Journal Of Theoretical And Computational Physics

ISSN: 2832-2746

Volume No: 1 Issue No: 2

Abstract

Gravity  Field ( Low Frequency) in Sun  system is described  by analogy to  description of Atom system . The system of electron-proton in Atom is explained  by  theory of new axioms and laws[ 10]. The theory of new axioms and laws  is published by the same author[ 2,6,8,9].It  describes nonparametric and nonlinear processes and contains 2 new axioms and 8 new laws. Unlike Classical field theory, it describes  longitudinal or transverse non-uniform motions which are accelerating or decelerating. According to the Axiom1 every unevenly rotation  of one vector forms open vortex which can be transverse or longitudinal and accelerating or decelerating .It is well known that there is analogy between the electrons and  an planets including the planet Earth.  According the Law1  the model of the  electron  or the Earth  represents a decelerating transverse  vortex swirling into a plane in 2D  and  generating in its center  accelerating longitudinal Gravity Funnel  in 3D ,perpendicular to the same plane. Because of positive acceleration  in center the accelerating longitudinal Gravity  vectors   form the  accelerating Gravity Field  in-up. Because of  resistance  of environment   outside   in periphery   is formed   Back wave  or decelerating  Gravity vortex  that passes   outside the body of Earth and embraces it like a cocoon. According Axiom2  by analogy to electron-proton ,   the reason for the creation of  internal planets   is the Sun. More precisely- the reason is a specific  longitudinal  vortex  in 3D coming from  outside to the   third cylindrical   resonator   in the volume of the Sun. It generates  a Low Frequency  transverse vortex  in the third in a row cylindrical resonator  in Sun that corresponds to Earth.  According  Law2  the proton  is generated  as accelerating transverse vortex from center of  sphere  of atom  .The cylindrical resonator  inside the Sun generates an accelerating transverse vortex with an amplitude proportional to the width of the third cylinder. This transverse  vortex in 2D   is launched to the space  in direction to the Earth. Due to the friction later it decelerates and according to  Law1   it  is rolled up   as  a decelerating transverse vortex  and  in this way  it generates  the  body of Earth. According Law5  decelerating vortex emits decelerating secondary  cross vortices from itself . The similar is a  decelerating  transverse vortex generates Earth from  periphery  to the center .It emits energy  from surface ( periphery)  to inside (center) and warm the center of the Earth. That is why  the surface   of Earth is cool ,but the center of Earth is hot and empty . According Law6   the accelerating   vortex  sucks  accelerating cross vortices to  itself . The similar is a  super accelerated longitudinal  central   vortex  in  the 3D   funnel along the   y- axe of the Sun .It sucks energy from center of Sun  and  cool  it down. That is why  the  center of Sun is cool  .At the same time the outermost longitudinal vortices in the 3D funnel become slower  and more powerful. They begin  to rotate faster and faster the denser plasma in 2D  in the transverse direction (perpendicular to the funnel in 3D). In this way they accelerate  themselves  transverse  from center to periphery  That is why  in   the  periphery the transverse vortex  is extremely accelerated and  hot .The acceleration of the  Sun beams  in surface of Sun is so huge  that they radiate  huge temperature from  surface .The described algorithm only applies to the inner solid planets. For the outer gas planets, the  algorithm is orthogonal  and will be described  further.

1. Introduction

From the planetary model of Rutherford  it is known that there is analogy between the  structure of the solar system and the atom . By analogy - the electrons and  the internal planets   are similar .Gravitational  body ,for example as  a proton is similar the  transverse vortex  in the corresponding of a cylindrical  resonator inside the Sun. Gravitational  body, for example as  the electron is similar an  inner solid planet corresponding  to  its  resonator inside the Sun. Part of these phenomena will be described in the current report.

2.The Classic Axiom .The new Axiom1 and Axiom2

The Classic Axiom in the Theory of the Electromagnetic Field certifies Maxwell’s laws (1864) [1]. It postulates that the movement of an electric vector E in a closed loop is evenly:

div(rot E) = 0,                                   1.

where (rot E) is the movement of the vector E in a closed loop; div (rot E) is the divergence      (the variation in increase or decrease) of the vector E during its moving in a closed loop(rot E)

It is obviously that the movement of the vector E in a closed loop (rot E) with zero divergence (variation) of the vector E is equivalent to evenly movement or to movement with constant velocity V[1] . The   disadvantage of Classic Axiom (1)  is that it  does not describe movements in an open loop (or a vortex) or movements with a non-constant  or variable velocity V.

The New Axiom1 for rotor and for vortex (vor)

The New Axiom1 describes  the movements in an open loop or  in a vortex with a non-constant  ( variable )velocity V of vector E [2 ].

div (rot E) ≠ 0 ,                                                     2.

Definition: div (VorE) ≠ 0  for vector E in 2D ( in plane)   is named  transverse (cross) vortex.      

                 div (VorH) ≠ 0 for vector H in3D(in volume) is named  longitudinal vortex .

Definition: An unevenly cross vortex (E2D) is an unevenly vortex (E) spinning transversally in a 2D plain. The transverse open vortex in 2D is designated as  Vor E2D  (Figure 1c).

Definition: An unevenly longitudinal vortex (H3D) is an unevenly vortex (H) spinning in the volume of 3D. The longitudinal open vortex in 3D is designated as   Vor H3D  (Figure 1d).

The definitions for natural unevenly vortices  ignore the thickness of the vortex itself ( cross in 2D or longitudinal in 3D ).

It exists a vortex div (VotE) ≠ 0  as an  open loop (div (rotE) ≠ 0) in 2D . It exists a vortex     div (VotH) ≠ 0  as an  open loop (div (rotH) ≠ 0) in 3D  or:

div (VorE2D) ≠ 0   , div (VorH3D) ≠ 0.                    3.

The  existence of an open loop   means that  it can exists   a decelerating or an accelerating vortex in 2D  or in 3D:

 div (VorE2D) <0;     div (VorE2D)> 0;                         4.

 div (VorH3D) <0;     div (VorH3D)> 0.                          

Axiom 1.The moving  of  a vector  with  monotone-decreasing or monotone-increasing velocity becomes along an open vortex.                                    5.


Consequence : ( of variation of moving ):


We immediately received 4 types of movements – transverse (4a), which can be accelerated or decelerating  and longitudinal (4b) , which can also be accelerated or decelerating.            Therefore there are 4 types of vortices : a  transverse vortex in 2D (E2D)  that can be accelerated (E2D +)  or decelerated  (E2D - ) (Figure1c) and  a  longitudinal vortex in 3D (H3D) that can also be accelerated (H3D +)  or decelerated  (H3D -) (Figure1d) [2] .


Consequence : (of visual perception):


It is known that light  is spreading crosswise and  the cross vortex  reflect the light rays. Therefore an external observer will perceive the image of the transverse vortex. Thus  the cross vortex is well visible for an external observer. But the thread of the longitudinal vortex does not reflect the light. The reason is that the light crosses the thread of longitudinal vortex ,  surrounds   the thread, and continue its path without reflecting the longitudinal vortex. So the light   forms diffraction around the thread Therefore, the longitudinal vortex is invisible to an external observer [6] .

Consequence :( eccentric vortex ,vortex turns to a dipole).


The open vortex turns from concentric to eccentric vortex or to  dipole. The reason is in  the acceleration of velocity. For example, in decelerating vortex:  E1> E3 .Therafore the Geometric Center will aim to move to the bigger vector E1( to up). At the same time : E2> E4.

Therefore   the Geometric Center will aim to move to the larger vector E2( to the left).  Therefore, the Geometric Center will move to Gravity center ,or it moves to second quadrant (Figure1b) [8].


Consequence : (of complex vector)


The vector E is not a simple but complex vector. .When E2 = V + iA, the velocity V is reason,   the amplitude A is result (Figure1e).When E1 = A + iV,the amplitude A is reason ,the  velocity V  is result (Figure1f) [9].


Definition:The objects  with this vectors( E1 = A + iV ,E2 = V + iA)  are called  complementary  vortices or complementary pairs .


Figure 1.The  new Axiom1 ,Axiom2 and Law1,Law2,Law5, Law6



Axiom 2 . A pair of complementary vortices forms a  resonance  system .


Because one object pushes (E1 = A + iV) (Figure1h), the other- should be pulls (E2 = V+ iA ) (Figure1j)    (or inversely ) .So they form a pair of complementary objects. Something more, because of  one object pushes and the other  pulls, the both of them are active generators [8] .

Consequence : There is no energy losses in the pair of open complementary vortices. The reason is that the both of them are active.


For comparison in the Electromagnetic Field, the electrical circuit   contains one generator element and one or several passive consumers.They only  transform  energy from one view (kinetic) to the other view (potential).


Consequence: Pair of complementary objects (E1=A+iV,E2 = V + iA) exists at the same time.

Consequence:    Pair of complementary objects (E1 = A + iV , E2 = V + iA ) is connected by a links (1,2) in one  and the same direction (Figure 1g,h).

The link 1 transports energy by longitudinal vortex from accelerating object (proton-Sun) (Figure1h) to decelerating object (electron-Earth) (Figure1g). The link 2 is Back link and  it transports  many cross vortices that emit from transverse  vortex of decelerating object (electron-Earth) , which is strongly decelerating  in center, towards  the accelerating transverse vortex(proton -Sun) which sucks  them (Figure1g,h).

Consequence : There are two opposite directions of impact of  complementary pair: 

 (E1 = A + iV, E2 = V + iA) and (-E1= -A – iV , -E2 = -V - iA).

In straight direction : For proton:(E1 = A + iV)  amplitude (A) is the  reason (Figure1h) but the speed (V) is the result   .For electron: the velocity (V) (E2 = V + iA) is the reason but the amplitude (A) is the result  (Figure1g). An example of such straight direction  is the proton-electron and resonator  inside the Sun-Earth.

In the opposite direction:  For antiproton: (-E1=-A - iV)  amplitude (-A) can be the  reason but the speed (-V) is the result  .For positron:  the velocity (-V) (-E2 = -V - iA)  can be the cause and the amplitude (A) is the result [9] . An example of such opposite direction  is the antiproton-positron  and resonator  inside the Sun- Venus.

                                                                                                  

3. Law1 forms the electron and the planet Earth from outside , Law2 forms the proton and the star Sun from outside

Law 1 : The open cross vortex (E2D)  generates  (inward or outward) an open longitudinal vortex (Н3D) in its center through a cross-longitudinal transformation Δ1:

                   Δ1

           Vor (E2D)  => - Vor (Н3D),                                         6.

where Vor (for Vortex, meaning an unevenly vortex)  which replaces rot ( rotor, meaning closed loop) [8].

Therefore the cross vortex in 2D (E2D) continues its development in 3D as a longitudinal vortex (Н3D) (Figure1g ).While Maxwell’s Law     states that vector E generates vector H, the present law (6) postulates that the cross vortex Vor (E2D) of E in 2D generates a longitudinal vortex Vor (H3D) of H in 3D. The sign (-) for Vor (H3D) 3D means that E2D and H3D have opposite dynamics .For example when div (Vor E2D) < 0 (is decelerated) , div(Vor H3D) > 0   (is accelerated).

Consequence:  The open  cross vortex (E2D ) generates  inward (Δ1in) an  open longitudinal vortex (Н 3D) outward . This action takes place from the center of the cross vortex (E 2D)  through a  cross-longitudinal transformation Δ1:

                           Δ1in

                     Vor (E 2D) => -Vor (H 3D) .                                                    6a.

The   Consequence  (6a) of Law1 describes in 2D the model of electron (e-) as  the transverse    vortex   inward  in  the chain  of proton-electrons ( Figure 1h-Figure 1g).

Result by analogy : As analogy to the electron are planet Mercury, Earth (Figure2), Mars(Figure4)  without the  second planet Venus (Figure 3).

Result by analogy : The chain from  proton-electron has analogy to the chain from the first cylindrical resonator inside Sun and planet Mercury, third cylindrical resonator inside Sun and planet Earth (Figure 2a, b,c) and fourth cylindrical resonator inside Sun and planet Mars (Figure 4c,d,e).

Consequence:  The open  cross vortex (E 2D ) generates  outward (Δ1out ) an  open longitudinal vortex (Н 3D) inward . This action takes place from the center of the cross vortex (E 2D)  through a  cross-longitudinal transformation Δ1:

                       Δ1out

                     Vor (E 2D) => Vor (H 3D) .                                                      6b.

The Consequence (6b) of Law1  describes in 2D   the  model of positron (e+) as  the transverse   vortex  outward     in  the chain  of antiproton-positron ( not shown in figure).

Result by analogy : As analogy to the positron is a second planet Venus (Figure 3a,c).

Consequence: The open  decelerating cross vortex (E2D -) generates inward (Δ1in )  an open accelerating longitudinal vortex (Н3D+)  outward .This action takes place from the center of decelerating cross vortex (E2D-)  through a particular cross-longitudinal transformation Δ1in:

                          Δ1in

                Vor (E 2D-) => Vor (H 3D + ) .                                                6c.

The Consequence  (6a) of Law1  describes in 2D   the  model of electron  (e-) as  the decelerating  inward  vortex ( dec(e-) (Figure1g)  in  the chain  of proton-electron (Figure 1h - Figure 1g) . Every electron (dec(e-) of this type look likes to :” expanded  cross vortex and a shortened longitudinal vortex”.

Result: The generation of a maximally inflated transverse vortex in electron is due to maximum negative deceleration (-amax ) of the input vortex  in electron from the outside to the inside   (div Vor E  < 0 )  =  (-amax )( Axiom1).

Result : The greater negative acceleration (- amax ) of the one orthogonal element (electron) is due to  the greater the positive acceleration (+ amax ) of the second orthogonal element (proton)(Axiom2) . Therefore between this two orthogonal elements (electron-proton) forms some kind of parabola  with  a greater  distance (D) .  It follows that the repulsive force: (Frepuls e~ amax  . mfluid  ) is greater, and the distance (D) between the two orthogonal elements is greater ( Dmax ~ Fmax . T )  ,where the sighn ( ~ ) means  right proportionally .

Result : The greater the negative  acceleration of the transverse vortex(-amax ), the larger the diameter (dmax ) of this vortex in 2D and the smaller the perpendicular vector (hmin ) in  3D (Law1).

Result: Because distance (D) is greater this type of  electrons ( dec(e-) : ” expanded  cross vortex and a shortened longitudinal vortex” are located in outer orbits.

Result by analogy: By analogy with the planets :  the expanded planets with shorten  perpendicular longitudinal vortex are located in outer  orbits.

For example: The planet Earth  is an example of an expanded  planet inouter orbit.

-The planet Earth is generated  by an expanded transverse vortex(dec(e-)in 2D and has as a result an shortened longitudinal vortex in 3D.This decelerating transverse vortex(dec(e-)is generated in cylindrical resonator inside the Sun as an accelerating transverse vortex(acc(p+) .

-Due to the bigger radius of the third cylindrical resonator, the transverse vortex is longer and is  coiled in  more rotations .In output it forms longer parabola and longer distance (D) which keeps the planet Earth at an outer orbit.

- Something more – the planet Earth has the most privileged position of all the inner planets. Because of the Earth is the third planet in a row, it corresponds to the third cylindrical  resonator  inside the Sun . But the third cylindrical  resonator   has the maximum volume. That is why and planet Earth has the maximum volume  and maximum  density in comparison with other inner solid planets.

-The maximum volume of the third resonator inside the Sun means the maximum  power of transverse vortex (acc(p+) .The maximum power   cause the maximum acceleration  and  respectively maximum  eccentricity  in cylindrical resonator  (Fg ) inside  the Sun  .

-According to Axiom 2, the planet Earth is an orthogonal object of the Sun. Therefore, in the third resonator inside the Sun, the maximum   expanded  and inflated   a transverse vortex is generated  which is shot from Sun to  the  spherical resonator of the Earth . This fact leads to maximum eccentricity and maximum vector  and of eccentricity (F g,max  ) inside the Earth (Figure1b ).

-As a result of maximum vector of eccentricity( Fg, max   ) inside the resonator of the Earth,  the maximum component of the Fg,max   on the   x-axis is obtained. This x-axis component  keeps the Earth's mass at the possible maximum distance (D)  to the Sun( Figure g,h) [10 ]. 

-Due to the decomposition of the eccentricity vector along the y axis ,the maximum component of the Fgmax on the y-axis rotates the planet Earth with maximum orbital speed [10].  

-According to the  Law5 the decelerating  transverse vortex with  maximum deceleration        (-amax ) emits to  inside the secondary cross vortices with maximum amplitude (+Wmax). .Since these emitted  secondary vortices are also  decelerated, they are curved from right to left. Therefore  they rotate the Earth around its axis from right to left with maximum speed. The direction of rotation is determined by an independent observer looking against the direction of the longitudinal vortex - from top to bottom [3,10].

Consequence:  The opened accelerating cross vortex (E 2D+) generates  inward (Δ1in ) an opened decelerating longitudinal vortex (Н 3D-) outward . This action takes place from the center of accelerating cross vortex (E 2D+)  through a  cross-longitudinal transformation Δ1+:

                                        Δ1in

                     Vor (E 2D+) => Vor (H 3D-) .                                                    6d. 

 The   Consequence  (6b) of Law1  describes in 2D   the  model of electron  (e-) as  the accelerating  inward  vortex  (acc(e-)  (Figure 1g)   in  the chain  of proton-electron          (Figure 1h - Figure 1g) . 

Result: The Consequence  (6a) and   (6b)  describe decelerating or accelerating cross vortex  to inwards .We immediately obtain 2 types of electrons: ( dec(e-)) and (acc(e-))  that look likes to ” expanded transverse vortex and a shortened longitudinal vortex” and   “shrunken transverse vortex and  longer  longitudinal vortex.

Result : The less the negative  acceleration of the transverse vortex(-amin) the less the diameter (dmin) of this vortex in 2D and the elongated  perpendicular vector (hmax ) in  3D (Law1).

Result: The second  type of electron (acc(e-) look likes to: “shrunken cross vortex and  longer  longitudinal vortex“. This type of shrunken electrons are located in inner orbits (Dmin ).

Result by analogy : By analogy with the planets - the shrunken planets with elongated longitudinal vortex are located in inner orbits.

For example: The planet Mercury is an example of a shrunken planet generated by a shrunken transverse vortex and an elongated longitudinal vortex in the innermost (first) cylindrical resonator in the Sun. Due to the minimal radius(dmin ) of the cylindrical resonator, the transverse vortex has a minimum transverse acceleration(-amin) that keeps the planet Mercury at a minimum distance (Dmin ).

Law 2: The opened longitudinal vortex (H3D) generates (inward or outward)  an opened cross vortex (E2D) in its center through a longitudinal-cross transformation Δ2:

                  Δ2

              Vor (H3D) => - Vor (E2D)                                                   7.



Consequence : The open  longitudinal vortex (H 3D ) inward (Δ2in) generates  an open  transverse vortex (E 2D) outward .This action takes place in the center of  cross vortex (E 2D)  through a particular longitudinal-cross transformation Δ2in:

                              Δ2in

  Vor (H 3D ) => -Vor (E 2D_).                                                7a.

The Consequence (7a) of Law2  describes in 2D   the  model of proton(p +) as  the  transverse  outward   vortex  in  the chain  of proton-electron (Figure 1h - Figure 1g ).

Result by analogy: As analogy to the  proton   are the first ,third and fourth cylindrical  resonators  inside  the Sun . They rule planets  Mercury ,Earth and Mars (Figure 2 ).

Consequence : The open  longitudinal vortex (H 3D ) outward (Δ2out) generates  an open  cross vortex (E 2D) inward .This action takes place in the center of  cross vortex (E 2D)  through a particular longitudinal-cross transformation Δ2out:

                               Δ2out

  Vor (H 3D ) => -Vor (E 2D_).                                                7b.

The Consequence (7b) of Law2  describes in 2D   the  model of  antiproton(p-) as  the transverse  inward   vortex in  the chain  of antiproton-positron (not shown in figure ).

Result by analogy: As analogy to the antiproton   is a second  resonator  inside  the Sun . 

It rules the second  planet Venus  as positron (Figure 3c ).

Result by analogy: The chain from  antiproton-positron has analogy to the chain from the second cylindrical resonator inside Sun and  planet Venus (Figure 3a, b,c).

Consequence: In accordance with   the outermost electrons (Law1),the outermost protons, are inflated  protons  ( dec (p+))(Law2) .They also are  extremely  eccentric and highly polarized.

Consequence:  In accordance with  the innermost electrons(Law1) , the innermost protons, are shrank protons(acc (p+))(Law2).They are not   eccentric and they are  zero polarized.

Conclusions: The outermost layers of  atomic nucleus consist of inflated protons (dec (p+))which are  extremely  eccentric and highly polarized  .They control the outermost electrons, which are also inflated  electrons (dec (e-))  .They are also extremely  eccentric and highly polarized.  The innermost layers of of  atomic nucleus  consist of  shrunken protons (acc (p+))  . They control electrons from the innermost orbits (acc (e-) that are contracted and  are not  eccentric and polarized [10 ].

Result by analogy :The innermost first  resonator inside Sun corresponds to generator of Mercury. That is way this first cylindrical resonator  is a model of shrunken proton (acc (p+)). Therefore  planet Mercury is a model of shrunken electron  (acc (e-) . Because Mercury  is not eccentric and polarized  , its y-axe  is exactly perpendicular and has no slope. That is way it rotates  around Sun synchronously .

Result by analogy: The third resonator inside Sun  is more outer resonator .It corresponds to the  generator of Earth. That is way this third cylindrical resonator  is a model of expanded proton (dec (p+)). Therefore  planet Earth is a model of expanded electron  (dec (e-) . Because Earth   is  outer planet it is more  eccentric and polarized  and its y-axe  is not perpendicular and has any slope (23deg.). That is way it has not   synchronously rotation  around Sun (Figure 2) .

Result by analogy: The fourth  resonator inside Sun  is outermost resonator .It corresponds to the  generator of planet Mars . That is way this fourth cylindrical resonator  is a model of expanded proton (dec (p+)) . Therefore  planet Mars is a model of expanded electron          (dec (e-)  as well. Because Mars   is  outermost  planet it is the most eccentric and polarized  and its y-axe  is not perpendicular and has the most slope. That is way it has not  synchronous rotation  around Sun  as well(Figure4) .

4.Law5 forms the electron(positron) and the internal planets from inside , Law6 forms the proton(antiproton) and the star Sun from inside.

Law 5 for 3D:  The decelerating  vortex in 3D is described with a system of 4  nonparametric equations  in which:  longitudinal velocity (V) decreases in (n) portions  ( ψn) times;  the  angular velocity (w) , the  amplitude (W)  and the  number (N) of cross vortices increase  in (n) portions (ψ n) times:

                                     I V(t)2= V0 (Vo – V(t)),                                                                

                                     I W(t)2 = W0(Wo +W(t)),                    8.                                                                            

                                     I w(t)2 = w0 (wo+ w(t))                                                                                                      

                                     I N2 = N0 (No+ N )        

where the roots vn , wn and ω and nn are expressed as: vn= (1/ψn ).V0 , ωnn.W  ; wn= ψn.W0 , [ nn   ]=ψn.N0 ;  linear velocity V0 is the starting value of  Vn , amplitude of cross vortex W0 is the starting value of  ωn , angular velocity w0 is starting value of wn , number Nis starting value of  nn  , [ nn   ]   is the closest integer     ; ψ is a proportional  that fulfills the requirement: ψ-1/ ψ =1)[8].

Therefore a decelerating vortex (E2D-) with a velocity vector (V) emits to the environment decelerating vortices with increasing amplitude (W)(because of sign + in second equation of system 10a) (Figure 3b).

Result: The main decelerating  transverse vortex of electron   emits to center decelerating transverse secondary vortices  .At the same time electron emits to (outside) environment decelerating transverse secondary vortices .

Result: Two or more decelerating longitudinal vortices   repel each other  and form Decelerating Gravity Funnel.

The Result by analogy : On the one hand the  main decelerating vortex emits  secondary decelerating vortices  which are emitted inwards  to center of   planet Earth  .On the other hand  the main decelerating vortex emits  outwards to the surrounding space in direction to Sun the same secondary  decelerating vortices. Thus is formed  back link to Sun and it  closes a full circle (closed loop)  in 2D ( Law7).

Law 6 for 3D : The accelerating vortex in 3D is described with a system of 4  nonparametric equations  in which: longitudinal velocity (V) increases in (n) portions  ( ψn) times,  the  angular velocity (w) , the  amplitude (W)  and the  number (Nn) of cross vortices decrease  in (n) portions (ψ n) times:

                                     I V(t)2= V0 (Vo +V(t)),                                                                

                                     I W(t)2 = W0(W0 –W(t)),                    9.                                                                            

                                    I w(t)2 = w0 (w0+ w(t))                                                                                                      

                                   I N2 =  N0 (N 0+ Nn )       

where the roots vn , wn and ω  and nn are expressed as: vn= (ψn ).V0 , ωn =(1/ψ ).W  , wn=(1/ ψn   )  .W0 ,      nn =(1/ψn  ).N0 ;  linear velocity V0 is the starting value of Vn   ,  amplitude of cross vortex W0 is the starting value of  ωn , angular velocity w0 is starting value of wn , number N0 is starting value of  nn    ; ψ is a proportional  that fulfills the requirement: ψ-1/ ψ =1[9].

The first positive root of the first equation  is: v1= ψ.V0 = 1,62.V0. The periodic roots of the first equation    are obtained from  the expression:  vn = V0.  (vn-1+vn-2). 

The first positive root of the second equation  isw1=(1/ψ.)W0 = 0,62.W0  . The periodic roots of the second equation   are obtained from the expression:    wn-2= W0. (wn-wn-1).     

Result: The main accelerating vortex suck in from  environment  secondary accelerating cross vortices.

Result: Two or more accelerating longitudinal vortices   attract each other  and form Accelerating Gravity Funnel. The reason is due to the suction  of secondary   accelerating cross vortices  from environment to inside.

Law 7: A pair of orthogonal  open transverse objects  forms a closed loop by feedback  in 2D  of primary transverse  vortices .

The Result by analogy : It exists an  inverse movement in the space between internal planets ( including Earth) to the Sun .It closes  the Closed loop  from the Sun  to  internal planets  ( Earth ) and from internal planets to Sun  (Figure 3c).

The Result by analogy: On the one hand the main longitudinal vortices are sucked from outward to inwards to center of Sun from  the surrounding space  and transverse vortices are emit to inward planets. On the other hand  the secondary longitudinal vortices are emitted  from inward planet to Sun. (Mercury, Earth, Mars ) or sucked  (Venus)  by the Sun. Thus is formed closed loop in 3D(x,z) volume  (Law 8).

The Result by analogy : For   first, third and fourth resonator inside Sun ( corresponding to   Mercury,Earth and Mars ) the main longitudinal vortices are  pushed to inward  .The main  transverse vortices are emitted  from Sun to planets Mercury, Earth and Mars .At the same times the secondary longitudinal vortices are emitted from Mercury, Earth and Mars to Sun.

For second resonator (corresponding to Venus) longitudinal vortex is pulled out. The secondary longitudinal vortex  is sucked  from Venus. At the same time Venus sucks secondary longitudinal vortex from  second cylindrical resonator in Sun


The Result by analogy : The closed loop in 3D  (x,z)  plane (Law8)  is  perpendicular to  the 2D(x,y)  plane  (Law7).


Law 8: A pair of open longitudinal objects in 3D forms a closed loop in 3D by feedback  in 3D  of primary longitudinal  vortices.

On one hand the Law 8 show that the longitudinal decelerating vortices are emitted  (Mercury, Earth, Mars )   or sucked  (Venus)  by the Sun . On other hand this Law 8 describes the closed loop between longitudinal vortices of  internal planets and    planets which are placed outside the  Asteroid Belt (between  Mars and Jupiter)  and  also internal planets (Earth, Mars) and  satellites  of internal planets ( Moon , Phobos  and Deimos ). The longitudinal vortices of internal planets generate   outer gas  planets and its satellites.

The Result by analogy : The closed loop in 3D  (x,z) plane (Law8)  is  perpendicular to  the  closed loop in 2D (x,y) plane  (Law7).

The Result by analogy : The Sun generates the inner planets by emitting (Mercury, Earth, Mars) or sucking( Venus) by a transverse vortex (in 2D). But the planets also emit free transverse vortices during the   motion of the main transverse vortex (in 2D)  that generates them.

The Result by analogy: The inner solid planets generate the outer gas planets through the main  longitudinal vortices  which  they emit (Mercury,Earth,Mars) or suck (Venus) through their poles( in 3D ).

The Result by analogy: The internal planets(Earth, Mars)  generates their  satellites planets ( Moon , Phobos  and Deimos) by means of secondary  longitudinal vortices shooting through their poles.

The Result by analogy: The outer gas planets generates their  satellites by  orthogonal algorithm .It means  that he outer gas planets generates their  satellites by    transverse  vortices which are targeted to their  solid  satellites .

The Result by analogy: It was shown that the internal planets are model of elecrtons  (Mercury, Earth, Mars) or positron (Venus). Mercury, Earth, Mars generate    correspondingly Jupiter, Uranus, Neptune  by  their main longitudinal vortices as protons  .They generate  their satellites as electrons. This is a reason their satellites to look like to Earth with  solid and  dense  bodies  and hot nucleus. Venus generates Saturn through  sucking   from  its main longitudinal  vortex as antiproton . Its satellites look like to positrons.


5. Structure of the Sun

The proton

It is well known that the protons  are arranged in layers inside the nucleus. According the author the outermost layers consist of inflated protons( dec (p+)).  They control the outermost electrons, which are also inflated  electrons (dec (e-))  .They  also are extremely  eccentric and highly polarized. The innermost layers of the nucleus consist of  shrunken protons (acc (p+)). They control electrons from the innermost orbits (acc(e-) that are contracted and not polarized.  In  central protons the longitudinal velocity is maximum  (vmax) but the transverse   ( angular  velocity ω )  tends to zero (ωmin).Therefore in center the mode is : (vmax , ωmin ).

In periphery  protons the longitudinal velocity is minimum  (vmin ) but the transverse ( angular velocity ω) is maximum (ωmax).Therefore in periphery of nucleus  the mode is :(vmin  ,ωmax ).

[10 ].

Such a structure of protons  is possible because  the generating vectors are  coming in from  all directions  to the nucleus  from the outside to the inside in condition of new space-time (Vconst)   [11 ].

The Sun

On one hand, in the Gravitational funnel which generates  Sun  there are in addition to central strongly accelerated longitudinal vortices and slower peripheral less accelerated and more coiled vortices. These more peripheral vortices have low longitudinal velocity (v min ) and high transverse velocity (ω  max) vortices and generate the periphery of  body of Sun(Law 2)

On other hand the generating Funnel   comes towards the Sun  from only one direction of the  space  . It is  a powerful bundle of many vortices inserted into each other in space-time with Sconst. which  form   this generating  Gravity Funnel .  The  longitudinal vortices   are nested into each other according to their velocities. Thus, in the center of this package is found  a longitudinal vortex with maximum longitudinal velocity(v max   ) and minimum transverse rotation speed ( ω min ). Or   in center is found the vortex : (v max , ω min  ). However a longitudinal vortex with minimum longitudinal speed (v min) and maximum transverse rotation speed ( ω  max)  is wound in the periphery .Or  in periphery  of Sun is wound  a transverse  vortex:  (v  min , ω  max )  (Figure2a ) [3,4]  . Therefore Sun look likes to the proton [10]

Consequence:  Sun look likes to the proton.

Consequence:  In the generating funnel coming to the Sun in special space-time (Tconst., S~V) there is an increase in the linear velocities from the center(vmin  )   to the periphery      (vmax ) and a decrease in the transverse velocities from ( ωmax)   to ( ωmin) [11 ]. Here the sign (~ )   means direct  proportionality  

Consequence:  In atom nucleus   the velocity distribution  corresponds to the distribution of  longitudinal (vi) and transverse velocities ( ωi)  ) in layers outside to the center in extremely  special space-time (Sconst.,V~ 1/T )  [11 ]. Here the sign (~ )   means inverse  proportionality.  

The Result by analogy:  The   velocity distribution of protons in atom nucleus in real  space-time  (Tconst., S~V)  completely  corresponds to the distribution of  longitudinal (vi) and transverse velocities ( ωi)  ) from  the outside to the center in space-time  of the generating Gravity  Funnel (Sconst.,V~ 1/T ) .

Consequence:  Sun look likes to the very extended  proton.

The longitudinal vortex which comes  from outside to inside and generates the   transverse  vortex from center to outside  creates  Sun’ s body as proton (Law2) .  At the transverse  exit the accelerating vortex   is shot out to Earth .

In particular for Earth ,the   longitudinal  Funnel from   longitudinal vorticesthe coming from the outside space   generates  in  the third  resonator of Sun (corresponing to Earth)    transverse  vortices from center to outside (Law2)(Figure2d). At the exit of the Sun this connection is an accelerating vortex, and at the entrance of the Earth this connection turns into a delayed vortex. The reason for this transformation is the natural friction  of the medium. 

On other hand According in center of this longitudinal Funnel has extremely accelerating vortices  .Their   positive acceleration  are the reason to suck  in free cross vortices (quanta)  from center of Sun (Law6) .This phenomena strongly cools down   the central interior of the Sun .So the  central part of Sun  is  cooler and therefore is denser then the surface  of Sun. 

The Result by analogy: The  central part of Sun  is cooler and   denser then the surface  of Sun.


6.The third resonator corresponding to the planet Earth

It is known that the Earth is the third planet after Mercury and Venus. The  new vision of author shows  that in  the  third is  cylindrical resonator  the beams of longitudinal vortices coming from outside  generates transverse vortex which   corresponds to Earth .  Outside the resonator of Earth follows another - the resonator on Mars. Before the resonator of Earth  are resonators of Mercury and Venus .Obviously the third cylindrical resonator on Earth has maximum volume compared to the other 3 resonators (Figure 2d) [3].

Figure2. Two complementary pairs:   Sun- Earth and Earth- satellite Moon

The System of  Sun and Earth - System of one complementary pairs


The System of Sun- Earth    (System of one complementary pairs)

It is obviously  that the third resonator is located in the middle of the sphere and the dimensions along the x- axis and along the y-axis are almost are the same.

Consequence:  In the third  cylinder  the diameter is equal to the high of cylinder .

This mathematical  problem has been solved long ago: Because in this (third cilindrical resonator ) cylinder diameter is equal to the high of cylinder it has been proven that  this kind of  cylinder    has a maximum volume inscribed in the sphere  (of Sun) .

The Result by analogy: The third  cylinder    has a maximum volume inscribed in the Sun  sphere   .

That is way the third planet (Earth) has maximum volume .The density of  the  Earth  is also maximum .The reason is that the amount of transverse vortices placed inside this maximum volume is also maximum. Therefore Earth has maximum density as well.

The Result by analogy: The third  cylinder    has a maximum volume inscribed in the sphere  (of Sun) 

The Result by analogy: The third cylinder has maximum density of transverse vortices

The Result by analogy: The third cylinder has maximum density of transverse vortices.

Consequence:  Earth look likes to an expanded electron.

The Gravity and Magnetic Field for electron and Earth

-We can describe that the electron generates Gravity Funnel  in its center and through the center  passes the  maximal accelerating vortex (Law1). The   Gravity Field passes through  center of electron  in direction North (N) to South ( S)( from  down to up). This very accelerating   central   vortex    of  the Gravity field springs from the center of electron  to up

-But the periphery vortices   sharply reduce their speed outside the electron surface and sharply change the direction of movement in the opposite direction to the original. Thus, this field of external and slow vortices creates   a reverse wave that envelops electron from the outside and form the   Magnetic field  in opposite direction (from up to down) .Unlike the internal Gravity field, the Magnetic field has a reverse polarization South-North ( from up to down) .Therefore, the Gravitational field through the center of the electron  and the Magnetic field outside the electron surface have opposite directions.

Consequence: The Gravitational field through the center of the electron  and the Magnetic field outside the electron surface have opposite directions.

The Result by analogy: The Gravity Funnel  which springs from  Earth  owns  in  its center  maximal accelerating vortices. They pass through  center of Earth in direction from down to up (North -N to South - S).

But  when this very accelerating   vortices  of  the Gravity field comes out  from the Earth  because of friction  by environment they sharply reduce their speed outside the Earth's surface and sharply change the direction of movement in the opposite direction to the original.

Thus, this field of external and slow vortices forms a reverse wave that envelops  the Earth from the outside and is called a Magnetic field. Unlike the internal Gravity field, the Magnetic field has a reverse polarization  from up to down( North-South ) .Therefore, the Gravitational field through the center of the Earth and the Magnetic field outside the Earth's surface have opposite directions.

The Result by analogy: The Gravity field through the center of the Earth and the Magnetic field outside the Earth's surface have opposite directions.

This is the reason  the North of the Magnetic field  to coincide with the South of the Gravity field, and the South of the Magnetic field to coincide with the North of the Gravity field. This is the reason in  the North Magnetic pole  is posed  the South  Gravity pole.

The Result by analogy: In the North Magnetic pole of Earth  is posed  the South  Gravity pole of Earth.

The System of  Earth - Moon  ( System of one complementary pairs)

The connection between Earth and Moon  is through the  longitudinal vortex. At the exit of the Earth along y-axe  springs an accelerating vortex from center of Earth  .But in periphery is formed less accelerating vortices .Thus this  less accelerating  longitudinal vortex comes  at the entrance to the Moon or it acts  and more decelerating vortex. The reason for this transformation is the natural  friction  of the medium.

In the body of the Moon  this  less decelerating vortex enters longitudinally along y-axe  from outside to inside in a volume 3D. In the   center  of the Moon has an accelerating transverse vortex in 2D  plane which generates the body of Moon (Law2).

Consequence:  The accelerating transverse vortex generates  the Moon’s body as proton.

In the center of longitudinal Funnel  exists  an  accelerating vortex which sucks from  periphery  to center  a  primary transverse  vortices(quanta) .This  action cools down   the  Moon’s center  and it becomes denser than the surface(Figure2a).

The Result by analogy: Moon looks like a shrunk proton with denser and cool center and rarer and warm surface.


7.The second resonator corresponding to the planet Venus

We saw from the previous point that the Earth is formed as a large extended peripheral electron: It is generated by a delayed transverse vortex moving from the periphery inwards to the center. As a delayed vortex it emits secondary transverse vortices(quanta) nd they  are phased in the center by place and time .As  this phased transverse vortices are accelerated they shrink their radius and generate a vector perpendicular to the plane of the transverse vortex (Law1).

But for difference to the Earth  , the planet Venus is  formed as a  positron: It is generated by a decelerating  transverse vortex moving from the center to the periphery . As it is  a decelerating  vortex  from center to periphery it emits secondary transverse vortices (quanta) that are  bent from left to right .Therefore Venus rotates around its own axis to the right or back to Earth and other inner planets.

The Result by analogy: The planet Venus is  formed as a  positron.

The Result by analogy: Venus rotates around its own axis to the right or in inverse direction to Earth and other inner planets.

Figure3. One complementary pairs :   Sun- Venus


The center of the eccentricity of the Earth is in the second quadrant (Figure1b) and the center of eccentricity of Venus is in the first quadrant (Figure 3a). But in the projection of the Force of eccentricity along y axe  both the Earth and Venus shows in the same direction(Figure1b, Figure 3a). According  to the center of eccentricity the direction along y axe  is to left.  That is why  and the Earth and Venus rotate  in an orbit around the Sun from right to left.

The Result by analogy: Venus rotate  in an orbit around the Sun from right to left or in  the same direction as Earth.

8.The fourth resonator corresponding to the planet Mars and its satellites

The fourth   resonator in Sun corresponds to the planet Mars. For this resonator the width is much more than the height. That is way  Mars  is  formed as a extremely  extended peripheral (valence) electron. It is generated by a  less ( than for Earth)  decelerating  transverse vortex.

It was fired from Sun and  moving from the periphery inwards to the center of body of Mars. As a less decelerating transverse vortex (in comparison of vortex of   Earth ) it emits less number , smaller in amplitude  and shorter secondary transverse vortices (quanta) .They are phased in the center    of body of Mars by place and time  . That is the reason   to  generate a  smaller  longitudinal vector perpendicular to the plane of the transverse vortex (Law1). 

The Result by analogy: Mars is generated as very expanded (valence) electron.

The planet Mars  emits 1  main central accelerating longitudinal vortex.  For difference to the Earth  , Mars emits 2 (not 1 as Earth ) peripheral  decelerating   vortices . The main   central   accelerating longitudinal vortex generates   the outermost gas  planet  Neptune as proton. But the 2 decelerating   longitudinal vortices generate   2 satellites of Mars ( Phobos and Deimos) (Law2).

The Result by analogy: Neptune  is generated as very expanded (periphery ) proton.

 For comparison the bigger central accelerating vortex of planet Earth generates   1outer gas planet ( Uranium) but   only 1 peripheral decelerating vortex generates  1 satellite of Earth  (Moon)(Law2).

Mars  is generated by the fourth cylindrical resonator in Sun through shooting  an less  accelerating-decelerating  transverse vortex .It is winding  from  the periphery to the center of body of Mars (Law1). As a  less decelerating  vortex from  periphery to the center  it emits  less secondary transverse vortices from  periphery to center .They  are bent from  right to left as in Earth (Law5) .

This is the reason Mars rotates around its own axis from right to left   or it  rotates  around its y- axis  as   Mercury and Earth , except Venus.

The Result by analogy: Mars  rotates around its own axis from right to left   as   Mercury and Earth .

As an outermost  solid planet Mars has maximum eccentricity and it is maximum polarized  This is the reason that the vector of eccentricity   is maximum as well. The projection of the eccentricity vector to the y-axis has direction from right to left as well as in all inner planets.

That is the reason Mars rotates along the orbit  around the Sun to the left as  all other inner planets in the Sun system.

The Result by analogy: Mars rotates along the orbit around the Sun from right to left as  all other inner planets in the Sun system.

Two satellites Phobos and Deimos

The planet Mars   emits 2 peripheral decelerating longitudinal  vortices  in 3D longitudinal Funnel  ,perpendicular to the plane of  transverse  generating vortex in 2D .They  generate 2 satellites Phobos and Deimos  by 2 longitudinal vortices  (Law 2). In both of satellites  the longitudinal vortex  push   from outside  to center  of the bodies  as  is generated protons (Low2).Therefore Phobos and Deimos are models of proton.

The Result by analogy: Phobos and Deimos are generated as protons.

It is known that he inner vortices has more velocity    then the periphery vortices in longitudinal Funnel .So the inner  longitudinal vortex  is much more powerful than the  outer  longitudinal vortex.The reason is that the inner cross vortices are more powerful ,than the outer cross vortices and that  is way  the  inner longitudinal vortices to be more powerful than outer  external longitudinal vortices .

The Result by analogy: More powerful longitudinal vortex is the inner and less powerful longitudinal vortex is the outer.

Therefore   in the inner orbit should be the more massive satellite (Phobos ) and in outer orbit should be the less massive satellite (Deimos)

The Result by analogy: In the inner orbit is placed the more massive satellite (Phobos ) and in outer orbit is placed the less massive satellite (Deimos)

The Result by analogy: The inner satellite Phobos is  generated  as an expanded  proton.   

Because satellite  Phobos  is the most internal  satellite  it should  has synchronous movement  around Mars.

The Result by analogy: Satellite  Phobos  has synchronous movement  around Mars.

The Result by analogy: The outer satellite Deimos is generated as a shrunk proton.

The orbits of the Martian satellites are very different from those of our Moon.

The ten times the more massive  Phobos  has only  two  times larger surface gravity. It  rotates  synchronous  but faster than Deimos around  Mars.

Figure4 . Two complementary pairs: Sun- Mars and

Mars –satellites Phobos and Deimos



9.Conclusions

-The system of Sun ,Earth and Moon  splits into 2 mutually orthogonal pairs : Sun-Earth and Earth- Moon. The Sun is similar to proton : the center of the Sun  is colder and denser   than its surface. The speed of the central  transverse vortices of Solar plasma  is less than the speed of  light. But according  new law  of structure of proton  (Law2)  it is very likely  the accelerating moving of transverse vortices toward periphery of Sun  to reach   the speed of light .It is very likely ,  the  reason for  thermonuclear process of the Sun    to be the enormous  longitudinal acceleration  of accelerating  vortex from center   towards periphery .Therefore   the reason is acceleration but the  itself thermonuclear  conversion to be  only  one of  results of described acceleration .

- Because   Sun is in form of proton then  Earth is in form of electron and Moon in form of proton as well. The Earth is similar to an   expanded electron: the center of the Earth   is hotter  and  rarer   than its surface. The North of the Magnetic field  of Earth coincides with the South of the Gravity field of Earth  (and  inverse).The reason is that Gravity Field (with high velocity)  passes along central  y -axe of Earth and Magnetic Field(with  much less velocity ) envelopes outside the surface of Earth in opposite direction. Earth(electron ) generates Moon(proton ) by longitudinal vortex which is pushed along y-axe from outside to inside. So Moon is similar to a shrunk   proton : the center of the Moon is colder  and denser than its surface or it looks like to  an  outer  gas  planet. Because Moon  rotates  in least distance to Earth  it  rotates around Earth synchronously . This is the reason Moon to show only one part of its surface  . At the same time Earth generates   also and an outer(the third ) gas planet Uranium by  very power longitudinal vortex emitted along y-axe  from bottom  to up.

 -Planet   Mercury is similar to a very shrunk  electron : the center of the Mercury is  very slightly warmer  than its surface . Because Mercury   rotates  in least distance to Sun it  rotates  synchronously . This is the reason Mercury to  show only one part of its surface .At the same time Mercury (electron ) generates Jupiter (proton )  by emitting an accelerating   a very powerful and fast rotating  pillar (vortex)  from longitudinal vortices along its y-axe  from the bottom up. When this accelerating   vortex  starts to be late  it becomes to decelerating vortex and  they both   form a parabola . The decelerating vortex   inserts   , presses and rotates the primary matter  of  Jupiter from top to bottom along the y-axis .At the same time  it start rotating  and accelerating  this primary matter transversely  from center to periphery of Jupiter.

-Venus is similar to a positron  : the center of the is colder  and surface is hotter .Venera looks like  to gas planet more than to the solid planet. It   rotates around its y-axe in inverse direction or  to right .Venus generates  an outer(the second ) gas planet Saturn by   not very power longitudinal vortex emitted along y-axe  from bottom  to up.

-Mars is similar to a very expanded (valence) proton: hot center and cool surface. Mars generates two satellites (Phobos  and Deimos) by emitting two decelerating  longitudinal vortices along y-axe  from bottom to up. At the same time Mars generates and an outer( the fourth)  gas planet Neptune by emitting  an accelerating longitudinal vortex along y-axe.

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