Dark Matter - Gravo-Dynamic Force

Laszlo I. Orban & Laszlo T. Orban

Astronomic measurements shows that the stars situated at the margins of the galaxies are moving at a higher speed than the circumferential speed that would result from the mass of these galaxies.   This can be observed even in much larger scales, at galaxy clusters. Where it was determined that the galaxy cluster’s elements are moving at a faster speed than what belongs to the circumferential speed corresponding to the gravific mass of the galaxy cluster.  An assumed explanation for this phenomenon is that beside the visible matter, the 2/3 part of the Universe is filled up of such matter that only gravific effects manifest in cosmic movement of matter. The nature of “Dark Matter” is the fundamental question in modern astrophysics.

However, the gravitational effect of “Dark Matter” could be eliminated assuming that between the streams of matter, such gravo-dynamic forces appears that is similar to Lorentz’s electrodynamic force. This force in case of same stream directions it attracts, and in case of contrary stream directions it repels. Generally, a body of mass   m₁   with a velocity   v₁   on a body of mass   m₂   with a velocity   v₂   has a force   F_1,2   that the following connection provides:

F_{1, 2} = (G_d∙m₁∙m₂∙r ^-3_{1, 2}) v₂ x (v₁ x r_{1, 2})

Here, r_{1, 2} is the position vector oriented from m₁ to m₂. The dimension of G_d gravodynamic constant is kg ^-1m. Presumably, the numeric value of G_d gravodynamic constant is so small that in case of earth’s streams of matter the gravodynamic force is negligible and only the cosmic sized movements can be observed. The possible explanation for the gravodynamic force can be found in the study which’s located at http://members.shaw.ca/laszlo.o/....
G_d’s numeric value can be estimated, if we presume that excess velocity of the Milky Way’s peripheral stars are caused by the attraction effects of the gravodynamic forces’ sum resulting from the moving perceptible matter and not from the “Dark Matter’s” attracting effect.

Presuming in the first approximation that all stars of Galaxy of masses M are placed on a circular plain disk with a radius of R₀≈3.78 ∙ 10²¹m with a uniform density ( ρ=M/π R₀² ).

The Milky Way’s circulational periodic time T=240 million year that has an angular velocity of ω=2 π/T≈8.3 ∙ 10^-16rad ∙ s^-1. For the easier calculation let the star be m mass on the x axle the distance of R₀ from the centre of Galaxy (0) and be moving at the velocity of v=R₀ ∙ ω (Fig. 1.). The part of matter with the mass dm and with speed v₁=r₁∙ ω will have a gravodynamic affection of

dF = G_d ∙ m∙ρ∙ds∙r^-3∙ v x (v₁ x r)

on the star of m mass and v velocity.

Based on fig.1 the x and y components of vectors are the following: v_x=0; v_y=R₀ ∙ ω; v_1x=-r₁∙ ω ∙ sin a; v_1y = r₁ ∙ ω ∙ cos a; r_x = R₀-r₁∙ cos a; r_y = -r₁ ∙ sin a. After the completion of the three-vector multiplication, we will have a vector with the module |v_x x (v₁ x r)| = r₁ ∙ R₀ ∙ ω² ∙ (r₁ – R₀ ∙ cos a). This vector falls in the x axis and points towards the centre of Galaxy:

dF   =   Gd . p . R0 . w^2 .	r1 . ( r1   -   R0 . cos a ) . ds
	( R0^2   -   2 . r1 . R0 . cos a + r1^2)^3/2

Thus, the sum of the gravo-dynamic forces provided by all the “elements” of the Galaxy on the peripheral star with the mass “m” and velocity v are the following:

Thus:

|F| = G_d ∙ m ∙ ρ ∙ R₀ ∙ ω² ∙ I

Here, l ≈ 1.2 ∙ 10¹⁶ m means the average star distance in the Galaxy while I is the approximate value of the integral.

This force substitutes the F_g force that’s assigned to Galactic “Dark Matter” referenced to the peripheral star with m mass. Based on observations the hypothetic dark matter’s M_g mass is 2/3^rd of the whole M_tot mass, while the visible galactic matter is only 1/3^rd. This way M_g = 2M so:

F_g = G ∙ M_g ∙ m ∙ R₀^-2 = G ∙ 2M ∙ m ∙ R₀^-2 (G = gravitational constant)

Equalizing the two forces will result:

G_d ∙ ρ ∙ R₀ ∙ ω² ∙ I ∙ m = G ∙ 2M ∙ m ∙ R₀^-2

Substituting the value of ρ = M/ π R₀² after simplification:

The approximate value of I is I≈1.2669 ∙ 10²² m so G_d ≈ 1.27 ∙ 10^-23 kg^-1m. The dimensions of G_d are corresponding with the dimensions of the expression G/c² (c = speed of light). This fact refers to the deep structure of gravodynamic force. In the study: http://members.shaw.ca/laszlo.o/.... based on another hypothesis, for the expression of gravodynamic constant derived:

Here m_e = 9.1 ∙ 10^-31 kg, this is the mass of electron; m_k = 3 ∙ 10^-35 kg is the mass of neutrino while G is 6.67 ∙ 10^-11 kg^-1m³s^-2 and finally c = 3 ∙ 10⁸ ms^-1

So after substituting these values we’ll have G_d = 1.59 ∙ 10^-23 kg^-1m. The G_d values resulted from two different ways differentiate little from each other. This fact confirms the reality of hypothesizes.

It is presumed that the complicated movement of Galaxy clusters’ excess speed is not produced by the undetectable “Dark Matter”, but the gravodynamic forces.

The important part of astrophysical researches is constituted of the determination of the exact value of G_d with the help of more detailed models and modern computer technologies.