Keith Dixon-Roche (one of CalQlata's Contributors) asked himself the question; "does dark matter really exist?", given that a celestial *atmosphere* would have caused all celestial satellites to stop orbiting long ago. And he discovered that Isaac Newton actually told us that it doesn't 300 years ago. And in doing so, Keith also ...

... identified the properties and behaviour of the force-centre at the heart of our Milky Way, the total mass of the Milky Way and confirms his own predictions for collapsed stars.

Note: All the theories are provided by CalQlata's Laws of Motion and Planetary Spin

All the theories and calculations presented below are the sole copyright property of Keith Dixon-Roche © 2017

Keith Dixon-Roche is also responsible for all the other web pages on this site related to planetary motions.

The purpose of this paper is to determine an accurate description of the behaviour of our sun in the Milky Way by applying Isaac Newton's laws of motion and Keith Dixon-Roche's planetary spin theory and thereby discount the need for universal dark matter.

The dark matter referred to today by the scientific community is nothing more than a galactic force-centre. Since having discovered the mass and spin-rate of our own galactic force-centre, Keith Dixon-Roche has given it the name 'Hades' for easier reference.
A calculator is now available for you to prove it for yourself: Newton's Laws of Motion

99% of the world’s physicists believe that 85% of universal mass is dark matter, and that this dark matter comprises sub-atomic particles that cannot be seen, which is the reason it is called dark. This myth was first postulated by two physicists who believed that the Milky Way had no force-centre, simply because they couldn't see it.

However, the laws of orbital motion and planetary spin theory together provide all the evidence necessary to demonstrate that it does exist.

An accurate value for the mass of Hades may be established from the orbital properties of any of its satellites, e.g. our sun, from; m₁ = 2π / G.K = 1.76572E+41kg;

Its diameter is dependent upon is density, which is expected to be similar to all other planets; ≈>5000kg/m³. But because it is likely to comprise more iron than a conventional planet, it is estimated here to be 7870 kg/m³, giving it a diameter of 3.4993E+12m

planetary spin theory predicts its rate-of-rotation to be 3.6465E-07ᶜ/s based upon 100 billion equivalent suns in the Milky Way.

We can't see it simply because it is cold, i.e. dark, and that is because it is not in orbit.

Moreover, if dark matter did exist, it would act just like an atmosphere. I.e. it would gradually slow down all universal orbits, which we know doesn't happen!

Also, these very same scientists have replaced it with 'Black-Holes'. Why, therefore, should they still believe in it?

CalQlata can now confirm that dark matter does not exist because; a) **our orbits are not slowing down**, and; b) **there is no need for it**.

The only information required to establish Hades' properties is;

Our sun's orbital perigee and eccentricity; and,

The equivalent satellite population.

1) Use Newton's Laws of Orbital Motion to;

a) replicate the Sun's orbit in the Milky Way:

b) find the mass of the Milky-Way's galactic force-centre

2) Use Planetary Spin Theory to;

a) find the angular velocity of the Milky Way's force centre

Newton's constant of proportionality: K = t²/a³ = (2π)² / G.m

our sun's orbital;

period is: 230 million years (t = 7.258248E+15 s)

perigee is: Rᴾ = 2.4653729E+20 m

apogee is: Rᴬ = 2.54525098196E+20

half the major axis is: a = (Rᴾ+Rᴬ)/2 = 2.50531194098E+20 m

note; based upon an orbital eccentricity of 0.0167112

therefore;

K = 3.350257445997440E-30 s²/m³

Hades mass is; m = (2π)² / G.K = 1.76572E+41 kg

as all of its matter is the same as all other matter in the universe, its density should be about 5300 kg/m³

so Hades has a diameter of about; Ø = 3.992232235E+12 m

because it is cold, Hades 'Δ' is ≈1.0

You may change any of the above values you wish, but the outcome will be the same; it is self-evident that our Milky-Way galaxy has a cold dark force-centre that is simple to define.

The following Table provides the sun's orbital parameters according to Newton:

Sym. (units) | Formula | Result | Description |
---|---|---|---|

Force-Centre: | |||

G (m³/kg/s²) | Constants | 6.67359232E-11 | gravitational constant |

m₁ (kg) | Input | 1.76572019E+41 ⁽¹⁾ | mass |

Orbiting Body: | |||

m₂ (kg) | Input | 1.9885E+30 | mass |

r₂ (m) | Input | 6.9571E+08 | radius (of body) |

J (kg.m²) | ⅖.m₂.R₂² | 3.900081153490E+46 | polar moment of inertia |

Orbit Shape: | |||

T (s) | Input | 7.258248E+15 ⁽²⁾ | orbit period |

a (m) | ³√[G.m₁ / (2.π/T)²] | 2.505311941E+20 | major semi-axis |

b (m) | √[a².(1-e²)] | 2.504993572E+20 | minor semi-axis |

e | [-R̂ + √(R̂² - 4.a.{R̂-a})] | 0.015941744 | eccentricity |

p (m) | a.(1-e²) | 2.504675243E+20 | half-parameter |

ƒ (m) | a.(1-e) | 2.465372900E+20 | focus distance from Perigee |

x' (m) | a-ƒ | 3.993904106E+18 | focus distance from ellipse centre |

L (m) | π . √[ 2.(a²+b²) - (a-b)² / 2.2 ] | 1.574033901E+21 | ellipse circumference |

K (s²/m³) | (2.π)² / G.m₁ | 3.350257446E-30 | factor |

A (m²) | π.a.b | 1.971597673E+41 | orbit total area |

Orbital Properties at Perihelion or Perigee: | |||

R̂ (m) | Input | 2.465372900E+20 ⁽³⁾ | distance from force centre to body |

F̌ (N) | G.m₁.m₂ / R̂² | 3.8551556343E+20 ⁽⁴⁾ | centripetal force on orbiting body |

F̌c (N) | m₂.v̌²/R̂ . ƒ/p © | 3.9166135377E+20 ⁽⁴⁾ | centrifugal force on orbiting body |

g (m/s²) | -G.m₁ / R̂² | -1.9387254887E-10 | gravitational acceleration on body |

v̌ (m/s) | h / R̂ | 2.2036056214E+05 | body velocity |

h (m²/s) | √[F.p.R̂² / m₂] | 5.4327095813E+25 | Newton's motion constant |

PE (J) | m₂.g.R̂ | -9.5043962261E+40 | potential energy |

KE (J) | ½.m₂.v̌² | 4.8279564378E+40 | kinetic energy |

E (J) | PE+KE | -4.6764397883E+40 | total energy |

Orbital Properties at Aphelion or Apogee: | |||

Ř (m) | x' + a | 2.54525E+20 ⁽⁵⁾ | distance from force centre to body |

Ř (m) | (E - ½.m₂.v̌²) / m₂.g | 2.54525E+20 ⁽⁵⁾ | distance from force centre to body |

F̂ (N) | G.m₁.m₂ / Ř² | 3.616978470E+20 ⁽⁶⁾ | centripetal force on orbiting body |

F̂c (N) | m₂.v̂²/Ř . p/ƒ © | 3.616059254E+20 ⁽⁶⁾ | centrifugal force on orbiting body |

g (m/s²) | -G.m₁ / Ř² | -1.81895E-10 | gravitational acceleration on body |

v̂ (m/s) | h / Ř | 213444.9459 | body velocity |

h (m²/s) | h | 5.4327095813E+25 | Newton's motion constant |

PE (J) | m₂.g.Ř | -9.2061180022E+40 | potential energy |

KE (J) | E-PE | 4.5296782139E+40 | kinetic energy |

E (J) | E | -4.6764397883E+40 | total energy |

Table 1: Calculations for the Sun's orbit1) The mass necessary for the orbital period of the sun and its distance from its force-centre at its perigee 2) Taken from NASA 3) This value gives zero error, NASA specifies 1.0E+21 4) Must be equal to each other for calculations to be correct 5) Must be equal to each other for calculations to be correct 6) Must be equal to each other for calculations to be correct |

The following Table provides the calculation sequence for Hades' angular velocity according to planetary spin theory:

Property | Formula | result | comment |
---|---|---|---|

JH (kg.m²) | ⅖.m₁.(Δ.r)² | 2.814190398E+65 | Polar moment of inertia of Hades |

E₀ (J) | ½.J.ωₒ² | 0 | Orbital spin energy of Hades |

E₁ (J) | δKE . (r/R)² | 0 | Spin energy induced by a force-centre |

E₂ (J) | E₁-E₀-E₃ | -4.378161565E+51 | Spin energy in Hades |

E₃ (ᶜ/s) | Σ(KEᴾ + PEᴬ) . Sign[Cos(θ)] | 4.378161565E+51 | Spin energy generated by all Hades' satellites |

ω₂ (ᶜ/s) | √[2.E₂ / J₂] | 1.76394139222867E-07 | Angular velocity of Hades |

Table 2: Hades' angular velocity (based upon a satellite population of 100bn)The authour of this paper consider's a Milky-Way population of 10bn more realistic figure than the 100bn used in the above calculations. 10bn stars in the Milky-Way would induce an angular velocity of 5.5781E-08 ᶜ/s in Hades. |

'Dark Matter' was proposed early in the 20th century by a couple of physicists (Fritz Zwicky & Jacobus Kapteyn) simply because they ...

a) ... didn't believe there was anything at the centre of our galaxy because they couldn't see anything there, and;

b) ... claimed that Newton's laws of orbital motion predicted that the Milky Way’s stars should be thrown into outer space because of centrifugal force.

However, they should have realised that there *must* be a mass at the centre of every spiral galaxy because that is how orbits work.

I.e. we know that Hades *must* exist because it is a fundamental law of nature that every orbital system must have a force-centre ('m₁').

That these physicists omitted the force-centre from their calculations is no doubt the reason for their confusion and therefore the reason they invented dark matter to solve their problem.

However, they should have realised that, according to Isaac Newton's laws of orbital motion, dark matter could not possibly account for the gravitational force required to keep galactic satellites in orbit.

So, dark matter was invented by two scientists that didn’t understand Newton's laws of orbital motion.

Why can’t we see Hades?

Hades has no force-centre of its own, so it cannot generate heat energy (through internal friction). It is therefore cold and emits almost no electro-magnetic radiation; so it is dark.

However, we can predict its principal properties simply from the orbital properties of our own sun (see calculations)

It has a diameter of ≈3.5E+12m,

whilst our Milky Way has a major axis of ≈1E+21m

the ratio being; 3.5E-09

So, it would be like looking for a dark atom in the centre of a 1m diameter disc of black-iron.

That’s why you can’t see it.

But it is there, and it is the primary source of the heat energy generated in all its orbiting stars.

What is even more confusing; almost all scientists still believe in the existence of dark matter despite having removed its justification with the invention of 'Black-Holes'.

'Dark Matter' must - by definition - possess mass, just like an atmosphere possesses mass. Anything travelling through an atmosphere will slow down unless it is independently re-energised (fueled). So, if dark matter did exist, all of the universe's satellites would have ceased orbiting long ago. But they haven't. Therefore dark matter cannot exist - fait accompli.

- Refer to Table 1. The density of iron is used for this calculation as an example. It is expected that the actual density of the Milky Way's force-centre is similar to all other matter in the universe.

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