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with a limit in the distance


 Attention! They exist translational errors

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


The longest distance (removal) in the finite and isotropic space theoretically corresponds in divergence 180. The return behind (approach) in the initial point begins in the -180 degrees.

The variation of the straight line motion, in the perfect circle theoretically becomes the longest divergence in the 90 degree and at the return in -90 (or 270) degrees. 

circular motion

If this length of longest distance in the finite space, we dynamically see it so as a body that is moved with constant speed. In equal times are covered equal arcs. The longest length of the first semicircle (arc of 180 degrees) is covered in the same time lapse t that is covered the other arc of 180 in the return. In the circular motion with constant speed it is considered that exists acceleration (centripetal), because the address of motion changes. 

It can become a paradoxical theoretical observation in the phenomenon of circular motion, in that leads the view about the curve space, that imposes a space finite and isotropic, with a limit in the longest removal for all things. We can consider the phase of removal such as a motion slowed down, concerning a arbitrary point of departure. The rythm of deceleration increases with the lapse of time and, in the longest distance that finds in the 180 degrees, where the removal stops, we can consider that the speed is zeroed for a moment.

In the phase of return and approach behind in the initial point, the motion can be considered accelerating to the initial point, up to speed acquires the biggest value in the point of departure. 

In the circular motion coexist two opposite motions and equivalents two opposite time intervals and intermediary phases, where the angle of divergence of straight line becomes biggest. The observation of circular motion with constant speed and its cross-correlation with equivalent phenomenon of regular deceleration or acceleration in straight line remind us an other strange equivalence in the physics. It reminds the coincidental equivalence that it tried unsuccessfully understands Einstein, about the inertia mass and gravitational mass. A observer that is accelerated in a closed laboratory and pushed contrary to the address of the motion he can consider, that a gravitational field attract him, if he does not find a way to search outside of his laboratory. Similarly, here we observe the case of the circular motion it is described as phenomenon of straight line motion, that is altered and reversed periodically

The above short description of the circular or periodical motion such as a phenomenon of immobility or stagnant situation and such as a phenomenon of periodical change with limits and inversion in the motion acquires particular theoretical interest from the application of this idea in the motion of the light. Do not forget, that the motion of the light does not become only to a direction (as the material bodies) except when the conditions prevent its transmission. After we immediately consider the finite space with a limit in the longest distance and inevitable the divergence from the rectilinear motion, comes in the brain the thought about the propagation of the light. Because the radius in the finite space (not Euclidean space, as if the motion becomes always on the surface of very big ball) cannot be unlimited straight line and becomes circumference with the increase of the distance. How it can influence the motion of electromagnetic waves, this phenomenon of obligatory divergence of the straight line, which we can consider also as if an opposite and small force does prevent smoothly the rectilinear motion ? The " spheres " of the waves they are removed in a radius where ceases to is straight line with the increase of distance (and this means not concentric circles and deformity in the spherical form).

It exists an important detail still, when we observe this detail in the above theoretical form of the equivalent circular motion. We can detect some phenomena of high speed in periodical change. This detail results when the circular motion is not perfect circular, but almost circular (≈360). In the case where the circular motion, (which we describe equivalent as periodical phenomenon of deceleration/acceleration), does not become in perfect circle 360, then the two phases of longest removal and approach in the initial point, probably are not precisely equal. In other words, the rythm of equivalent deceleration and the rythm of equivalent acceleration and the times that develop these two motions possibly have a small difference. 

They exist clues, that with a very small difference in these two phases of the circular motion (or in corresponding phenomena of periodical change) in the microscopic creation of matter is result a leftover or a alleviation of energy or a new phenomenon...

If the rythm of deceleration (in a natural process) differ from the rythm of acceleration (at the inversion of process), then the time interval t in which the speed Vmax is acquired theoretically will  differ than the time interval t' in that the speed is decreased. The rythm of deceleration with the rythm of acceleration (in the natural changes) likely they are not equal and this inequality rather is related with that the motion is not interrupted perfectly and the changes does not acquire null value. This thought springs from a lot of observations. (...)


They exist all clues, that multitude of particular phenomena that is observed in the structure of matter and which can be described with different terminology in the scientific area, they constitute special cases of more general phenomena that are observed in the daily experience and are analyzed with philosophical thought. Phenomena, such as are the motion, change of speed, time interval, covered length, circular motion, frequency and rythm etc.

 Attention! Many translational errors are exist.




If the most minimum rythm 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 rythm 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 script 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 x 10-11 N and with a limit in the superior speed c, was the initial thought from that began the effort to expressed with terms of physics, the philosophical interpretation about the Universe as completed and constant on contrary to the individual materially things).  


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

1N =1kgr m/sec2

1ly = 9,46073 x1015 m

1 Mpc = 106 pc ≈ 3,2615 x106 ly x 9,46073 x1015 m ≈ 30,856170 x 1021 m


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

a =F/Ma = 6,6725 x 10-11 Ν /1kg = 6,6725 x 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 ? It's law of the speed : 

V=a t

a=V / t → t = V / a

If  V=c  then  Tm = 2,9979245 x 108 m/sec / 6,6725 x 10-11 m/sec2 = 4,49295x1018 sec = c/G


A body M=1kg and acceleration a=6,6725 x 10-11 m/s2 takes the speed c in time inerval T=4,49295 x1018 sec, in other units 14,2372994125 x1010 years. In this time interval T how much distance S in linear motion (straigh line) it can have covered ? This we find from the law of distance : S=1/2 a t2

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

Sm = 1/2 x (6,6725 x10-11 m/sec2 ) x (4,49295x1018 sec)2 = 6,73475432 x1026 m


1pc (parsec)= 3,086333 x1016 m

0,673475432 x1027 m / 3,086333 x1016 = 2,1821216 x1010 pc


Also, if we multiply the time T= 4,49295 x1018 sec multiplied by the meters where the light moved per sec, so we find the meters where the light will have moved in this number T, with its regular speed from the start. In time 4,49295 x1018 sec of the body 1kg, the light will have moved twofold distance Slight :


S light= (4,49295x1018 sec) x (2,997924 x108 m/sec)= 1,346952 x1027 m = c2/G


1,346952 x1027 m / 3,086333 x 1016 = 4,36424 x 1010 pc


Finally, in the time Τ=4,49295 x1018 sec where the body M=1kg is need to arrives in speed of the light c with acceleration a= 6,6725 x 10-11 m/sec2 , the light in same time do double distance S Universe ( 0,673475432 x1027 m x 2 )= 1,346952 x1027 m (Theorem Merton about the speed until a limit in the increase).


Dividing the time T = Vc / amin = 4,49295x1018 sec by 2π we find :

T / 2π = 0,449295x1019 sec / 6,2831852 = 0,07150752 x 1019 sec


(0,07150752 x 1019 sec) x (31,68808781 x 10-9 ) = 2,2659365 x 1010 = 22,659365 x 109 years


1 earthly year ≈ 31,5576 x 106 sec  |  1sec = 31,688087 x 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.





ΤUniverse = 4,492955 x1018 sec  or  fUniverse = 2,225706689 x10-19 Hz

SUniverse = 6,734769 x1026 m = 2,1823619 x104 Mpc (1st scenario)

SUniverse = 1,346954 x1027 m = 4,364724 x104 Mpc  (2d scenario)

SUniverse = 6,734769 x1026 m / 2π = 1,07187183 x1026 m = 3,473337 x103 Mpc  (3d scenario)

SUniverse = 1,346954 x1027 m / 2π = 2,14374297 x1026 m = 6,946674 x103 Mpc  (4d scenario)


Do not lose the continuity !

 Useful relations


1 year = 365,25 days x24hours x60minutes x60sec =31,5576 x106 sec (31 557 600 sec)

1 sec = 1/ 31,5576 x106 = 3,168808781 x10-8 earthly years  

1 light year (ly) = 31,5576 x106 sec x 2,9979245 x108 m/sec = 9,46073 x 1015 m

1 parsec = 3,2615 ly = 3,0857 x1016 m  

1Mpc = 106 pc = 3,2615 ly x106 x 9,46073 x1015 m = 3,0857 x1022 m


pi = 3,14159265358979323846...

√2 = 1,4142135

Observe that when we describe the free space as finite and with divergence from the rectilinear motion, then are presented trigonometrical relations and numbers of geometry in the circle. 

Angle in degreesº for arc length: S 360 / 2π r

Length of arc S per degree = φº 2π r / 2 x 180º

Stotal = V T = 2π r  (For regular speed V)

Radius r = Stotal / 2 π         |        Diameter d = Stotal

String of arc 180º = Diameter d

String of arc 90º = √2 x r

Unit of angular speed is the radian per second (1rad /sec)

1rad/sec = 0,159Hz   and   1Hz =6,283 rad/sec

Centripetal acceleration acentr = V2 / r  (Observation: The centripetal acceleration results without the mass. The mass however in the nature is presented as a result by the change in a speed).

Acceleration (relation with length S)

a = V2 / S  ( a=V V / V t = V/t) → V =√ a S

Acceleration (relation with time t)

a = V / t  → V = a t

Acceleration (relation with frequency)

a = V f  → V=a / f

Acceleration  (relation with time and length)

a = S / t2


The type Vκ = 2π r / T has particular importance for the case, because it connects the speed with time and with the perfect circular motion between them and concerning the radius with the import of relation 2pi. The type resolved as for period T, radius r and is become:

Vκ = 2π r / TT = 2π r / Vκ r = T x V / 2π2 π = Τ x Vκ / r




In order to we find the length of arc that corresponds in each degree on a perfect circle we use the type: Arc length = φ 2π r /360 (where φ is the angle in degrees)


Surface of ball: S = 4πR2   For radius: r =√S/4π





Linear speed V=S/t (length of arc where be the motion / corresponding time)

Angular speed ω=φ/t (angle where follows the επιβατ radius / cor. time)

Relation of linear and angular speed : V=2πR/t  and  ω=2π/t  It result: V=ω R

Relation between angular speed and frequency: ω=2π f 

ω = V / r = 2π f = 2π / T = φ T → φ = ω / T = ω f →


V = ω r = 2π f r = 2π r / T = S / t → T = 2π /ω = 2π r / V = 1 / f →


f = ω / 2π = V / 2π r = 1 / T → r = V / ω = V / 2π f = V T / 2π



Slight Universe = 1,346954 x1027 m = c2 / G

T Universe = 4,492954 x1018 sec = c / G

Smass Universe = 6,73477 x1026 m

4,492954 x1018 sec = 14,237312 x1010 years



R Universe = 2,14374 x1026 m

T Universe / 2π = 7,150758 x 1017

S Universe / 2 = 6,73477 x1026 m

T Universe x 2 = 8,985908 x1018

c2 / S Universe = 6,6725 x 10-11 =G

T Universe x π = 1,41150 x1019



S Universe2 = 1,814285 x 1054

T Universe2 = 2,01866 x 1037

1 / S Universe = 0,7424158 x 10-27 =G/c2

1 / T Universe = 2,225709 x 10-19 =G/c




S Universe / T Universe = 2,997925 x 108 =c

R Universe2 = 4,59562 x 1052

1/ R Universe = 4,66474479 x 10-27

D Universe2 = 1,838257 x 1053

1/ D Universe = 2,33237 x 10-27



For Smass Universe = 6,73477 x1026 m

Length of arc per degree = 1,87076 x1024 m

For Slight Universe = 1,346954 x1027 m

Length of arc per degree = 3,74153 x1024 m






www.kosmologia.gr 2009-10

ISBN 978-960-93-2431-1






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



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In the natural explanation, 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 has the material things in the minimal distance from 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 natural 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 the limits from observations in the most microscopic activities.






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