The compilation of formulas can be confusing, but if we concentrate on the units we need, and then apply suitable constants, the formula may appear automatically. Let me show you.

Let's say we're looking for a formula to give us the neutronic radius (Rₙ), which is a unit of distance (metres).

We know that the neutronic radius occurs as a result of the velocity of EME (c), and we also know that it is due to the potential energy between the two particles in a proton-electron pair; a proton and an electron, and this is how we can calculate its actual value:

Isaac Newton gave us a calculation method for the potential energy between two bodies.

PE = G.m₁.m₂/R; the units of which are Joules (kg.m²/s²)

and we know that the potential energy between a force-centre and its satellite in circular orbits is twice the satellite's kinetic energy:

PE = 2.KE = 2 . ½.m.v² = m.v²; the units for which are also Joules (kg.m²/s²).

therefore, this relationship must be correct;

m.c² = G.m₁.m₂/R

and because we are looking for the orbital radius;

R = G.m₁.m₂ / m₂.c² (= G.m₁/c²)

If we apply coincident values to the variables, say at the neutronic condition ...

Rₙ = G.mₑ.mₚ / mₑ.c² (= G.mₚ/c²)

G = 6.67359232004334E-11 m³ / kg.s²

mₑ = 9.1093897E-31 kg

mₚ = 1.67262163783E-27 kg

v = c = 2.99792459E+08 m/s

... the orbital radius may be calculated thus;

R = G.mₚ/c²

Rₙ = 6.67359232004334E-11 x 1.67262163783E-27 ÷ 2.99792459E+08² = **1.2419839246748E-54 m**,

however, this is the attraction due to *magnetic* charge (mass).

But the dominant attraction between a proton and its electron partner is *electrical* charge, so let's try Coulomb's approach;

k = 8.98755184732667E+09 kg.m³ / s².C²

e = 1.60217648753E-19 C

the relationship now looks like this;

mₑ.c² = k.e²/Rₙ

and the orbital radius may be found thus;

Rₙ = k.e² / mₑ.c²

which gives us the following orbital radius;

Rₙ = 8.98755184732667E+09 x 1.60217648753E-19² ÷ 9.1093897E-31 ÷ 2.99792459E+08² = **2.81793795383896E-15 m**.

Because electrical charge is the dominant cause of attraction in a proton-electron pair, this must be the orbital radius of an electron when travelling at velocity 'c'.

And the relationship between these two radii just happens to be ...

1.2419839246748E-54 ÷ 2.8179379538389600E-15 = 4.40742111792334E-40

… the coupling ratio!

But we could just as easily have derived the formula using the units of known constants.

Because we know that electrical charge is the dominant attraction in a proton-electron pair, we shall begin with Coulomb's constant; kg.m³ / s².C².

Don't forget, we are looking for a unit of distance (m), so we need to use constants containing kg, m, s & C;

let's assume the following;

kg; mₑ = 9.1093897E-31

(m/s)²; c² = 2.99792459E+08²

C; e = 1.60217648753E-19.

Now we need to isolate m;

kg.m³ / s².C² ÷ (kg x (m/s)² ÷ C²) = m.

Let's see if it works;

Rₙ = k ÷ (mₑ x c² ÷ e²)

Rₙ = 8.98755184732667E+09 ÷ (9.1093897E-31 x 2.99792459E+08² ÷ 1.60217648753E-19²) = **2.81793795383896E-15 m**

hey presto, it works!

Now let's try the ‘units’ approach to the heat transfer coefficient ‘X’, the units of which are K.s²/m²

First, we need to establish a temperature, the neutronic value for which is calculated like this;

Ṯₙ = PEₙ ÷ (K_{B}.Y) = (mₑ.c²) ÷ (KB.Y) = 623316124.717178 K.

So, the units we're looking for are;

K ÷ (m/s)².

Let's try Ṯₙ/c²;

X = 623316124.717178 ÷ 299792459² = **6.9353271647894E-09 K.s²/m²**

it works again!

And this approach works for any formula. Just keep trying with known constants of the correct units and coincident condition; you will always get the correct result because both your *values* and your *units* will always be correct.

This page has been recreated in video format in physics in three minutes

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