published by science and education publishing doi:10.12691

International Journal of Physics, 2021, Vol. 9, No. 2, 96-113 Available online at http://pubs.sciepub.com/ijp/9/2/5 Published by Science and Education Publishing DOI:10.12691/ijp-9-2-5

From the Contraction of Celestial Bodies to Their Shortest Rotation Period until the Heating of the Stars

and the Universe Global Theory

José Luís Pereira Rebelo Fernandes*

Independent Researcher since 2005, Engineer, Graduated from the University of Porto *Corresponding author: [email protected]

Received February 03, 2021; Revised March 09, 2021; Accepted March 18, 2021

Abstract Now we can deduct the variation of the atomic radius with the universal density of potential energy. We can look here and at “Ref. [4]”. In the same way as a lower ρ, gravitational radiation occurs more easily, so does electromagnetic radiation. With the decrease of ρ due to the expansion of the universe, the magnetic permeability of the vacuum U increases. Applying quantum mechanics, it turns out that the atomic radius varies in the inverse

proportion of U, that is, in the inverse proportion of the expansion of the universe. tt o

o

ρR R

ρ= Since all matter is

made up of atoms, we conclude that matter in the future will shrink. This notion associated with the increase in G allows us to better understand the universal formation. The centers of mass due to the increase in G move away and the large amounts of mass made up of larger atoms shrink giving rise to the protostars that over time gave rise to the stars and their ignition as well as greater regiment to the planets and moons. The contraction of the rotating celestial bodies, among them the Earth, justifies the fact that the day is currently shorter, since the angular momentum will always be constant. Keeping the angular momentum indicates that if a mass that turns one day a day shrinks by half it will start to turn four times a day. The average increased surface speed of rotation will be proportional to the expansion of the universe. Heating of stars and universal heating. Now that we know about the contraction of atoms and, consequently, the contraction of celestial bodies, we have to admit that this process leads to its heating. Assuming that the temperature increases in proportion to the kinetic energy.

Keywords: relativity, space, time, dilation, gravity, gravitational, speed, density, energy, potential, mass, ligh, galaxy

Cite This Article: José Luís Pereira Rebelo Fernandes, “From the Contraction of Celestial Bodies to Their Shortest Rotation Period until the Heating of the Stars and the Universe Global Theory.” International Journal of Physics, vol. 9, no. 2 (2021): 96-113. doi: 10.12691/ijp-9-2-5.

1. Introduction

In this article, we will describe the journey taken to date, in order to understand in a clear way all the development of the theory created.

-We start with The Relativity of Time with the Universal Density of Potential Energy in Different Stationary References Frames.

We can look here and at “Ref. [1]”, where the time in the satellites is composed of two different times, one, regarding the speed at which the referential moves, and another, regarding the distance to the center of mass in whose field it gravitates. For example at the limit of the

gravitational field, teremos, 0 R2

R 0

t ρ2GM1t ρRc

= − =

( ρ is the Universal Density of Potential Energy), It is concluded that time is inversely proportional to the root square of the potential energy density in each place.

The first finding is time variability, which means that the clock works more or less quickly, depending on the potential energy density uρ . No less important is to verify that uρ is not constant in all places as previously believed.

We also conclude that the relativity of time in the same location over time will be inversely proportional to the square root of uρ , because with the expansion of the universe, the universal masses will be further and further away from the location and thus will generate a lower density of potential energy, causing the contraction of time everywhere. The measurements made up to today over time from the radiation coming from space will have to be corrected, otherwise they will be wrong, as the contraction of time pushes the measurement towards the red, giving an apparent reading in which the emitting source is is moving away with increasing and accelerated speed. I think this is the mistake of thinking that the universe grows in acelerate motion.

Developing the joint expression of the speed of the satellite and the distance in relation to the gravitational mass, we will have, the relative time between two references is inversely proportional to the square root of

International Journal of Physics 97

the Universal density of potential energy traversed by each reference frame.

-Now we can deduct the variation of the atomic radius with the universal density of potential energy. We can look here and at “Ref. [4]”. In the same way as a lower ρ, gravitational radiation occurs more easily, so does electromagnetic radiation. With the decrease of ρ due to the expansion of the universe, the magnetic permeability of the vacuum U increases.

Applying quantum mechanics, it turns out that the atomic radius varies in the inverse proportion of U, that is, in the inverse proportion of the expansion of the universe.

t o t 0R R ρ / ρ=

Since all matter is made up of atoms, we conclude that matter in the future will shrink.

Both shrinks in the future and in a place with a smaller ρ. An object carried from Earth to the Moon will shrink. We cannot measure with a tape measure as it will behave in the same way.

This notion associated with the increase in G allows us to better understand the universal formation. The centers of mass due to the increase in G move away and the large amounts of mass made up of larger atoms shrink giving rise to the protostars that over time gave rise to the stars and their ignition as well as greater regiment to the planets and moons.

The contraction of the rotating stars, among them the Earth, justifies the fact that the day is currently shorter, since the angular momentum will always be constant. Keeping the angular momentum indicates that if a mass that turns one day a day shrinks by half it will start to turn four times a day.

The average increased surface speed of rotation will be proportional to the expansion of the universe.

The next step is to complete the universal gravitational variable.

We can look here and at “Ref. [2]”, when we do the verification that ρ varies from place to place and that varies in time due to the distance from all universal masses, shows us that the Universal Gravitational Constant is Variable after all.

The Moon has moved away from the Earth at a constant value, 3.82 cm per year, since the last 51 years, which indicates that G increases at a constant value. It also indicates that the universal masses are moving away at a constant value, so the universe expands at a constant value, “C”.

For this purpose, just look at the concept of the potential of the constant speed of light, given by,

2uC ,2Gρ= which implies that G varies in the inverse

proportion of uρ , that is, it varies in proportion to the expansion of the universe.

The smaller ρu , the greater G. A vacuum with a lower density of uρ , facilitates gravitational radiation, which is the same as saying that G increases. In a gravitational field, with the increase of G, a certain gravitational potential generated at a certain distance will in the future happen at a greater distance, causing the masses that gravitate in that field to move away from the field's generating mass, maintaining the speed of constant translation, the same potential in the void. This distance will increase in

proportion to the universal expansion because G increases in that proportion.

We can say that in a homogeneous Universe, when the whole expands, the part expands in the same proportion. The expansion and balance of the gravitational fields occurs automatically.

The gravitational orbits of all universal masses are increasing in proportion to universal expansion.

/U GM R= .R KG=

The Black Energy that was thought necessary to expand the Universe does not exist, we do not need it to understand universal expansion. G increases and the centers of mass move apart in proportion to its increase. In the Solar System, we learn that the planets are moving away from the Sun and that the Moons are moving away from the respective planets. The Sun is also moving away from the center of Via Lacteal.

We will now calculate the annual removal of the Moon from the Earth.

We can look here and at “Ref. [4]”,. With the current knowledge, that with the expansion of the universe, time and bodies contract, we have to take these phenomena into account, in order to determine the real distance, from the apparent annual measurement of 3.82 cm from the Moon in relation to Earth.

After that analysis we conclude that the centers of mass of the Earth and the Moon are moving away 2.53 cm by year much less than what is apparently measured.

With the previously calculated value we were able to determine the age of the Universe. Obtaining the value of the age / size of the universe, is of paramount importance in order to be able to quantify the behavior of the universe and the movements of celestial bodies in the future. We will then have the Age given by the ratio of the distance between the centers of mass of the Earth and the Moon by the annual displacement. I = 385000600 / 0.0253 = 15 224 021 588 years.

We can evaluate: Hubble constant. The definition of the Hubble constant. We can look here and at “Ref. [4]”, refers to the

expansion of the universe based on 1 mega parsec = 3.0856775815x10 ^ + 22 m, indicating the growth rate of that length. V=64,226kms−1Mpc−1 was the value found.

The annual go away of all masses from the centers of mass that gravitate. To calculate the annual deviation of any mass from the center of the gravitational field to which it belongs, it is enough to divide this distance by the age of the Universe. Example Earth. The Earth is 1,496x10 ^ 11 m from the Sun, so the value of the annual distance from the Sun will come from d=1,496x10^11/15224021588 = 9,827 m per year.

The contraction of time on Earth with an interval of 1 year will then be given by tt = to ((I + 1) / I) ^ 0.5 = 1.0000000000328, that is to say in a year, one day you will take more 2837 ns ( nanoseconds).

- The value of the contraction of the bodies. In turn, the radius of the Earth will decrease l = (1- (i / (I + 1))) * 6378100m = 0.000419 m / year.

The abandonment of the planets and moons of the respective proto-sun and proto-planets. For example, the

98 International Journal of Physics

Earth's abandonment of the proto-sun will be given by the product of the age of the universe by the square root of the ratio of the sum of the raises of the stars by the distance between their centers of mass, i=I*((Rsol+Rterra)/D(Sol-terra))^0.5=15224021588*((696000000+ + 6378100) / (1,496x10 ^ 11)) ^ 0.5 = 1 043 429 635 years

Shorter rotation period and translation due to the variation of ρu. Regarding the translation period, account must be taken of the increase in the perimeter and the contraction of time due to the expansion of the Universe.

As for the re-rotation period in addition to the contraction of time, we have to take into account the conservation of angular momentum, because if with an initial volume it would rotate once in a certain time, with half the volume it would start to rotate (2 ^ 2) four times during the same time.

In the case of the Earth, in addition to what was previously mentioned in relation to the rotation period, we have to consider the expansion of the Universe, the variation in the distance to the Sun, the speed of translation of the Earth around the Sun, the speed of the Earth's rotation and the contraction of the Earth. When the Earth approaches the Sun (December) the Earth increases its volume because ρu increases due to the Sun's influence, it will rotate more slowly because it swelled and time expande. In June, the opposite happens, the Earth shrinks, rotates faster and time contract.

Heating of stars and universal heating. Now that we know about the contraction of atoms and, consequently, the contraction of celestial bodies, we have to admit that this process leads to its heating. Assuming that the temperature increases in proportion to the kinetic energy.

The Galaxies and the Dark Matter. We can look here and at “Ref. [5]”. From the speed of

rotation of the Sun in the galaxy we were able to calculate the mass of the galaxy and the type of distribution of its matter. The difference between the speeds found in the model and the apparent speeds measured from the Solar System is perfectly explained by the autonomous rotation of the Solar System in the same direction as the rotation of the galaxy. We conclude too, that we don't need Dark Matter to explain the rotation of galaxies. We reevaluate this article taking into account the new data made available by the GAIA Project.

This papper covers all subjects published to date; “Ref. [1] ”,“ Ref. [2] ”,“ Ref. [3] ”,“ Ref. [4] ”,“ Ref. [5] ”, explaining them with greater care.

2. The The Relativity of the Time with the Universal Density of Potential Energy at Different Stationary Reference Frame, “Ref. [1]”

2.1. Methods Used for the Analysis

2.1.1. Method 1- Schwarzschild Geometry Through the analysis in GR, of Einstein's relativity

throw the metric derived from the Schwarzschild geometry for a static field with spherical symmetry it is proposed to vary the time between the reference frame A,

within the gravitational field of the mass M, with a radius RA , located on its surface and another reference frame C on the limit of the gravitational field, RC = ∞.

This expression is the one usually used to calculate time on satellites.

The relativity of time between A and B.

A2 2

B A B

t 2GM 2GM1t R C R C

= − + (1.2)

At C, on the limit of the gravitational field, with RB= ∞.

A2

B A

t 2GM1t R C

= − (2.2)

2.1.2. Method 2- The Variation of Time between Different Locations belonging to the Perpendicular Path

We will study the difference between the times at different reference frame belonging to a gravitational field, created by a mass M with a radius AR . . We will study the time difference found along the path of the escape of object launched at a speed with a potential U from the reference frame A located on the surface of mass M . We will measure the differential time between reference frame A, the reference frame C located on the limit of the gravitational field and the reference frame B located at a distance RB from the center of mass M. Mediation will be based on the observer's referential O the observer's referential.

2AV U=

2C

A

2GMV UR

= −

2B

A B

2GM 2GMV UR R

= − +

22A2 2

B2

U1t UC( ) 1t 0 C1

C

−= −

−

= (3.2)

A B

22B2

B2

2GM 2GMUR R1

t C( )t 01

C

−

−

=

− +

(4.2)

2B2 2 2

B A B

t U 2GM 2GM( ) 1t C R C R C

= − + − (5.2)

2 2A B2 2

B B A B

t t 2GM 2GM( ) ( )t t R C R C

− = − + (6.2)

This differential is independent of U. Whatever, the time difference between A and B will always be the same.

When subtracting the time of reference frame B from the time of reference frame A, we take the time of B


2 2

A B2 2 2

B A B

t t 2GM 2GMt R C R C−

= − + (7.2)

2 2A B2 2

A B

2GM 2GMt tR C R C

1

= −

+

(8.2)

A2 2

B A B

t 2GM 2GM1t R C R C

= − + (9.2)

At C, on the limit of the gravitational field, with BR = ∞

A2

C A

t 2GM1 .t R C

= − (10.2)

2.2. The Relativity of Time with the Universal Density of Potential Energy at Local

We learned from Einstein that the speed of light is a structuring element of the theory of relativity it makes its potential, 2

uC 2 ,Gρ= depend on G and ρu , which in turn will also be structuring elements of physics. When analyzing the expression Eq.(9.2 and 10.2), we senses the importance of ρu .

Multiplying the numerator and denominator in Eq. (1.2)

or in Eq. (8.2) by 2C ,

2G we have:

2

A A B2

B

C M Mt 2G R Rt C

2G

− += (11.2)

A

A A B

B A

M Mρt R Rt ρ

− += (12.2)

A B

B A

t ρt ρ

= (13.2)

ρu - Universal density of potential enegy, generated by all the universal masses, at A, ρA .

uMρR

− - Universal density of potential enegy, generated

by all the universal masses, we have to subtract the

influence of the Earth on its surface MR

, at C, ρC .

If we managed to remove the A

MR

part of the whole, ρu ,

it is a sign that this part is part of that whole. The density of potential energy created by the Earth on

its surface A

MR

is part of the ρu .

Yes, the time is inversely proportional to the square root of (ρ) the Universal Density of Potential Energy at local.

The universal density of potential energy varies from one location to another location. If this didn’t happen we would have the same time in all referential frames.

It's not just the speed variation that makes time vary, now we know that (ρ) the Universal Density of Potential Energy at local also makes varies the time.

2.3. The Relativity of Time with the Universal Density of Potential Energy at Local and Different Speeds

Now, we have the relativity between two reference frames, A and B, given by:

2 2

A A B2 2

B AB

t C V ρt ρC V

−=

− (14.2)

Expression deduced from:

2

2 2A B B

2B A

2 2A

Ct C V ρt ρC

C V

−=

−

(15.2)

Time is inversely proportional to the square root of 𝛒𝛒𝐮𝐮 traversed by the moving object.

2.4. The Variation of Time with the Universal Expansion

With universal expansion, the universal density of potential energy at local decreases, because the masses will be increasingly apart, and will cause the contraction of the time, too in the Earth reference.

tt – Tempo futuro.

t 0

0 t

t ρt ρ

= (16.2)

The contraction of time will have an implication in the values read from the universe over time. The reading of radiation from space will also, be altered due to the contraction of time. The radiation is, pushed to the red, giving the apparent reading that the source is moving away with increasing speed. A constant removal will appear to be occurring at an accelerated rate.

2.5. The Time on Satellites in a Gravitational Field

To do the calculation we need: M – Generating mass of the gravitational field. 𝑹𝑹𝑴𝑴 – Mass radius 𝑹𝑹𝑺𝑺 – Satellite gravitational radius 𝑽𝑽𝑴𝑴 – The rotational velocity of the mass

2 2

Mass SatellM2 2

Satel MassSatel

t ρC Vt ρC V

−=

− (17.2)


2

2 2Mass Sat

22

Sat

C M Mt 2G R RC V

GMt CCR 2G

− +−

=−

Mass M

Satel (18.2)

2.5.1. The Time on Satellites in the Earth Gravitational Field

To do the calculation we need: M – Generating mass of the gravitational field. 𝑹𝑹𝑴𝑴 – Mass radius 𝑹𝑹𝑺𝑺𝑺𝑺𝑺𝑺 – Satellite gravitational radius 𝑽𝑽𝑴𝑴 – The rotational velocity of the mass, Earth 355,313

m/s. To do the calculation we need:

22

Sat2 2 2

Earth Sat

GM CCt R 2G

tEarth C 355.313 C M M2G R R

−=

−− +

Sat (19.2)

Within a day, we will have:

Table 1. Satellite Radius, relative time satellite / Earth, Daily time delay

Satellite Radius sat (m) tSat /tEarth Delay/day

(ns) GPS 26 578 100 1,000000000446 38 522

GALILEO 29 600 100 1,000000000471 40 730

ISS 6 737 500 0,999999999709 -25 177

3. The Universal Gravitational Variable, “Ref. [2]”

3.1. The Constant Velocity of Light There is a data in the local universe that has come to us

through Einstein, the constancy of the "speed of light" C in all directions. This is the maximum speed allowed in any direction of space. We are in the presence of local maximum escape potential, given by:

C2 = 2 G ρu Where: ρu – Universal density of potential energy at in place, generated at the locality by all the universal masses. G – "Universal gravitational constant":

As postulated, C constant.

Gρu = C2/2 (1.3)

Gρu = W(constant) (2.3) In an expanding Universe, with the removal of all

masses from the location, we will have in time:

Gtρt= G0ρ0 (3.3)

0

t

ρGtG0 ρ

= (4.3)

G is inversely proportional to ρu .

G is no more than the coefficient of the gravity radiation capacity through the vacuum, through the ρu .

The lower ρu , the lower the resistance to radiation propagation through the void, causing G to increase in inverse proportion.

We have a Universal Gravitational Variable and not a Constant.

But why will G be variable and increasing? The contraction of time will have an implication in the

values read from the universe over time. The reading of radiation from space will also, be altered due to the contraction of time. The radiation is, pushed to the red, giving the apparent reading that the source is moving away with increasing speed. A constant removal will appear to be occurring at an accelerated rate

3.2. G and 𝛒𝛒𝐮𝐮 In universal terms: Einstein characterized the speed of light as result of the

escape potential anywhere and in all directions. The same happens in the local escape potential where

the escape velocity to abandon a mass is the same in all directions.

In gravitational potential, M/R is the density of potential energy created by mass M at distance r. Since we are facing a universal escape potential,C2 , then ρu can only be the density of potential energy created by all the universal mass, in the place.

Ci2 = 2 Gi ρui (5.3)

n

u eji ji1umi n

uji1

M RR

M=∑∑

(6.3)

Where: Rumi - The Universal average distance that creates density of potential energy in location.

n

ujiui 1ui

umi umi

MMρ

R R==∑ (7.3)

The amount of universal mass / energy will always be constant.

ρui = Y (constant)/ Rumi (8.3) In an expanding universe, all the universal masses will

be more and more distant from location i, so the average radius of universal mass emission to the site will be increasing.

If the average radius of radiation increases, then the local density of universal potential energy decreases.

On the other hand, as we have seen, and according to Eq. (3.3):

umi

WGY

R

= (9.3)

WY

P = (10.3)

G = PRumi (11.3)


G increases in proportion to the increase of the average universal emission radius, then G will also grow at the ratio of the average radius of universal mass emission to the local. Because we are in a homogeneous Universe, then we can say that G increases in proportion to the expansion of the Universe.

G = QRu (12.3)

ut

u0

RGtG0 R

= (13.3)

We have a Universal Gravitational Variable and not a Constant.

3.3. Black Holes and the Nature of 𝛒𝛒𝐮𝐮 Most of the time we discover the existence of a Black

Hole through the gravitational field it generates. If the radiation that generates ρu and the gravitational

fields were corpuscular, it would not be able to abandon the black hole. Either it is very low energy radiation or it will be immaterial radiation (pure energy?), Not directly detectable by our material equipment. Its effect would be felt only indirectly.

If they are not subject to gravity, then it will move in a straight line, at speed “C”, creating the void impregnated with ρuat the outer limit.

3.4. Impact of the Universal Gravitational Variable on Local Gravitational Fields

With the available information, that the Moon is moving away from Earth, at a rate of a constant 3.82 ±0.07 cm per year [11] obtained as measured since 1969, i.e. measurements taken for over 51 years, through the Apollo Laser Ranging Experiments Yield Results and “Jupiter has more than 60 natural satellites, but only the top four deserve particular attention: Io, Europe, Ganymede and Calisto. They have nearly circular orbits, and exhibit the same face toward Jupiter. They are also slowly moving away from the planet. Saturn has over forty satellites, except for two, always run with the same face toward the planet, and they are slowly moving away."(Extracted from the book "Discovering the Universe", PhD Teresa Lago from the Astrophysics Center of the University of Porto), [3].

These phenomena require an analysis of the local universe and the laws that govern it.

It´s known by all the expression that allows us to calculate the gravitational potential of a body around the other:

MU GR

= (14.3)

The gravitational potential will always be constant. (Constant velocity of the gravitational bodies in void U=V2): A body in the void, in a null working system is always constant. U= Constant.

The mass generanting the gravitational field will also remain constant, solving Eq.(1.1): M= Constant

r MG U= (15.3)

( )r KG

constant= (16.3)

r =K G (17.3) In an expanding Universe, with the removal of all

masses from the location, we will have in time:

t

0

R GtR G0

= (18.3)

As we have seen before, bodies belonging to a gravitational field are moving away from the masses that generate these fields. In the Earth / Moon System, the Moon is moving away from the Earth every year, that is, the radius of gravitation increases, r_1>r_0. The same happens with the moons of Jupiter and Saturn. From Eq. (5.3), we know that the gravitational radius increases indicating that G increases proportionally to the radius.

Increasing G, we have the same gravitational potential, generated the largest distance of mass M and hence the Moon to adjust to the location of this potential, moving away.

4. The Variation of the Atomic Radius with the Universal Density of Potential Energy, “Ref. [3]”and “Ref. [4]”

Remember, the variation of G with the Universal density of Potential Energy.

to - Time on our site tt - Time on future site

ot o

t

ρG G

ρ= (1.4)

The permeability (U) of vacuum. Transformer, G to U

2

o 0CG U4π

W= (2.4)

U0 = KG0 (3.4)

Ut = oo

t

ρU

ρ (4.4)

4.1. The Relativity of the Atomic Radius with (ρ)

Applying the expression for the calculation of the atomic radius and taking into account the Magnetic Permeability Variable of the Vacuum,

As:

2

2o 2 2

o

4π hR n2πmU C ze

= (5.4)

2

2t 2 2

t

4π hR n2πmU C ze

= (6.4)


2

2t

2 2oo

t

4π hR nρ 2πmU C zeρ

= (7.4)

tt o

o

ρR R

ρ= (8.4)

The atomic radius of the matter is directly proportional to the local universal density of potential energy.

As ρt is inversely proportional to the expansion of the Universe, as such the atomic rays will always tend to decrease.

4.1.1. Potential Electron Energy

22 4 2 4

oo 2 2

mU C z e 2π 1Eh2(4π) n

= (9.4)

22 4 2 4

tt 2 2

mU C z e 2π 1Eh2(4π) n

= (10.4)

Given relativity:

2tt o

0

UE E ( )

U= (11.4)

20t o

t

ρE E ( )

ρ= (12.4)

4tt o

o

tE E ( )

t= (13.4)

4.2. The Evolution of the Radius of the Celestial Bodies in Time

Since the radius of the atoms varies in the inverse proportion of ρ, so the radius of the celestial bodies that are made up of atoms will also vary in the same proportion.

tt o

o

ρR R

ρ= (14.4)

In an expanding universe, the universal density of potential energy will decrease, so the atomic radius will decrease, which will cause the celestial bodies to shrink.

Our planet Earth is shrinking. Our moon is shrinking, too. The Sun, for this purpose, without taking into account

the loss of mass, will shrink too. Por exemplo, o comprimento dos mesmos objetos na

superfície lunar será menor do que a mesma superfície da Terra

Dois habitantes locais medirão, a e b,

LuaLua T

Terra

ρL L

ρ= (15.3)

4.3. The Speed of Rotation of the Shrinking Celestial Bodies

We need take into account the contraction of the celestial bodies.

As a better approximation we will consider the sphere as the usual form of the masses in question. So we will have;

Ith the conservation of angular momentum, w. we will have:

2 2t t o o

2 2mR W mR W5 5

= (14.3)

2

ot 0 2

t

RW W

R= (15.4)

2

ot 0 2

2 to 2

o

RW W

ρRρ

= (16.4)

2

0t 0 2

t

ρW W

ρ= (17.4)

2

tt 0 2

o

ρT T

ρ= (18.4)

The angular velocity of the celestial bodies will vary in inverse proportion to the square of the universal density of potential energy, ρ, in place, that is, in proportion to the square of the universal expansion.

As the radius contracts, then we will have a surface rotation speed inversely proportional to ρ.

0t 0

t

ρV V

ρ=

In other words, the surface rotation speed will be proportional to the expansion of the Universe.

tt 0 0

0

T I nV V VT I

=+

=

The same will happen with our Earth, it will shrink and rotate at the highest speed.

4.3.1. Relativity of time Earth/Planets.

4.3.1.1. Dependent on 𝛒𝛒 and v

2

ECρ2G

=

E P E PP E

E E P E P P

M M M Mρ ρ

R R R R− −= − − + + (19.4)

E P E PE

P E E P E P P

E E

M M M Mρ –ρ R R R Rρ ρ

− −− + +

= (20.4)

P

E

ρl 1

ρ∂ = − (21.4)

P E

E P

t ρt ρ

= (22.4)


Table 2. Mass, Radius, translation radius, Translation velocity and rotation velocity.Differential in length, Time dependent on ρ, Time dependent on speed, v, and relative Time

Syst. solar Mass Radius Rtransl. Vtranl Vrot Dif. L tρ t vel. t Var./Day

kg m m m/s m/s nm ns Sun 1,9891E+30 6,9600E+08

Mercury 3,3011E+23 2,4397E+06 5,7909E+10 47 880 3,0 30,08 -1,504E-08 -7,816E-09 -2,285E-08 -1974642 Venus 4,8685E+24 6,0518E+06 1,0821E+11 35 026 1,8 7,36 -3,679E-09 -1,888E-09 -5,566E-09 -480923 Earth 5,9736E+24 6,3781E+06 1,4960E+11 29 790 355,3 0,00 0 Mars 6,4174E+23 3,3962E+06 2,2794E+11 24 133 253,4 -7,90 3,949E-09 1,697E-09 5,646E-09 487804

Júpiter 1,8986E+27 7,1492E+07 7,7855E+11 13 058 12 732,4 22,10 -1,105E-08 3,087E-09 -7,962E-09 -687913

Moon 7,3490E+22 1,7374E+06 3,8500E+08 1 018 3,7 -1,31 6,527E-10 4,932E-09 5,585E-09 482508

Ganimedes 1,4819E+23 2,6340E+06 1,0704E+09 96 26,8 -17,26 8,629E-09 9,018E-10 9,530E-09 823420

4.4. Celestial Mechanics Locally with the increase of G the centers of mass move

away in proportion of the growth of the universe and with the increase of U the radius of the atoms vary in inverse proportion to that growth, will decrease, therefore all celestial bodies vary too in inverse proportion to that growth, will shrink.

The increase in G will stabilize our Universe. The same gravitational potentials will remain but the greatest distance from the generating mass of the field. The gravitational field will be increasing.

From our perspective we now have a clearer idea of the evolution of the universe.

The stars were created from large clouds formed by large atoms that with the passer of time were subject to a higher G due to the decrease of ρ, causing their contraction, increased pressure and temperature. The planets were formed within these protostars in places where the local gravitic potential was able to concentrate the original masses. If we look at the past we will have to imagine much larger and more fluid stars and planets. In the future the Earth will shrink and become more rigid.

When the universe was half the age that it is today, the Earth would have twice the diameter, 25512.4 km, the our Moon would have a diameter of 6949.6 km, the Sun would have a radius of 1392600 km. The Earth had an average density of 689.4 km / m3 much less dense than today's water. The Earth gravitated in an orbit to the Sun of 7.48x10^10 km and the Moon in an orbit to the Earth of 192500.3 Km. )

4.5. LIGO, Gravitational Wave Detector or ρ Variation?

We are convinced that the gravitational wave detector is nothing more than a detector for the variation of ρ (Universal density of potential energy).

As we saw earlier, ρ interferes with the size of atoms, therefore with the size of objects.

In the case of the detection of waves in the Ligo, it is two black holes with a mass of 29 and 36 solar masses located at a distance of 1.3 thousand millions light years separated from 3000 km gravitating around each other. The impact of this movement on ρ is around ∓ 2.76x10 ^ -13 Kg / m which seems very low and difficult to detect.

On the other hand, the variation in the distance between Earth and the Sun in its annual translation movement causes a much greater variation of ρ, in the order of 4,45x10^ 17 kg / m between perihelion and aphelion,

causing a variation of 6.60E -10 parts, in the length of the objects. In the 4000 m of LIGO the variation should be in the order of 2640 nm.

The terrestrial equatorial diameter will vary between the periods considered above, of 8.42 millimeter.

5. The Annual Removal of the Moon from the Earth, “Ref. [4]”

There are values already known such as: Dc – Actual distance between center of the Earth and

center of the Moon, 385 000 600 meters. Rt – Radius of the Earth, 6 378 100 m Rl – Radius of the Moon, 1 737 400 m D= 385 000 600-6 378 100-1 737 400 D= 376 885 100 meters Dm – Aparent removal, actualy calculated, 3.82+-0.07

cm per year. d – Real annual average removal of the Moon. t0 – Value of the measure of the time of the light beam. tt – Value of the measure of the time of the light beam,

conseding the variation of time.

0D 0.0382t

C+

= (1.5)

Taking into account the shrinking of the Earth and the Moon, we will have:

( )

t

dD d Rt RlDc dt

C

+ + ++= (2.5)

ρ is inversely proportional to the expansion of the Universe [1]"and this proportional to the increase in the radius of gravitation, we will have:

t 0

0 t

t ρt ρ

=

2t

o

1t Dc( )

1tDc d

=

+

(3.5)

t

0

t Dc dt Dc

+= (4.5)

t 0Dc dt t

D=

+ (5.5)


The reading made will be conditioned by the contraction of time on the watch.

In the following year, the clock will mark more time. So it is necessary to take this into account and make the correction.

tt = ( ) dD d Rt Rl Dc dDc d

C Dc

+ + + ++ (6.5)

( ) dD d Rt RlD 0.0382 Dc dDc d

C C Dc

+ + ++ ++= (7.5)

d= 0,02528902m (8.5)

6. The Age of the Universe, “Ref. [4]”

Now we can calculate how many years it took the mass centers to move away as far as today.

I= Dd

(1.6)

I= 15 224 021 588 years (2.6) d=(0,02482560; 0,02575240) m

I=(14 950 088 889; 15 508 209 194) years

7. The Hubble Constant, “Ref. [4]”

For the first time, we can evaluate the expansion of the Universe, from nearby and therefore more accurate medics.

We have the distance from the Earth to the Moon and the value of the moon's annual remoteness from the Earth. In order to obtain the equivalent value of Hubble constant, let's consider Megaparsec.

Mparsec = 3,0856775815*10^22 m T–One year=365.256363 dias=31 558 150 seg

V = 3,0856775815*10^22 0,0252890231558150 385000600

(1.7)

V = 64 225,81 m s−1Mpc−1 (2.7) V = 64,226 km s−1Mpc−1 (3.7) V = (63,049; 65,403) km s−1Mpc−1

Finally, we were able to determine the Huble Constant from very close and thus more reliable data. We avoid errors in measurements made from distant points over time caused by the contraction of time over time.

8. Annual Removal of the Masses in Relation to the Mass Generating the Gravitational Field and the Contraction of Their Radius, “Ref. [4]”

As we saw earlier [2], the masses belonging to a gravitational field move away from the mass that

generates the field, in the same proportion of the expansion of the Universe. ∂R – Annual increase in gravitational radius. ∂RP- Annual retraction in mass radius. I - Age of the Universe

∂R = GravitationalRI

PlanetP

RR

I=∂

8.1. Annual Removal by Year of Planets belonging to the Solar System in Relation to the Sun and Mass Radius Retraction: m (E 10^)

Table 3. Star, Gravitational radius, Annual away from Sun, Star radius, Annual radius retraction

Solar System

Grav. Radius (m)

Annual away (m)

Radius (m)

Annual radius ret.

(mm) Sun 6,96E+08 45,717

Mercury 5,79091E+10 3,80 2 439 700 0,160 Venus 1,08209E+11 7,11 6 051 800 0,398 Earth 1,49598E+11 9,83 6 378 100 0,419 Mars 2,27939E+11 14,97 3 396 200 0,223

Jupiter 7,78547E+11 51,14 71 492 000 4,696 Saturn 1,43344E+12 94,16 60 268 000 3,959 Urano 2,87668E+12 188,96 25 559 000 1,679 Neptun 4,50344E+12 295,81 49 527 998 3,253

8.2. Annual Removal of Moons belonging to the Solar System in Relation to Their Planets: cm

Table 4. Planet, Gravitational radius, Annual away from Planet, moon radius, Annual radius retraction

Gravitational Radius

m

Annual go away cm

Radius m

Annual retraction

Radius (mm) Earth Moon 385 000 600 2,53 1737400 0,057 Mars Fobos 9 377 000 0,06 22200 0,001

Deimos 23 460 000 0,15 12600 0,000 Jupiter

Io 421 700 000 2,77 3642645 0,120 Europa 671 034 000 4,41 3121600 0,103

Ganimedes 1 070 412 000 7,03 5262400 0,173 Calisto 1 882 709 000 12,37 4820600 0,158 Pasife 23 570 790 000 154,83 60000 0,002 Sinope 24 057 865 000 158,03 38000 0,001 Saturno

Tétis 294 619 000 1,94 1062000 0,035 Dione 377 396 000 2,48 1123000 0,037 Reia 527 108 000 3,46 1527000 0,050 Titã 1 221 870 000 8,03 5150000 0,169

Jápeto 3 560 820 000 23,39 1470000 0,048 Urano

Miranda 129 390 000 0,85 471600 0,015 Ariel 191 020 000 1,25 1157800 0,038

Umbriel 266 300 000 1,75 1169400 0,038 Titânia 435 910 000 2,86 1576800 0,052

Oberona 583 520 000 3,83 1522800 0,050


8.3. Annual Removal of Sun in Relation to the Center of Milk Way: m (E 10^)

Table 5. Gravitational radius, Annual away from center galaxy, Sun radius, Annual radius retraction

Gravitational Radius

m

Annual go away

m

Radius m

Annual retraction

Radius (mm) Sun 2,04355E+20 1,342E+10 6,96E+08 45,717

9. Calculation of the Age when Planets and Moons Left Their Original Mass, “Ref. [4]”

As we have already seen, in balanced gravitational fields, the centers of mass will move apart between them and the masses will shrink.

If we go back to the past, the process is reversed, the centers of mass will be much closer and the masses will be much larger. If we step back significantly we will see the moons plunge into their protoplanets and planets in the proto-star.

Will be: Ro – Current radius of the generating mass of the field. R1 - Radius of the mass belonging to the field RR- Gravity radius. On the date of abandon, the gravity radius must be

equal to the sum of the radii of the two masses.

( )Io IRR Ro R1I Io= +

Ro R1Io IRR+

=

9.1. We Will Indicate the Ages when the Planets Left the Protostar Sun. Years

Although the sun is essentially a gas, we will consider that it maintains the plastic conditions as a result of this forecast. We will not take into account the loss of matter by radiation for now.

Table 6. Universe’s Age, Proto-Sun and Planets radius

Age Universe

years Proto-Sun

m Planet radius

m Mercury 1 671 939 774 6 337 500 422 22 214 942 Venus 1 226 259 594 8 640 844 951 75 133 140 Earth 1 043 161 619 10 157 504 683 93 082 731 Mars 843 299 049 12 564 841 659 61 311 372

Jupiter 477 995 542 22 167 401 355 2 276 999 796 Saturn 349 685 472 30 301 284 676 2 623 847 449 Urano 241 112 434 43 945 966 800 1 613 814 606 Neptun 195 879 507 54 094 066 139 3 849 383 333

9.2. We Will Indicate the Ages when the Moons Left Ther Proto Planet. (E 10^)

If we notice, 2 210 325 983 years after the Big Bang, when the Moon separated from Earth, the density was extremely low, about 16.82 kg / m3. Only after counting

another 6 415 000 000 years did the density reach a value similar to that of water today.

Note that at the time of the separation, the Sun had a radius of 4.7938E + 09m and an average density of 4.3 kg / m3.

Table 7. Universe’s Age, Proto-planet and Moons radius.

Earth Age Universe years

Proto-Earth m

Moon m

Moon 2 210 325 983 43 930 322 11 966 658 Mars

Proto-Mars Sat.

Fobos 9 191 975 815 5 624 887 36 768 Deimos 5 803 181 421 8 909 565 33 055 Jupiter

Proto-Jupiter Sat.

Io 6 426 103 410 169 371 030 8 629 756 Europa 5 076 520 282 214 397 991 9 361 394 Ganimedes 4 076 669 903 266 981 575 19 652 043 Calisto 3 065 038 379 355 100 203 23 943 882 Pasife 838 789 935 1 297 578 459 1 088 999 Sinope 830 127 807 1 311 118 290 696 896 Saturn

Proto-Saturn Sat.

Tétis 6 946 011 499 132 093 264 2 327 654 Dione 6 140 208 218 149 428 374 2 784 364 Reia 5 212 622 275 176 019 148 4 459 767 Titã 3 522 617 768 260 465 765 22 257 229 Jápeto 2 004 613 538 457 704 847 11 163 903 Urano

Proto-Urano Sat.

Miranda 6 828 434 124 56 983 894 1 051 434 Ariel 5 693 537 566 68 342 531 3 095 856 Umbriel 4 823 144 672 80 675 740 3 691 154 Titânia 3 798 413 930 102 440 328 6 319 805 Oberona 3 279 746 531 118 640 500 7 068 577

10. Calculation of the Delay in the Gravitational Translation Period, “Ref. [4]”

10.1. Delay in the Earth's Translation Period One of the consequences of the contraction of time and

the expansion of the universe is the delay in the Earth's translation period.

-Ro -Distance Sun/Earth – 1,496x10^11 m -Vo -Earth's translation speed – 29788,64 m/s Will be:

Tt =

I N2πRo I NIVo I

++ (1.10)

Tt = 322πRo I N( )

Vo I+ (2.10)

Tt − T0 = 322πRo I N( ) 1

Vo I

+ −

(3.10)

Tt − T0 = 0,003108944s (4.10)

Tt − T0 = 3,1089442 milliseconds (5.10)


10.2. Delay in the Moon's Translation Period One of the consequences of the contraction of time and

the expansion of the universe is the delay in the Moon's translation period.

With an interval of one year, we will have: -Ro -Distance Moon/Earth – 385000600m -Vo -Moon's translation speed – 1022 m/s

Tt = 0

t

I N2πRo ρIVo ρ

+

(6.10)

Tt =

I N2πRo I NIVo I

++ (7.10)

Tt = 322πRo I N( )

Vo I+ (8.10)

Tt − T0 = 322πRo I N( ) 1

Vo I

+ −

(9.10)

Tt − T0 = 0,000234248 seconds (11.10)

Tt − T0 = 0,23425 Milliseconds (12.10)

11. The Contraction of the Earth and Its Period of Rotation

One of the consequences of the contraction of time due to the expansion of the universe is the delay in the Earth's translation period, but, on the other hand, the shrinking of bodies causes an increase in the angular velocity of bodies, reducing the period of Earth's rotation. We will see.

With an interval of one year, we will have: -Vo -Earth's rotation speed – 355,313 m/s

2 2t t o o

2 2mR W mR W5 5

= (1.11)

Wt=2

o0 2

t

RW

R (2.11)

Wt=2

o0 2

2 to 2

o

RW

ρRρ

(3.11)

Wt=2

00 2

t

ρW

ρ (4.11)

Tt=2

t0 2

o

ρT

ρ (5.11)

Tt = 2 00

T T0

T0 T0

ρIT ( )M MI I NI N (ρ )R I N R I

++ − ++

(6.11)

t 0

2 00

E E0

E0 E0

2 2

22 2 0

2t

T T

ρIT ( )M MI I NI N (ρ )R I N R I

C VrEo 1ρC VrEo *ρ

9,85285 11E

−

×++ − +

+

−

−

= −

=

−×

−

(7.11)

Tt − T0 = -0,008512864 mls/year (8.11)

Bearing in mind the three factors that we said earlier, we will have monthly during the year: August is the first month

Figure 1. 1-year forecast graph for measuring day differential.

The cycle of increasing and decreasing is fundamentally due to the greater or lesser proximity to the Sun. The decreasing direction is due to the decrease in the rotation period.

Since the Earth is not a sphere or other of perfect contour, then its real behavior will depend on the real deformed ones. Phenomena such as erosion, transporting materials from the highest to the lowest areas, including the ocean beds, the current melting with the descent of glaciers and the movement of tectonic plates (earthquakes), can also increase the process of decreasing the Earth's rotation period . The global model is presented.

An article was published on this subject in Sience / Space magazine, entitled The Earth is Spinning Faster Now Than the Last 50 Years

https://interestingengineering.com/the-earth-is-spinning-faster-now-than-the-last-50-years?fbclid=IwAR0WM6i86ohVsrGGN1qUXmO-vi5SGlvnoxWA40ImockAdWKU3CxIU9TkbHM

- 0.05000

- 0.04000

- 0.03000

- 0.02000

- 0.01000

0.00000

0.01000

0.02000

0.03000

1 2 3 4 5 6 7 8 9 10 11 12 13

Monthly change in daily time (mls)


Figure 2. The Earth is Spinning Faster Now Than the Last 50 Years Sience / Space magazine

In the next 5 years, we will have:

Figure 3. 5-year forecast graph for measuring day differential.

12. The Sun's Contraction. Solar Heating

Now that we know about the contraction of atoms and consequently the contraction of celestial bodies, we have to admit that this process leads to the heating of the stars.

Assuming that the temperature increases in proportion to the kinetic energy, we will have;

Ut= tt

MGR

(1.12)

Ut= 00

ttt

0

ρ MGρρ Rρ

(2.12)

Ut=2

00 2

t

ρU

ρ (3.12)

Tt=2

00 2

t

ρT

ρ (4.12)

The temperature that reaches a planet will be given by: TS – Temperature on the Sun TP – Temperature on the Planet RS – Radius of the Sun. DS – Distance from the Planet to the Sun

Tpt =

12 44 St

St 2t

R1 T4 D

(5.12)

Tpt = 0p0

t

ρT

ρ (6.12)

We also have to take into account the contraction of the Sun due to loss of mass.

A)- Theoretical abandonment from the protostar. B)- Real abandon from protostar. C)- Radius of the planets D)– Temperature on the planets The temperatures on the planets were analyzed in three

phases. When the planet was created, when it had an average temperature of -25ºc and when it had or will have an average temperature of + 35ºc.

We consider these last two temperatures because we think they are necessary to make human life viable. - Mass of the planet.

- 0.08000- 0.07000- 0.06000- 0.05000- 0.04000- 0.03000- 0.02000- 0.01000

0.000000.010000.020000.030000.04000

1 5 9 13 17 21 25 29 33 37 41 45 49 53

Monthly change in daily time (mls)


Table 8. Theoretical abandonment from the protostar. Real abandon from protostar, Sun’s radius and solar temperature Radius of the planets, Radius of the planets, Value of gravitational variable, Mass of the planet and value of gravity (E10^)

Grav. Radius

m

Annual go away

m

Radius m

Annual retraction

Radius (mm)

Rotational period

h

Perímetro m

Vel.Rot. m/s

Sun 2,04355E+20 1,342E+10 6,96E+08 45,717 Age of

Universe ly

Sun Radius

m

Planet Radius

m 25,38 4 373 096

974 47 862,457

Mercury 5,79091E+10 3,80 2 439 700 0,160 1 671 939 774 6 337 500 422 22 214 942 1407,5 15 329 087 3,025 Venus 1,08209E+11 7,11 6 051 800 0,398 1 226 259 594 8 640 844 951 75 133 140 -5832,5 38 024 581 -1,811 Earth 1,49598E+11 9,83 6 378 100 0,419 1 043 161 619 10 157 504 683 93 082 731 24 40 074 784 463,829 Mars 2,27939E+11 14,97 3 396 200 0,223 843 299 049 12 564 841 659 61 311 372 24,622778 21 338 954 240,732

Jupiter 7,78547E+11 51,14 71 492 000 4,696 477 995 542 22 167 401 355 2 276 999 796 9,8 449 197 484 12 732,355 Saturn 1,43344E+12 94,16 60 268 000 3,959 349 685 472 30 301 284 676 2 623 847 449 10,566667 378 675 012 9 954,653 Urano 2,87668E+12 188,96 25 559 000 1,679 241 112 434 43 945 966 800 1 613 814 606 -17,23992 160 591 933 -2 587,533 Neptun 4,50344E+12 295,81 49 527 998 3,253 195 879 507 54 094 066 139 3 849 383 333 16,1112 311 193 589 5 365,377

Regarding mercury, we see that a period of

441,000,000 years was possible in which life would be bearable. The gravity value was very low, making it impossible to create an atmosphere and therefore life.

We found no continuity on Venus, whose life span began 195,000,000 years after it ended on Mercury and lasted 462,000,000 years. Gravity would be lower than we currently have on Earth so it would have a more rarefied atmosphere.

The life possibility period on Earth, on the other hand, started 120,000,000 years before it ended on Venus, will continue for a period of 471,000,000 years. At the end of that period, 156,000,000 years are still to go.

On Mars, life will be possible for a period of 486,000,000 years, with an overlap with the life span on Earth of 15,000,000 years. The value of gravity will be lower than that of Earth, so the atmosphere should be rarer.

13. Galaxies and Dark Matter (After information gathered in the GAIA Project.) “Ref. [5]”

13.1. Dark Matter Concept In cosmology, dark matter is a speculative type of

matter that interacts only gravitationally and, therefore, its presence can be inferred from gravitational effects on visible matter, such as galaxies. Although not directly observable, scientists believe that dark matter exists due to its consequences on gravitational effects, as visible matter moves and distributes itself in space, explaining the rotation curves of galaxies.

Figure 4. Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Dark matter can explain the 'flat' appearance of the velocity curve out to a large radius. Dark matter – Wikipedia

13.2. Study Method

13.2.1. Galactic Structure Analysis Four arms were drawn, the outer arm in orange, the

Scutum-Centaurus arm in yellow, the Sagittarius arm in blue and the Perseus arm in red.

We divided the plane of the galaxy into eight quadrants, 0.125 turns, to study the radius value of each arm between each quadrant.

We consider that there is a symmetry at the moment of the galaxy's initial creation and, therefore, we measure what the gravitational radius is for an initial exterior location and which gravitational radii for the locations located in multiple positions of +0.125 turn, that is, in the locations of n + 0125, n + 0.25, n + 0.375, etc.

Figure 5. Milk Way, Marking of arms and 8 quadrants from Milky Way – Wikipedia

It can be seen that the masses located at the same distance from the center of the Galaxy made about the same number of turns. So we can consider the largest radius in which matter is, 62570 ly and make the calculations for every tenth of that radius.


Table 9. Radius and nº of laps

Orange Radius Laps

ly n

62 570 n

55 880 n+0,125

45 960 n+0.250

40 510 n+0,375

34 230 n+0,500

29 000 n+0,625

22 930 n+0,750

19 750 n+0,875

14 960 n+1,000

12 390 N+1,125

Yellow Radius Laps

52 320 n

43 660 n+0,125

35 480 n+0,250

30 410 n+0,375

25 280 n+0,500

19 960 n+0,625

16 220 n+0,750

14 040 n+0,875

10 450 N+1,000

Blue Radius Laps

50 570 n+0,125

42 730 n+0,250

35 520 n+0,375

29 800 n+0,500

25 600 n+0,625

21 200 n+0,750

17 550 n+0,875

13 890 n+1,000

10 940 N+1,125

Red Radius Laps

50 000 n

45 900 n+0,125

39 900 n+0,250

30 420 n+0,375

25 810 n+0,500

20 230 n+0,625

17 450 n+0,750

15 090 n+0,875

10 000 N+1,000

13.2.2. Motion Analysis We take for granted the information that the Sun is

26100 ly (light years) from the center of the galaxy and that it has a rotation speed of 240,000 ms-1 within the galaxy. We were thus able to define the number of turns taken at each point in the galaxy.

For this purpose, we must not forget that the galaxy is expanding, "Ref. [2]", "Ref. [3]", "Ref. [4]" and as such we should consider the average translation perimeter of the Sun, for calculations.

The average perimeter. Being:

L – Total distance traveled by the Sun in its translation movement.

Pm – Average translation perimeter of the Sun. I – Age of the universe, 15 224 021 588 years, "Ref. [4]" VtSun – Sun's translation speed. C – Speed of Light

*365.2564*24*3600* tSunL I V= (1.13)

1,15306x10+23m (2.13)

Pm = 2*π*26100*365.2564*24*3600*C2

(3.13)

7,75752 10 20x ∧ + (4.13)

Nº Laps=m

LP

=148,6378962 (5.13)

Table 10. Radius, Average Perimeter and Rotation Velocity (E10^)

Radius Perimeter Aver. Perimeter Velocity ly m m m/s

6 257 3,71945E+20 1,8597E+20 57 731 12 514 7,43889E+20 3,7194E+20 115 345 18 771 1,11583E+21 5,5792E+20 172 842 25 028 1,48778E+21 7,4389E+20 230 222 31 285 1,85972E+21 9,2986E+20 287 485 37 542 2,23167E+21 1,1158E+21 344 631 43 799 2,60361E+21 1,3018E+21 401 661 50 056 2,97556E+21 1,4878E+21 458 573 56 313 3,34750E+21 1,6738E+21 515 369 62 570 3,71945E+21 1,8597E+21 572 048

Table 11. Radius, Travelled distance, nº of laps and Mass (E10^)

Radius Travelled dist. Nº of laps Mass ly m n kg

6 257 2,7736E+22 149,1422 2,9561E+39 12 514 5,5416E+22 148,9912 2,3601E+40 18 771 8,3040E+22 148,8401 7,9491E+40 25 028 1,1061E+23 148,6891 1,8804E+41 31 285 1,3812E+23 148,5381 3,6652E+41 37 542 1,6558E+23 148,3871 6,3206E+41 43 799 1,9297E+23 148,2361 1,0016E+42 50 056 2,2032E+23 148,0851 1,4921E+42 56 313 2,4760E+23 147,9341 2,1202E+42 62 570 2,7484E+23 147,7831 2,9024E+42

Table 12. Radius, Mass variation, Volume density, Density Accretion Disc with 5 ly thickness. (E10^)

Radius Mass var. M/(4/3πR^3) M/(πR^2*(5ly)) ly kg Kg/m^3 Kg/m^3

6257 2,9561E+39 3,4020E-21 5,6764E-18 12514 2,0645E+40 3,3941E-21 1,3214E-17 18771 5,5890E+40 3,3853E-21 2,1465E-17 25028 1,0855E+41 3,3763E-21 2,9778E-17 31285 1,7848E+41 3,3673E-21 3,8081E-17 37542 2,6554E+41 3,3582E-21 4,6355E-17 43799 3,6959E+41 3,3491E-21 5,4592E-17 50056 4,9048E+41 3,3400E-21 6,2790E-17 56313 6,2808E+41 3,3309E-21 7,0945E-17 62570 7,8223E+41 3,3219E-21 7,9057E-17


13.2.3. Analysis of the Quantity of Matter and Its Distribution

Figure 6. Speed measured from the Solar System (Blue), speed calculated based on the visible masses (orange). Milky Way - Wikipedia

For the calculation of the material necessary to bring about the balance of the previous table, we will consider that only the material inside the calculation radius participates in the calculation of its potential.

2

tSunRVM

G= (6.13)

When considering the measured masses, from Figure 4. we will have an external speed of 183000 m/s for a radius of 51500 ly which will imply a quantity of matter of 2,445 x 10 ^ 41 Kg.

If we take into account the speeds measured by man, from Figure 4. we will have a speed of 238000 m/s, for a radius of 51800 ly which will imply a quantity of matter of 4.159x10 ^ 41 Kg.

As we see the calculation we did, it gives us a quantity of matter of 2,9024x10^42 kg for a speed of 572048 m/s in a radius of 62570 ly, which is 7 and 12 times more than we imagined.

Thus, most of the matter continues to gravitate out of the Accretion Disc.

The distribution of matter necessary to obtain the results we can see, is practically a density of constant, in volume proportion, distributed in the Accretion Disc. There is a variation in density from the periphery to the central zone of +2.13%.

This distribution did not seem unreal to us because the galaxy, before presenting a significant accretion disk, started like all other structures in its spherical shape and the accretion disk captured much of the matter in the respective gravity ray, that is, it maintained the position now associated with the accretion disk.

The existence of Dark Matter does not seem necessary to explain the movement in galaxies.

Perhaps some feel that there is a flaw in the number of stars in the periphery, but if we take into account that considering 5 ly of the disk thickness, we can have between a maximum density around 7,9057^-17kgm^(-3) and a minimum of less than 5,6764x10^-18kgm^(-3). If we discount the star material then this density drops significantly. As the largest amount of this gas will

undoubtedly be hydrogen and helium, they would be very dispersed. Much of that gas and others elements, will continue to belong to the initial spherical surface. If the material is hydrogen, we would have a maximum part in volume of 1,002x10^-23. In the case of being helium we would have a maximum part in volume of 1.663x10^-24, which seems to be undetectable.

Today it is news that the solar system is going through material from a supernova and in reality nothing tells us that it is not residual material that gravitates our galaxy. It can also happen that the phenomenon called star rain is also material that gravitates in the Galaxy crossing the stratosphere.

13.2.4. Values Measured from the Solar System. The values measured from the Solar System regarding

the rotation of the galaxy are apparently at odds with the proposal previously made.

13.2.4.1. Regarding Speeds We will now analyze these measured values in Figure 4.

Corrected the 20,000 m / s to obtain the 240 000 m / s measured by the GAIA project.

Table 13. Radius and Speeds

Radius Speed al m/s al m/s

1 496 270 000 6 157 225 900 8 557 216 070 10 393 219 150 13 002 233 680 17 598 245 310 22 397 247 070 26 000 241 550 30 455 229 760 40 011 253 570 46 104 257 190

What will be equivalent for the radius considered

previously to:

Table 14. – Radius and Speeds equivalents

Radius Speed al m/s

6 257 225 492 12 514 230 963 18 771 234 110 25 028 244 044 31 285 231 828 37 542 247 418 43 799 255 821 50 056 257 631 56313 258 330

Let us compare the two speeds obtained, the apparent

measured from the Solar System, the theoretical and the differential between them.


Table 15. Radius, Apparent speed. Theoretical speed and Differential Speeds

Radius Apparent speed Theoretical speed Differential Speeds

ly m/s m/s m/s

6 257 225 492 57 731 167 761

12 514 230 963 115 345 115 619

18 771 234 110 172 842 61 268

25 028 244 044 230 222 13 822

31 285 231 828 287 485 -55 657

37 542 247 418 344 631 -97 213

43 799 255 821 401 661 -145 840

50 056 257 631 458 573 -200 942

56 313 258 330 515 369 -257 039

Let see its graphic representation.

Figure 7. Radius, V Apparent Med, V theoretical and differential

Now, we see that the Solar System rotates about itself in the same direction as the Milky Way.

Discounting the translation speed of the solar system, we will have:

Table 16. Differential of speeds and respective rotation

Radius Diff.Theor. Vel. Diff.Theor. Vel. Difference

ly m/s m/s m/s

-14 508 -182 269 167 761

-9 037 -124 655 115 619

-5 890 -67 158 61 268

4 044 -9 778 13 822

-8 172 47 485 -55 657

7 418 104 631 -97 213

-4 179 161 661 -165 840

-2 369 218 573 -220 942

-1 670 275 369 -277 039

Rotation (m/s/ly) 0,2565 9,1425 +8,8860

Let's see its graphic representation.

Figure 8. Radius, V Apparent Med, V theoretical and differential centered on the Solar System.

As it turns out, Milk Way has an apparent rotation of 0,6560 ms−1ly theoretical of 9,1425 ms−1ly, t follows that the solar system has a same rotation to the Milk Way of 8,886 m s−1ly . This rotation is what causes the discrepancy between measured and actual values.

13.3. Verification, Pinwheel Galaxy We are going to look at another galaxy in order to

verify if the theory pointed out is verifiable in other galaxies with Accretion Discs and arms.

For this purpose, we chose the Pinwheel galaxy, with a diameter of 170000 ly.

Pinwheel Galaxy has a rotation speed of 241000 m / s on its periphery

Figure 9. Pinwheel Galaxy, Marking of arms and 8 quadrants from Milky Way – Wikipedia

-250,000

-200,000

-150,000

-100,000

-50,000

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

1 2 3 4 5 6 7 8 9

Solar System rotation in the GalaxyRot. Apar. Gal. - Rot. Real Gal. - Rot. Syst. Solar.

-250,000

-200,000

-150,000

-100,000

-50,000

0

50,000

100,000

150,000

200,000

250,000

300,000

1 2 3 4 5 6 7 8 9

Diferencial velocity in relation to the velocity of solar system.Rot. Apar. Gal. - Rot. Real Gal. - Rot. Solar System.


Table 17. Radius and nº of laps

Green Radius Laps

29 530,0 n0+0,375 47 770,0 n0+0,250 67 830,0 n0+0,125 85 000,0 n0 Yellow Radius Laps

20 340,0 n1+0,75 24 660,0 n1+0,625 29 560,0 n1+0,500 34 530,0 n1+0,375 39 450,0 n1+0,250 43 830,0 n1+0,125 49 200,0 n1

n1=n0+0,24109 Red

Radius Laps 25 420 n2+0,25 42 000 n2+0,125 60 000 n2

n2+no+0,17379

Blue Radius Laps

19720 n3+0,375 24290 n3+0,250 31410 n3+0,125 38730 n3

n3+0,43795 Magenta

Radius Laps 12000 n4+0,375 19720 n4+0,250 32740 n4+0,125 64370 n4

13.3.1. Motion Analysis We take for granted the information that it has a

rotation speed of 241.000 ms−1 at the outer edge of the galaxy. We were thus able to define the number of turns taken at each point in the galaxy.

For that purpose we must not forget that the galaxy is expanding, "Ref. [2]", "Ref. [3]" and "Ref.[4]" as such we should consider the average perimeter for the calculations.

Being: L – Total distance traveled by the stars at the outer edge

of the galaxy. Pm – Average translation perimeter. I – Age of the universe 15 224 021 588 years. VtSun – Travel speed at the edge of the galaxy. C – Speed of light

L= I ∗ 365.2564 ∗ 24 ∗ 3600 ∗ VtSun (7.13)

L= 1,1579∗ 10^ + 23 m (8.13)

Pm= 2* *85000*365.2564*24*3600*2

Cπ (9.13)

Pm =2,5264x10^+21 m (10.13)

Nº laps=m

LP

=45,83075 (11.13)

Table 18. Radius, Average Perimeter and Rotation Velocity (E10^)

Radius Perimeter Average Perimeter Velocity ly m m m/s

8 500 5,0528E+20 2,5264E+20 23 556 17 000 1,0106E+21 5,0528E+20 47 232 25 500 1,5158E+21 7,5792E+20 71 030 34 000 2,0211E+21 1,0106E+21 94 948 42 500 2,5264E+21 1,2632E+21 118 988 51 000 3,0317E+21 1,5158E+21 143 148 59 500 3,5370E+21 1,7685E+21 167 430 68 000 4,0422E+21 2,0211E+21 191 832 76 500 4,5475E+21 2,2738E+21 216 356 85 000 5,0528E+21 2,5264E+21 241 000

Table 19. Radius, Travelled distance, nº of laps and Mass (E10^)

Radius Travelled dist. Nº of laps Mass ly m n kg

8 500 1,1317E+22 44,79552 6,6856E+38 17 000 2,2692E+22 44,91055 5,3760E+39 25 500 3,4126E+22 45,02557 1,8237E+40 34 000 4,5617E+22 45,14060 4,3450E+40 42 500 5,7167E+22 45,25562 8,5296E+40 51 000 6,8774E+22 45,37065 1,4814E+41 59 500 8,0440E+22 45,48567 2,3644E+41 68 000 9,2164E+22 45,60070 3,5472E+41 76 500 1,0395E+23 45,71572 5,0761E+41 85 000 1,1579E+23 45,83075 6,9982E+41

Table 20. Radius, Mass variation, Volume density, Density Accretion Disc with 5 ly thickness. (E10^)

Radius Mass var. M/(4/3πR^3) M/(πR^2*(5ly)) ly kg Kg/m^3 Kg/m^3

8 500 6,6856E+38 3,0690E-22 3,47821E-18 17 000 4,7074E+39 3,0848E-22 6,9922E-18 25 500 1,2861E+40 3,1006E-22 1,05421E-17 34 000 2,5213E+40 3,1165E-22 1,4128E-17 42 500 4,1846E+40 3,1324E-22 1,77502E-17 51 000 6,2845E+40 3,1483E-22 2,14086E-17 59 500 8,8296E+40 3,1643E-22 2,51035E-17 68 000 1,1828E+41 3,1803E-22 2,8835E-17 76 500 1,5289E+41 3,1964E-22 3,26032E-17 85 000 1,9221E+41 3,2125E-22 3,64083E-17

13.3.2. Analysis of the Quantity of Matter and Its Distribution

Analysis of the quantity of matter and its distribution.

2

tSunRVM

G= (6.13)

Once again we verify that the mass distribution is very close to the proportionality to the radius cube and that its density is practically constant throughout the radius. In this galaxy we find that this density decreases from the periphery to the center by -4.47%.

The distribution of matter necessary to obtain the results we can see, is practically a density of constant, in


volume proportion, distributed in the Accretion Disc and all spherical gravitational field.

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© The Author(s) 2021. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

published by science and education publishing doi:10.12691

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