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 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 planetary motions

A 'pdf' version of this paper can be found at: Dark Matter - The Paper

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.

CalQlata can now confirm that dark matter does not exist simply by proving that there is no need for it.

The only part of the Milky Way required to establish the behaviour of the sun within it is the sun itself along with its own orbiting bodies and its force-centre. This has been demonstrated by Isaac Newton and the author's own planetary spin theory.

1) Use Newton's theories to replicate the Sun's orbit in the Milky Way:

a) Verify the density of the force-centre

b) Correlate Newton's gravitational force with the Sun's centrfugal force

2) Use Planetary Spin Theory to:

a) Calculate the angular velocity of the Milky Way's force centre for 250 billion orbiting solar masses

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 |

Body 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 |

Body 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 sun's angular velocity according to the author's planetary spin theory {FC stands for the force-centre of the Milky Way}:

ρ₁ (kg/m³) | Input | 7870⁽¹⁾ | FC density |
---|---|---|---|

JFC (kg.m²) | ⅖.m₁.(3.m₁ / 4.π.ρ₁)²/³ | 2.1621587048E+65 | Polar moment of inertia of the FC |

KE (J) | ½.(KETa + KETp) | 1.989651235897E+35 | Average kinetic energy of the sun's orbitals |

ωᵢ⁽⁵⁾ (ᶜ/s) | (2.KE / J)⁰˙⁵ | 2.865329084572E-06 | Angular velocity of the Sun due to orbitals |

J (kg.m²) | ⅖.m₂.(Δ.R)² | 3.900081153490E+46 | polar moment of inertia of the Sun |

ES (J) | ½.J.ωₒ² | 1.461301327544E+16 | Spin energy generated by the orbiting Sun |

ωₒ (ᶜ/s) | 2.π / T | 8.656614250684E-16 | Angular velocity of orbiting Sun |

EFC (J) | ½.(PETa + PETp) | -1.490043768819E+42 | FC ave. energy that induces spin in the Sun |

ωᵣ (ᶜ/s) | (2.EFC / JFC)⁰˙⁵ | 1.166416422318E-13 | FC induced angular velocity |

ω (ᶜ/s) | ωᵢ + ωₒ + ωᵣ | 2.865329084572E-06 | Calculated angular velocity of the Sun |

ωₐ (ᶜ/s) | 2.865329084572E-06 | Actual angular velocity of the Sun | |

error | 1 - ω/ωₐ | 0.0000000 ⁽⁵⁾ | |

Table 2: Calculations for the Sun's angular velocity |

**The number of Stars in the Milky Way** (Planetary Spin Theory)

m = 1.7657E+41 kg (the mass of Milky Way's force-centre)

ρ = 7870 kg/m³ (density of Milky Way's force-centre ⁽¹⁾)

R = (3.m / 4.π.ρ)⅓ = 1.7496567118E+12 m (radius of Milky Way's force-centre)

J = ⅖.m.R² = 2.1621587048E+65 kg.m² (moment of angular inertia of Milky Way's force-centre)

KEp = 4.8279564378E+40 J (kinetic energy of the sun at its perigee)

PEₐ = -9.2061180022E+40 J (gravitational energy of the sun at its apogee)

KEsun = KEₐ - PEp = 1.4034074440E+41 J (KE of the sun used to rotate Milky Way's force-centre)

KEFC = ½.J.ω₁² = 1.4375071338E+52 J (rotational KE in Milky Way's force-centre)

N = KEFC / KEsun = 1.02429E+11

(number of {our} solar systems needed to rotate Milky Way's force-centre)

ωFC = √[2.KEFC / J] = 2.0124E-07 ᶜ/s (actual angular velocity of the Milky Way's force-centre)

'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.

- 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 somewhere between the the earth's density and less than that of iron.

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