   # THE CIRCULAR MOTION AND THE FINITE FREE SPACE

with a limit in the distance Attention! They exist translational errors.

Attention to the decimal point. This is a different mark for many countries

©2009 ISBN 978-960-931414-5 | ©2010 ISBN 978-960-93-2431-1 | ©2012 ISBN 978-960-93-4040-3

LIKELY LIMITS OF THE SIMPLEST RELATIONS AND OBSERVATIONS

If the most minimum rate of acceleration amin is expressed by the constant G - that is fixed with masses M of one kilo where are attracted with force F when are found in distance 1m - then this rate amin in combination with the known limit of superior speed c us helps we advance in certain first calculations about the likely limits of the Universe. With the simplest conjecture that is based on two universal constants (c and G) finds following potential sizes of time and length (length of radius, diameter or perimetric) :

(The supposal of accelerating mass 1kg with a force 6,6725 × 10-11 N and with a limit in the superior speed c was the initial thought from that began this effort to expressed with terms of physics the rational interpretation of the Universe as completed and constant on contrary to individual / material things).

WE SUPPOSE that a force F size 6,6725 ×10-11 Ν accelerate a body mass =1kg

1N =1kgr • m/sec2

1ly = 9,46073 ×1015 m

1 Mpc = 106 pc ≈ 3,2615 ×106 ly x 9,46073 ×1015 m ≈ 30,856170 × 1021 m

The acceleration is result general from the formula a = F/m

a =F/Ma = 6,6725 ×10-11 Ν /1kg = 6,6725 × 10-11 m /sec2

In how much time T the speed of mass M =1kg will become equal with the speed of light c, when it begins from null speed, that is to say in how much time it will become Vm=c ? Law of the speed :

V=a t

a=V / t → t = V / a

If  V=c  then  Tm = 2,9979245 × 108 m/sec / 6,6725 ×10-11 m/sec2 = 4,49295 ×1018 sec = c/G

A body M=1kg and acceleration a=6,6725 ×10-11 m/s2 takes the speed c in time interval T=4,49295 ×1018 sec, in other units 142,372994125 ×109 years. In this time interval T how much distance S in linear motion (straigh line) body can have covered ? This we find from the law of distance : S=1/2 a t2

Sm = 1/2 × am × tm2 (Distance S of mass m = 1kg)

Sm = 1/2 × (6,6725 ×10-11 m/sec2 ) × (4,49295 ×1018 sec)2 = 6,73475432 ×1026 m

1pc (parsec)= 3,086333 ×1016 m

6,73475432 ×1026 m / 3,086333 ×1016 = 21,821216 ×109 pc

Also, if we multiply time T= 4,49295 ×1018 sec by the meters where light moved per sec, then we find the meters where light will have moved in this number T, with its regular speed from start. In time 4,49295 ×1018 sec of a body 1kg, light will have moved twofold distance Slight :

S light= (4,49295 ×1018 sec) × (2,997924 ×108 m/sec)= 1,346952 ×1027 m = c2/G

IN PARSEC:

1,346952 × 1027 m / 3,086333 × 1016 = 4,36424 × 1010 pc

Finally, in time Τ=4,49295 ×1018 sec where the body M=1kg is need to arrives in speed of light c with acceleration a= 6,6725 ×10-11 m/sec2 , light in same time do double distance S Universe ( 6,73475432 ×1026 m × 2 )= 1,346952 ×1027 m (Theorem Merton on the speed until a limit in the increase).

 Dividing time T = Vc / amin = 4,49295 ×1018 sec by 2π we find : T / 2π = 4,49295 ×1018 sec / 6,2831852 = 7,150752 ×1017 sec   (7,150752 ×1017 sec) × (31,68808781 ×10-9 ) = 2,2659365 ×1010 = 22,659365 ×109 years   1 earthly year ≈ 31,5576 × 106 sec  |  1sec = 31,688087 × 10-9 year

We supposed that a mass 1kg is accelerated with regularly applied the force that results from the constant G of gravity. Actually, the free space is not neither level neither absolutely empty.

SAMPLES

ΤUniverse = 4,492955 ×1018 sec

SUniverse = 6,734769 ×1026 m = 2,1823619 ×104 Mpc (1st scenario)

SUniverse = 1,346954 ×1027 m = 4,364724 ×104 Mpc  (2d scenario)

SUniverse = 6,734769 ×1026 m / 2π = 1,07187183 ×1026 m = 3,473337 ×103 Mpc  (3d scenario)

SUniverse = 1,346954 ×1027 m / 2π = 2,14374297 ×1026 m = 6,946674 ×103 Mpc  (4d scenario)

Do not lose the continuity !

 Useful relations [-]

CONCISE TABLE OF SAMPLES ABOUT MAX LENGTH S and TIME T OF UNIVERSE

 Slight Universe = 1,346954 ×1027 m = c2 / G T Universe = 4,492954 ×1018 sec = c / G Smass Universe = 6,73477 ×1026 m 4,492954 ×1018 sec = 142,37312 ×109 years R Universe = 2,14374 ×1026 m T Universe / 2π = 7,150758 × 1017 S Universe / 2 = 6,73477 ×1026 m T Universe × 2 = 8,985908 ×1018 c2 / S Universe = 6,6725 × 10-11 =G T Universe × π = 1,41150 ×1019 S Universe2 = 1,814285 × 1054 T Universe2 = 2,01866 × 1037 1 / S Universe = 0,7424158 × 10-27 =G/c2 1 / T Universe = 2,225709 × 10-19 =G/c S Universe / T Universe = 2,997925 × 108 =c R Universe2 = 4,59562 × 1052 1/ R Universe = 4,66474479 × 10-27 D Universe2 = 1,838257 × 1053 1/ D Universe = 2,33237 × 10-27 For Smass Universe = 6,73477 ×1026 m Length of arc per degree = 1,87076 ×1024 m For Slight Universe = 1,346954 ×1027 m Length of arc per degree = 3,74153 ×1024 m #### THE CONSTANT Ηubble IN KILOMETERS AND PERIOD

H 70,1 km/sec /Mpc = 70,1 km/sec / 3,086 ×1019 km

T = S / V = 1/f → PERIOD ΤH = 3,086 ×1019 / 70,1 = 4,402282 ×1017 sec

LENGTH SHUBBLE if the case 70,1km according to the formula : c / f  = c × T = λ

c  T = 2,997924 ×108 × 4,402282 ×1017 = 1,31977 ×1026 m

LENGTH SHUBBLE if the speed is 50km (rounded) :

c T = 2,997924 ×108 × 6,1720  ×1017 = 1,850319 ×1026 m

(Time TH again near in the result Tuni = c/G = 4,49295 ×1018 sec)

1pc =3,086 × 1016 m - 1 Mpc = 3,086 × 1022 m = 3,086 ×1019 km - 1year (y) = 31,5576 ×106 sec

1light year (ly) = 9,460730 ×1015 m

Attention! Many translational errors are exist

* Attention to the decimal point. This is a different mark for many countries.

Some thoughts of the investigation for mathematic formulation of the physical interpretation (of a complete Universe that appeared as free space). The aim was to become comprehensible: 1) The direct rela­tion of Hubble's constant (H) to the (balanced) energy of the " free " and finite space. 2) The close relation of Hubble's constant with the limit of a longest distance of the free space and 3) therefore the close relation of Hubble's constant to the structure of matter (since explanation, that matter is created with oscillations of balanced energy of the free space).

Hubble's Law : V=H d (the rate of "expansion"). The relative speed of removal between of two galaxies (because the phenomenon about so-called expansion of the free space) is proportional with distance d. The rate of removal initially had been found with higher speed and is calculated near: Hubble constant =70,1km/sec/ per 1Mpc. In certain theories it forecasted that this value of speed was not always constant and it is changed in time.

The constant Η= 70,1 km / sec / Mpc (In each 1Mpc distance away, the speed is increased  70,1Km/sec)

1 Mpc= 106 pc,

1pc= 3,2615 ly  = 3,0856778 ×1016 m

1 Mpc = 3,086 ×1016 × 106 = 3,086 × 1022 m

If the maximum speed of removal is fixed in 299792 km/sec (v = c) then finds as largest distance dmax :

d =c /H

dmax = (2,99792 ×105 km/s) / 70,1 = 4,276633 ×103 Mpc = 4,276633 ×109 pc

4,276633 × 109 pc × 3,2615 ly = 13,9482 ×109 ly

13,9482 × 109 × 9,46073 × 1015 m = 1,31960518 ×1026 m

4,276633 × 109 pc × 3,086 ×1016 m = 1,319768 ×1026 m

Conversely:

Hubble = c / dmax → c / 4,276633 ×103 = 70,1km/sec / Mpc

If the speed of removal is not same for the every Mpc distance, however always the limit for the maximum speed (c) exist and then a maximum distance dmax

H = V / dMpc = c / dmax

If the speed V for every Mpc is change, then we observe in second relation that only the average distance d will vary.

► From the relation T = S / V = 1/f  we find a time interval. The distance in kilometers is for each Mpc = 3,086 ×1019 km. The speed of removal... 70,1 km for each Mpc away →

ΤH = 3,086 ×1019 / 70,1 = 4,402282 ×1017 sec

The same time interval T we find from the relation T= Smax/Vmax

ΤH = 1,3197 ×1026 / 2,99792 ×108 = 4,40205 ×1017 sec

In this time interval Τ = 4,40205 ×1017 sec the removal Smax is the maximum with maximum speed c

 We observe the relation :   S1Mpc / VHubble =  Smax / Vmax = T

If dmax = Smax

The speed V=70,1 km/sec is result from relation V= S/T

VH = 3,086 ×1019 / 4,402282 ×1017 = 70,1 km/sec

While, if we take the maximum length Smax then we find the maximum speed c :

V= S/T

VH = 1,3197 ×1026 / 4,402282 ×1017 = c

► We find a time interval 4,492954 ×1018 sec in which a mass m=1kg needs until comes to in speed of light c with acceleration a= 6,6725 ×10-11 m/sec2 and in distance S=1,346954 ×1027 m for light (or S=0,673477 ×1027 m = 2,182362 ×104 Mpc for the 1kg mass). What speed of removal do we find for this mass per 1Mpc away ?

V = 3,086 ×1019 / 4,492954 ×1018 = 6,8685 km/sec

That is to say, if the Hubble's constant6,8685 km/sec /Mpc then we find the known maximum distance :

dmax =c /H = 4,364744 ×104 Mpc = 1,34696 ×1027 m  (= c2 / amin )

 We observe the relation :  c / VHubble in m/s =  dmax in meters/ 3,086 ×1022 or  c / VHubble in km =  dH in Mpc/ 1Mpc

The acceleration / deceleration ±a = 6,6725 ×10-11 m/s2 with which mass 1kg reached at the speed of light c or it was decreased by this speed, we can find from following relation :

c VH / 1Mparsec (2,99792 ×105 km/s) (6,8685 km/s) / 3,086 ×1019 = 6,6725 ×10-14 km/s2

c VH / 1Mparsec (2,99792 ×108 m/s) (6,8685 ×103 m/s) / 3,086 ×1022 = 6,6725 ×10-11 m/s2

From the speed of Hubble's constant = 70,1 km/sec we find :

c VH / 1Mparsec (2,99792 ×108 m/s) (7,01 ×104 m/s) / 3,086 ×1022 = 6,80993 ×10-10 m/s2 We observe the relation :   C VHubble / S1Mpc = Vmax Vmax / Smax = a

Vmax = C

 HUBBLE'S CONSTANT 70,1 km/sec / Mpc with limit of the speed c THE HUBBLE'S CONSTANT AS IT WOULD BE 6,8685 km/sec / Mpc Time interval Τ= 4,402282 ×1017 sec Time interval Τ= 4,492954 ×1018 sec Maximum length S= 4,276633 ×103 Mpc = 1,319768 ×1026 m Maximum length S= 4,36424 ×104 Mpc =  1,34696 ×1027 m Pace of change ±a = 6,80993 ×10-10 m/s2 Pace of change ±a = 6,6725 ×10-11 m/s2

► I will place in your mind something above of an astonishing idea, an explosive research: The Hubble's constant says to us about a speed V increased in each 1 Mpc distance away. What speed results for distance away 1m only? It needs a simple transformation in the units.

VH = c 1m / dmax

VH = 2,997924 ×108 ×1m / 1,319768 ×1026 = 2,271553 ×10-18 (m/s) /m = 1 / ΤH

Hubble = V / d3,086e22 = c / dmax σε μέτρα

where V= 7,01 ×104 m/s

We find like a speed the inverse of the maximum time 1/Τ=V/S that we find from the relation :

T S1Mpc / VHubbleSmax / Vmax = 3,086 ×1019 / 70,1

What speed results for distance 1 m away, when we insert the maximum distance, in according to the script about the accelerating mass of the 1 kg ?

VH = c 1m / dmax

2,997924 ×108 / 1,34696 ×1027 = 2,225696 ×10-19 (m/s) /m = 1 / Τuni

Hubble = c / dmax in meters = V / d3,086e22

where V= 6,87 ×103 m/s

We find like a speed the inverse of the maximum time 1/Τ=V/S that we find from the relation :

T S1Mpc / VHSmax / Vmax = 3,086 ×1019 /  6,8685 = 4,492975 ×1018 = c / amin

<•> That is to say, we find that the Hubble's speed is the reverse of a maximum time interval in which the maximum removal is realised. In shorter distances are correspond less speeds, that they are subdivisions of the reverse of the Universe's "age".

VH = c d / dmax = d / TH

For d = dmax the speed approaches V= c

For d = dmin the speed approaches V= Vmin

Because this speed is speed per length Mpc, if we erase mathematically the units of length, then it remains a frequency V/Mpc = f. This speed per longer distance gives frequency that is very lower and would is better to we speak reversely about a time interval. But, if we calculate this speed per shortest distance, then the frequency is higher. However, the speed that we calculate it varied in reference with a distance, this is always the maximum speed for all bodies, because all bodies are founded in a maximum distance in reference with another point after a longer distance. Therefore, a speed between the bodies or a frequency for fluctuations on the free space, that is varied after a distance? An expansion of free space or wave change of the free space, where after the longer distance, the length of waves appears increased?

Attention! Many translational errors are exist.

 1st PUBLICATION www.kosmologia.gr ©2009-10 ISBN 978-960-93-2431-1

What speed come out for distance away per radius (calculated with electron charge) approximately re = 0,2817936 ×10-14 m if the Hubble speed = 2,225696 ×10-19 (m/sec) /m ?

2,225696 ×10-19 m/sec          per 1 m

How speed V           per length re ?

V2,225696 ×10-19 × 0,2817936 ×10-14 / 1m = 6,271868 ×10-34 m/sec

While for the speed of constant Hubble = 2,271553 ×10-18 (m/sec) /m = 70,1 km / Mpc

V → 2,271553 ×10-18 × 0,2817936 ×10-14 / 1m = 6,40109 ×10-33 m/sec

Close to constant h = 6,62606 ×10-34

What speed come out for distance away per Compton's length of electron λ=2,4263 ×10-12 m  if the Hubble speed = 2,225696 ×10-19 (m/sec) /m ?

2,225696 ×10-19 m/sec           per 1 m

How speed V           per length λe ?

V → 2,225696 ×10-19 × 2,4263 ×10-12 / 1m = 5,4002 ×10-31 m/secV=λe / Tuni

Very near to mass of electron, after Me / 5,4002 ×10-31 = 1,686859

With this speed is result, moreover: For electron's period Te = 0,80933 ×10-20 sec

5,4002 ×10-31 / Te = 5,4002 ×10-31 / 0,80933 ×10-20 = 6,6725 ×10-11 m/sec2 = G

From all previous relations, we observe a small coincidence at least. The maximum distance in to free space (4,276633 ×109 pc), as it results with the Hubble's constant (which emanated from the observation of many distant galaxies, with the newer technical tools and methods and from the analysis of red shift of light), approaches suspectly the maximum distance that results (with the simpler and initial intellectual experiment) from the acceleration of gravity with mass 1kg (2,1821216 ×1010 pc). However the rate for the " removal " of galaxies is considered constant. For each 1Mpc distance, the speed increases with the same quantity ≈70,1km or similar speed.

Also we observe, that time t (4,49295 ×1018 sec ≈14,237312 ×1010 years) that hypothetically the mass m of 1kg needs to take the speed of light c does not appear irrelevant than the so-called age of the Universe. It could be an irrelevant number. With few numerical subterfuges it can are revealed relations with other known formulas of physics.

From the first observations on motion in the finite free space (with a limit in the maximum length of removal and divergence from the straight line motion) and from the analysis of Hubble's constant, we approached in a mathematic solution in question, on the relation between of a finite space with matter and with electro­magnetic phenomena, but the answer was not completed. The tight relation between the free space with matter has resulted theoretically from the philosophical interpretation of a Complete and simultaneous Universe. This relation is obligatory, not because thus we like it, but because only with this close relation (between structure of matter and change in the balanced energy of finite space) a multitude of phenomena are interpreted and revealed their relations and relations of phenomena that had not been observed in our experience and many of known phenomena are confirmed, without conflict with experience. Because the close relation between matter and finite space was known and indubitable in me, through the physical interpretation that I have formulated longly-lasting, with this view I thought easily the above intellectual experiment. Immediately I suspected such a relation about the constant of Hubble with change in the balanced energy of the finite space in its microscopic dimensions. Therefore a close relation with the electro­magnetic phenomena and with the structure of matter.

From the first reasonable questions, which are remain unanswered up to here they are: The increase of speed (of removal) does equalized to the speed of light c with the increase of distance? Is this speed superior? What can exist when we observe in the maximum distance of free space? How could replace the speed of space expansion with changes at frequency due to another phenomenon, which is related to the wave structure of space?

The phenomenon about motion of a material body and speed of a body also a small child can perceives. When however, we describe the phenomenon of motion or its change without a concrete material thing exists, the term of "speed" possibly is not best-aimed term. Still vaguer it is, when we handle the term "speed" in order to we describe a phenomenon of removal between galaxies, that happens without their own motion in to space, but with the inflation of space, with a gullible view about the space, as if the space was a material body with dimensions, as in the case of a bubble. We would wait from a scientist to thinks more intelligently and at least, he suspects the phenomenon of a wave change and the measurement of motion with the term of "frequency" and not the "speed". A phenomenon which we know well that it exists in substructure the nature, without some concrete material body, and we call it electro­magnetic phenomenon.

A most of unforeseen and important observations in the course of mathematic investigation in here, it is the possibility with the simplest numerical calculations and beginning from three physical constants (c, G, h) are result numbers, that are involved in the microscopic structure of matter. With the same constants come out numbers that they describe astronomical traits of the physical world. With common formulas of physics (even wrongly) and using sizes and relations of world in its biggest dimensions, we can to calculate sizes and relations of subatomic world, in microscopic dimensions and reversely. With the same initial numbers, with which we calculate invisible small quantities and their relations, with same numbers we can to " construct " our visible Universe in theory! The reverse of certain large numbers (for example a longest time ≈1019 sec, and largest length ≈1027 m) with these themselves are presented quantities, that we meet in the structure of matter and are not irrelevant numbers. Particularly, when in the calculations used the known physical constants, in order to we find quantities and sizes about the limits of the Universe, then from mathematical view it is obvious, that the quantities and sizes which we will find, they should to be connected with the quantities and sizes, which we find when we use the same physical constants for calculations about microscopic world. The numerical relations and formulas that need for the description of world with biggest dimensions, same they need for the description of changes and motions in microscopic dimensions. Naturally, this possibility confirms the theoretical ascertainment, according to which the theory for a Completed Time or Universe it imports in general and theoretically the necessary relation and coexistence between a minimal limit with a maximum limit, also imports a relation for the stability of limits (of time, length, speed, energy) at their change.

In the physical explanation of a complete universe already we have concluded the connection between of material carriers with the existence of simultaneous quantity of energy, which is presented with the form of " empty " but finite space. Already we have concluded the relation of nuclear force with the dynamic connection that have the material things in the minimal distance of the finite space and immediately with the total energy of the completed Universe. Already we have comprehended how the completed Universe is permanently present and participates in the presence of individual things, even in most microscopic dimensions. The research in microscopic dimensions is research about the limits of the Universe. The existence of limits in the Universe and in certain physical activities would not be revealed by the research in microscopic dimensions, if the limits did not exist. They are exist limits in the Universe such as roughly we have determined them and for this reason, we have the advantage we detect limits from observations in the most microscopic activities and not only if we travel in space.

CORRECTIONS AND INVESTIGATION WILL BE CONTINUED...

 Now, it is not privilege of few leading physicists to think about the Universe and its limits with terms of Science and with language of numbers. Whoever can thinks and searches theoretically with knowledge of medium education! Because the Universe has constant min and max limits... forever and everywhere.

MASS AND ENERGY: TWO SIDE OF VELOCITY IN THE STRUCTURE OF MATTER

#### THAT DIRECT RIGHTLY THE RESEARCH  In the physical explanation of a complete universe already we have concluded a substantive connection between material carriers with a simultaneous quantity of energy, which is presented to the form of " empty " and finite space. Already we have concluded a close relation of nuclear force with dynamic connection that material things have in minimal distance of the space and with the total energy of the complete Universe. Already we have comprehended how the complete Universe is permanently present and participates in the presence of individual things in most microscopic dimensions. The research in microscopic dimensions is a research about the limits of the Universe. The existence of limits in the Universe and in certain physical activities would not be revealed by the research in microscopic dimensions, if the limits did not exist. They are exist limits to the Universe such as roughly we have determined them and for this reason, we have the advantage to detect limits from observations in the most microscopic activities and not only if we travel in space.

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