a single electron (an hydrogen atom) following a circular path that obeys Isaac Newton's and Charles-Augustin de Coulomb's force laws. Not only does this calculator provide all the properties of the pair, it also defines the properties of the electro-magnetic radiation it emits.

The crowning glory for this theory is the discovery of the neutronic radius (Rn), which is a fundamental part of almost all scientific constants. This discovery has confirmed that all electrons orbit their protons in circular orbits, and forms the basis for Henri Poincaré's formula 'E = m.c2' which applies to the potential energy (PE) in circular orbits, where PE is always twice a satellite's kinetic energy (KE):
PE = 2.KE = 2.½.v2 = m.v2
E = m.c2 refers to the instant at which the electron achieves light-speed and the resultant magnetic field generated by the proton-electron pair exceeds electrical repulsion energy. At this instant, the two particles unite to create a neutron. The plot-co-ordinates for this event can be accessed through the calculator's menu item; 'Data Listing>Plot Co-ordinates' (Fig 1).

In fact, Fig 1 is the most compelling evidence that Bohr and Einstein were both wrong, because:
a) Rn, which forms the basis of all the universally accepted physical constants, proves that electrons orbit protons in circular orbits, and;
b) Rn proves that space and time do not deform with gravity (magnetism). If they did, the electron would be orbiting inside its proton at 'c'

All proton-electron pairs are paired for life until physically separated. An electron will remain attached to its proton even when united with other proton-electron pairs inside an atom. A proton can and will only accommodate a single orbiting electron.


The structure of an atom
Fig 3. The Structure of an Atom

An atom is a collection of proton-electron pairs with one or two neutrons attached; deuterium or tritium.

Elements are atoms, all of which were created by fusion in the cold cores of the galactic force-centres and the great attractor⁽²⁾ during previous universal periods. These are the only bodies cold enough and with sufficient mass to generate the core pressures necessary to push the nucleus of one atom inside the electron shells of another.

Every electron shell of an atom (except its outermost) contains two electrons. The outermost shell contains either one or two electrons dependent upon its atomic number. All electron shells are circular and filled; there are no valences. This calculation option calculates the overall properties of a single atom; its number of shells, outer shell radius, total mass, minimum temperature (that of the outermost proton-electron pair) and its total energies, all of which are calculated simply from its atomic number and its temperature.

Temperature is a convenient way to describe the kinetic energy of an orbiting electron. As half (two electrons per shell) of its electrons orbit at different radii, their kinetic energies will also differ, resulting in different temperatures for each atomic shell. Whilst an atom's heat is the combined kinetic energy in all of its electrons, its temperature (that which we measure) is the highest kinetic energy, which occurs in the innermost proton-electron pairs; Shell-1.

Whilst the physics calculator displays only general atomic data, the properties of every electron-pair (shell) can be displayed via menu item 'Data Listing>Shells'. You may use this listing to establish/confirm the properties calculated in the 'Proton-Electron Pair' and 'Matter' calculation options, because they all interrelate.


Collections of atoms will exist as viscous matter if their temperatures are below the gas-transition temperature, i.e. when the magnetic field energy generated by the innermost proton-electron pair is greater than the electrical charge held by the proton. When the temperature of adjacent atoms rises above their gas-transition temperature, they exist as a gas. The validity of this atomic model is confirmed by the fact that the pressure of this gas can be calculated either by using the ideal gas law or by using the potential energy in an atom's innermost proton-electron pair (p = ρ.PE / mA.Y), both of which provide exactly the same result.

This atomic model is also confirmed by the fact that it is now possible to predict an atom's gas-transition temperature, specific heat capacity, and gas pressure, simply from its atomic number.


Isaac Newton gave us the laws that govern all orbits; celestial and atomic.

Celestial orbits can be calculated using the 'Solar System Planets', 'Solar System Moons' and 'Celestial Orbits' calculation options. Physics contains all the data necessary to automatically calculate the orbital properties of all our neighbouring planets, moons and some of our comets. It also contains the orbital properties of our sun in the Milky Way, including the mass of its force-centre; Hades.


Each and every orbiting body (satellite) spins because of their kinetic and potential energies. These energies not only influence a satellite's body spin, but also generates internal friction, which is responsible for its mantle heat. If a satellite's sub-satellite population is sufficiently energetic (and massive), the planet's crust will melt. This generates a dense gas cloud around the planet that prevents us from identifying its spin-rate. We only know the spin-rate of the gas cloud.

Mantle heat generated by planetary spin
Fig 4. Mantle heat generated by planetary spin

The internal heat within stars is similarly generated, but from planetary (not lunar) orbits. However, in the case of stars, the internal heat generated is sufficient to create neutrons, which are responsible for a star's additional energy through fission. In the case of our sun, almost 40% of its energy is generated through fission.

The difference between the angular velocity of a satellite's inner core and its outer mantle is also responsible for generating its magnetic field. This field is generated by the combined electro-magnetic charge (in the core Quanta) revolving around the combined electro-magnetic charge of another (mantle Quanta).


This is the pressure generated inside a body of viscous matter. The ability to calculate the internal pressure within a body of matter was given to us by Isaac Newton;
p = F/A = G.mo.mi / A.r2

This option allows the user to calculate the pressure anywhere within a body that comprises up to seven internal layers of different densities.

This option cannot be used to determine the internal pressure within a satellite, such as a star or a planet, because there is no way to enter suitable radial modifiers for each layer. This capability is, however, available in CalQlata's Cores calculator.


Amazingly enough, it is still believed by all scientists that the universe was created from 'inflation', a cosmic egg or a singularity. They also believe that the solar system was born from the accretion of hydrogen atoms 4.6 billion years ago. In fact, all of the current beliefs defy the most fundamental laws of nature; the conservation of energy, the first law of thermodynamics, the 'constant of motion', 'like-poles' repel, and the only evidence to explain the perceived age of the solar system is the age of meteorites we find.

There is no evidence to prove any of these theories and the age of the earth's rocks simply shows us how long ago they were recycled. Our rocks could have been recycling for the entire age of the universe. Meteorite age simply tells us how old the rocks were that formed on a planet that was impacted, perhaps 65 million years ago �€“ perhaps in our asteroid belt?

In fact, it is far more believable that all the matter in the universe was ejected from an ultimate body⁽¹⁾ 15 billion years ago and is of that age. Age is a moveable feast. The oldest rocks on earth may be only three and half billion years old, but the matter from which they comprise may have been recycled three or four times during the actual age of the earth.

This calculation option can tell you how large the ultimate body needs to be to work according the known laws of physics. Moreover, it is reflected in what we see of it.

Physics Calculator �€“ Technical Help


You may only use the metric units provided in the calculator. But Imperial conversion factors are provided in the Technical Help page of this calculator.

Input Data

All the input data for this calculator is pre-defined in its code.

You may alter it if you wish, but doing so will similarly alter all related calculations throughout all calculation options. However, after alterations, if you wish to recover the correct values, you may do so via menu item; 'File>Reset Default' �€“ this action will reset all the input data throughout all options.

Constants (calculations)

The input data for this option comprises the only Primary Constants required to calculate all others. They are the only values that remain fixed and taken for granted. All other calculations depend on the accuracy of these values.

You may access all the constants, including the above Primary values and those calculated using them, via menu item; 'Data Listing>Constants'.

Data listing of all constants
Fig 5. Data Listing of all Constants

There are two constants which may be disputed: 'g' and 'NA' gravitational acceleration (g) is provided for information only, it is not used in any calculation. So, whilst it may be modified in this calculator's Data File, changing it won't make any difference to any of Physics' calculations.

Avogadro's number (NA) is used only to define the gas constant (Ri) neither of which is used in any of Physics' calculations. Changing it in the Data File will only alter its own value and that of 'Ri' in the list of constants.

Proton-Electron Pairs (calculations)

The input data is limited here only to the 'temperature' of the proton-electron pair. All other input properties (particle mass and charge) are pre-defined.

Whilst orbital shape is common to both calculation methods, the velocities (v), accelerations (g), forces (F) and energies (KE, PE, E, SE) will differ according to the charge used;
magnetic (Newton; m) electrical (Coulomb; e).

The properties of the electro-magnetism (�’, λ, A, E, e�žŒ) emitted by the proton electron pair is always the same for the same temperature, even within an atom.

Atom (calculations)

An atom is simply a collection of proton-electron pairs. You either enter the atomic number (Z) or you select the element from the list provided. In either case, the calculation will be identical for the same temperature.

Temperature () only applies to the innermost proton-electron pair. The temperature of all other proton-electron pairs in the atom will vary with electron velocity, which varies with orbital radius. But the input temperature () does refer to the temperature that we measure in any substance.

Matter (calculations)

Input values for atomic number (Z) and temperature () are as defined above for the atom.

Input 'RAM' is the calculator's default value, which you may alter as you wish. It should be understood, however, that values less than 'Z' and greater than '1.6 x Z' are unreal, the calculation results for which will therefore be meaningless.

The 'number of molecules' (N) only applies to calculations for the matter in gaseous form. The input value provided is that most common for the atom concerned.

Gas density (ρg) only applies to matter in gaseous form. If the temperature entered is less than the gas-transition temperature calculated (<Ṯg), the calculated pressure (pg) will be meaningless (unreal).

Orbits (calculations)

All of the input data for every planet, comet, moon and star (our sun) is pre-defined in the calculator's code.

You may alter it if you wish, but the orbital properties of the planet, comet, moon or star concerned will no longer be true.

To select a particular lunar orbit, you first select a planet from the drop-down list and all of its moons (if any) will appear in the list below. Simply select the desired moon from the list.

To calculate the properties of a generic satellite, you may do so in the 'Celestial Orbits' calculation option. Its default data is that of our sun's orbit in the Milky Way galaxy.

Spin (calculations)

The following input data is accurately known for all non-gas planets in our solar system:

to, R, E1, E3, all of which are calculated using the planetary and lunar orbital data for the planet concerned. All input data may be altered if preferred, but altering these values will generate unreal values for the planet's spin. The correct default values can be recovered via menu item;
'File>Reset Defaults'

The default values for 'r' and 't2' are correct for all but for the gas planets, which only apply to their gas-cloud rotations. You should alter these values to achieve a radial modifier (�”) slightly less than that for the earth (< 0.33).
For example, Jupiter's radial modifier, based upon its gas-cloud rotation is 0.02278, which is obviously incorrect for the planet beneath. If you alter 'r' to 4E+07m and 't2' to 2.8E+05 seconds you will achieve a radial modifier of 0.312; a much more realistic value, but it is of course, just a guess. You have no way of knowing how much smaller the planet is than its gas-cloud nor how much slower it is spinning. However, these revised values are much closer to reality than the default values.

Core radius (rc) and core density (ρc) are also estimates, but the default values have been factored on the earth, so they should not be far off the mark.

Core-Pressure (calculations)

The input values for core density are simply the outer radii (r1 to r7) and density (ρ1 to ρ7) for each layer within the body.

This is a straight forward calculation based on homogeneous matter in each layer. You cannot calculate the internal structure of a planet using this calculation option as there is no way of guessing the radial modifier for each layer.

The internal structure of planets and stars should be calculated using CalQlata's Cores calculator, which accounts for density variations within each layer.

'Big-Bang' (calculations)

The 'Big-Bang' undoubtedly originated from a massive body of matter, maybe 100 times the mass of the observable universe, that compromised its innermost neutrons, due to its mass being sufficient to overcome the coupling ratio.

This option calculates both the theoretical 'minimum mass' necessary to achieve this condition, assuming a perfectly spherical ultimate body of homogeneous matter and one perfect crystal, or a more 'realistic mass', based upon a variable mass full of voids; remember, this body will be cold.

Constants 'k', 'G,', 'e', 'me' and '�†' should not be altered as they were fixed by others a long time ago, and are universally accepted.

The energy stored in every neutron (En) is also unchangeable.

The neutronic ratio (�ˆ) is the average expected in the rock of which the ultimate body is made. This value may be changed according to preference, but is unlikely to be outside the bounds;
'1.1 < �ˆ < 1.2'

The energy factor (FE) is a guess. 1/63rd of the uranium mass of the Little-Boy atom bomb was converted to pure energy, but being non-crystalline, considerably less of the ultimate body's matter will be converted to energy, e.g.; FE > 1000

The mass factor (Fm) is also a guess. It represents the mass that was actually ejected from the ultimate body to form the observable universe. The remainder, the mass left behind will constitute the mass of the Great-Attractor, which is gradually slowing down universal expansion and will re-collect all universal matter for the next 'Big-Bang', e.g.; Fm < 1/100

Output Data

The output data from most calculations includes the following common items:
KE is kinetic energy; of a satellite (usually positive)
PE is the potential energy; between a satellite and its force-centre (usually negative)
E is the total energy (E = KE+PE); it is constant
g is the potential acceleration; between a satellite and its force-centre (usually negative and usually called gravitational acceleration)
F is the potential force; between a satellite and its force-centre (usually negative)
h is Newton's constant of motion
v is the curvilinear velocity; of the satellite (usually positive)
m is the mass; of the satellite, its force-centre, the proton, the neutron or the electron
R is orbital radius (or distance)
r is body radius (or dimension)
t is time (usually period)
K is orbital constant of proportionality

Constants (results)

The output data displayed is a selection of the best known and most used physical constants that have been calculated using the 7 primary constants listed as input data.

You may obtain a complete list (>70) of the physical constants (including their formulas) - all of which have been calculated using the 7 primary constants - via menu item:
'Data Listing>Constants'

X, XR and Y are new constants related to the velocity and orbital radius of an electron.

Proton-Electron Pairs (results)

R, t and K define the orbital shape of the electron

m1 is the mass of the force-centre (proton) and m2 is the mass of its solitary satellite (electron).

ve, re, Fe, PEe, KEe, Ee, he; relate to the orbital properties of the pair due to the electrical properties of its particles

vm, rm, Fm, PEm, KEm, Em, hm; relate to the orbital properties of the pair due to the magnetic properties of its particles

SE1 & SE2 refer to the spin energies in the proton and the electron respectively

The properties of the electro-magnetic energy radiated at the entered temperature:

�’ is the frequency

λ is the wavelength

A is the amplitude

E is the energy

e�žŒ is the electrical charge

Atom (results)

Ψ is the neutronic ratio of the atom selected (N:P). It is a default value provided for information only in this calculation as it is not used in the calculation.

n is the number of atomic shells �€“ there are no valences in atomic shells. All electrical forces must balance.

R is the orbital radius of the outermost electron shell

m is the total mass of the atom based upon Ψ

KE, PE & E are the total energies of all proton-electron pairs in the atom

min is the temperature of the electron(s) orbiting in the atom's outermost shell

Matter (results)

R is the separation distance between adjacent atoms when the matter is viscous

ζ is the lattice [mathematical] factor for the atom. It applies to both its nucleus and its crystal structure.

SHC is the calculated value for the atom's specific heat capacity

Fe is the repulsive potential force between adjacent atoms at the temperature entered

Fm is the attractive potential force between adjacent atoms at the temperature entered

When Fe>Fm, the matter will exist as a gas, otherwise it will be viscous

ρv is the matter density when viscous �€“ this value should be ignored when Fe>Fm

ρg is the matter density when gaseous �€“ this value should be ignored when Fe<Fm

Ṯg is the [calculated] gas transition temperature of the matter based upon Fe & Fm

Orbits (results)

Superscript 'P' refers to the orbital perigee

Superscript 'A' refers to the orbital apogee

No superscript [R, v, g, F, KE, PE] refer to the orbital position at 'θ'

The shape of the orbit is defined by output data; RA, a, b, e, p, �„, x�žŒ, A, L, K, v, g. These values will not alter by changing the mass of the satellite (m2)

The performance of the satellite in its orbit is defined by the forces (F) and energies (KE, PE, E). These will change if the satellite mass is altered.

E and h both remain constant throughout a satellite's orbital position (θ)

Spin (results)

�” is the radial modifier and J is the polar moment of inertia both of which apply to the entire satellite mass and is calculated based upon known planetary information
(see 'Input Data>Spin' above regarding gas planets)

Eo is the satellite's spin energy due to its orbit alone �€“ assuming it presented the same face to its force-centre throughout its orbit

E2 is the satellite's total spin energy

�‰o, �‰1, �‰2, �‰3 are the angular velocities (radians per second) associated with each spin energy (Eo, E1, E2, E3)

mc, Jc & �‰c refer to the spin properties of the satellite's core (�” for the core defaults to 1)

mm, Jm, �”m, Em, �‰m all refer to the spin properties of the satellite mantle

� is the differential spin-rate (angular motion) between the satellite's core and its mantle. is the spin energy associated with �. It is the energy generating the earth's internal heat and its magnetic field; "quite important then!"

Core-Pressure (results)

P1 to p7 refers to the pressure (N/m2) at the radii entered

J is the polar moment of inertia of the body and m is its mass

'Big-Bang' (results)

m is the minimum possible mass of an ultimate body that would compromise its innermost neutron due to overcoming the coupling ratio, and Q is the number of protons (and an equal number of electrons) of which the m comprises. It is based upon a perfect sphere of homogeneous mass (highly unlikely).

mu and Qu are the mass and Quanta of the 'probable' ultimate body based upon the energy factor (FE).

mU is the mass of matter ejected from the ultimate body, and comprises the mass of the observable universe. The remaining mass (that left behind), constitutes the mass of the 'Great-Attractor', which is gradually pulling the universe back together.

E was the energy released during the 'Big-Bang', and v was the initial velocity of the matter ejected from the ultimate body. It will be travelling quite a bit slower today due to the magnetic (gravitational) attraction induced in all universal matter during this universal period.


The calculator applies to every aspect of natural physics.


The calculations in this calculator are 100% accurate, based upon the accuracy of the primary constants and the orbital input data, most of which has been sourced from generally available NASA data.


  1. The 'Ultimate-Body' is the mass of collected universal matter of sufficient magnitude to overcome the coupling ratio and compromise the innermost neutrons �€“ releasing their stored energy: the 'Big-Bang'.
  2. After the 'Big-Bang', most of the Ultimate-Body's matter remained pretty much where it was previously. This matter is what has been referred to as the 'Great-Attractor'. Its magnetic (gravitational) attraction is slowing down universal expansion, which will eventually stop and eventually re-accrete and will once-again explode into another universal period.

Further Reading

You will find further reading on this subject in reference publications(67)