The longest distance (displacement) in the finite and
isotropic space theoretically corresponds in divergence 180º. The return back (approaching) in
the initial point begins in the 180º degrees.
The declination of the straight line motion, in perfect circle theoretically is the longest in the 90º degree and at
the return in 90º (or 270º) degrees.
If we see this length of longest distance in the finite space as dynamical so as a body that is moved with constant speed. In equal times equal
arcs are covered. The longest length of the first semicircle (arc of 180º degrees) is covered in the same time
lapse t that
is covered the other arc of 180º in the return. It is considered that acceleration exists (centripetal) in the circular motion with constant speed, because the
direction of motion changes.
We can a paradoxical thought observing the phenomenon of circular motion. This same observation help us
for the view about a curve space, as a finite and isotropic space with a limit in the longest distance imposes for all things. We can
consider a motion with slowed down, in concerning to a arbitrary point of departure. The rate of deceleration increases with the lapse of time and, in
the longest distance that finds in the 180º degrees where the straight line distance stops, we can consider that the speed is zeroed
for a moment.
In the phase of return and approach back to the
initial point, motion can be considered accelerating to the initial point, up to speed acquires the maximum 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 increases at maximum. The observation of circular motion with constant speed and its
crosscorrelation with equivalent phenomenon of regular deceleration or acceleration in straight
line remind us an other strange equivalence in physics. It reminds the
coincidental equivalence of inertia mass and gravitational mass, that Einstein tried unsuccessfully to understands. An observer that is accelerated in a closed
laboratory and pushed contrary to the direction of motion 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 is described as phenomenon of straight line motion, that is altered and reversed
periodically.
The above brief 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 motion acquires particular theoretical interest from the
application of this concept in motion of light. Do not forget, that motion of
light does not only to a direction (as material bodies) except when the conditions prevent its transmission. Since we immediately consider a finite space with a
limit in the longest distance and inevitable divergence from the rectilinear motion, comes in our brain the thought about propagation of bodiless light. Because
the radius in a finite space (not Euclidean space, as if motion happens always on the surface of a large ball) cannot be unlimited straight line
and forms a circumference with increase of distance. How does such a phenomenon of obligatory divergence of the straight line can influences motion of
electromagnetic waves? Can
we consider as an opposite and weak force prevent smoothly the rectilinear motion? The " spheres " of waves run along in a radius where ceases to is
straight line as the
increase of distance (and this declination means not concentric circles and deformity in the spherical form).
An important detail exists still, when we observe this detail in the above theoretical form of a 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 is almost circular (≈360º). In this case where the circular motion (which we describe equivalent as periodical phenomenon of
deceleration/acceleration), does not formed in
perfect circle 360º, then the two phases of longest distance and approach to the initial point
probably are not precisely equal. In other words, the rate of equivalent deceleration and the
rate of equivalent acceleration and the corresponding times in that these two motions happen possibly have a small
difference.
They exist clues, that from a extreme small difference in
these two phases of the circular motion (or in corresponding phenomena of periodical change) in microscopic creation of matter a leftover is result or an alleviation of energy or a new
phenomenon...
If the rate of deceleration (in a
physical process)
differ from the rate of acceleration (at the inversion of process), then time
interval t in which the
speed Vmax is acquired theoretically will differ than time interval t' in that the speed is decreased. The rate of deceleration and the rate of
acceleration (in the physical changes) likely are not equal and this inequality rather is related with that 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 science, they constitute special cases of more general phenomena that are
observed in the daily experience and are analyzed in rational thought. Phenomena, such as are motion, change of speed, time interval,
covered length, circular motion, frequency and rate etc.

Attention! Many translational errors
are exist.
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 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 ×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 × 10^{11} Ν
accelerate a body mass =1kg
1N =1kgr • m/sec^{2}
1ly = 9,46073 ×10^{15} m
1 Mpc = 10^{6} pc
≈ 3,2615 ×10^{6} ly × 9,46073 ×10^{15} m ≈
30,856170 × 10^{21} m
The acceleration is result general from the formula
a = F/m
a =F/M → a = 6,6725 × 10^{11} Ν /1kg = 6,6725 × 10^{11} m /sec^{2}
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 × 10^{8} m/sec / 6,6725 × 10^{11} m/sec^{2} =
4,49295×10^{18} sec
= c/G
A body M=1kg and acceleration
a=6,6725 × 10^{11} m/s^{2} takes
the speed c in time inerval T=4,49295 ×10^{18} sec, in other units 14,2372994125 ×10^{10} 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 t^{2}
Sm = 1/2 × am × tm^{2} →
(Distance S of mass m = 1kg)
Sm = 1/2 × (6,6725 ×10^{11} m/sec^{2} ) ×
(4,49295×10^{18} sec)^{2} =
6,73475432 ×10^{26} m
1pc (parsec)= 3,086333 ×10^{16}
m
0,673475432 ×10^{27} m / 3,086333 ×10^{16}
= 2,1821216 ×10^{10} pc
Also, if we multiply time T= 4,49295 ×10^{18} sec
multiplied by
the meters where light moved per sec, so we find the meters where light will have moved in
this number T, with its regular speed from the start. In time 4,49295 ×10^{18} sec
of the body 1kg, light will have moved twofold distance Slight :
S light= (4,49295×10^{18} sec) × (2,997924 ×10^{8} m/sec)= 1,346952 ×10^{27} m
= c^{2}/G
IN PARSEC:
1,346952 ×10^{27} m / 3,086333 × 10^{16}
= 4,36424 × 10^{10} pc
Finally, in time Τ=4,49295 ×10^{18} sec
where the body M=1kg is need to arrives in speed of light c with acceleration a= 6,6725 × 10^{11} m/sec^{2}
, light in same time do double distance S Universe (
0,673475432 ×10^{27} m × 2 )=
1,346952 ×10^{27} m (Theorem Merton about the speed until a limit
in the increase).
Dividing time
T = Vc /
amin =
4,49295×10^{18} sec
by 2π
we find :
T / 2π = 0,449295 ×10^{19} sec / 6,2831852 = 0,07150752 × 10^{19} sec
(0,07150752 × 10^{19} sec) × (31,68808781 × 10^{9} ) = 2,2659365 × 10^{10} =
22,659365 × 10^{9} years
1 earthly year ≈ 31,5576 × 10^{6}
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 ×10^{18} sec
SUniverse =
6,734769 ×10^{26} m
= 2,1823619 ×10^{4} Mpc
(1st scenario)
SUniverse =
1,346954 ×10^{27} m =
4,364724 ×10^{4} Mpc
(2d scenario)
SUniverse
= 6,734769 ×10^{26} m / 2π =
1,07187183 ×10^{26} m
= 3,473337 ×10^{3} Mpc (3d scenario)
SUniverse
= 1,346954 ×10^{27} m / 2π =
2,14374297 ×10^{26} m =
6,946674 ×10^{3} Mpc (4d scenario)
Do not lose the continuity !
1 year = 365,25 days ×24hours ×60minutes ×60sec =31,5576 ×10^{6} sec (31
557 600 sec)
1 sec = 1/ 31,5576 ×10^{6} = 3,168808781 ×10^{8}
earthly years
1 light year (ly) =
31,5576 ×10^{6} sec
× 2,9979245 ×10^{8} m/sec =
9,46073 × 10^{15} m
1 parsec = 3,2615 ly = 3,0857
×10^{16} m
1Mpc = 10^{6}
pc =
3,2615 ly
×10^{6}
×
9,46073 ×10^{15} m = 3,0857 ×10^{22} 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 × 180º
Stotal
= V
T = 2π r (For regular speed
V)
Radius r =
Stotal / 2 π
 Diameter d =
Stotal /π
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
= V^{2} / r (Observation:
The centripetal acceleration results without mass. The mass however in nature is presented as a result by the change in a speed).
Acceleration (relation with length S)
a = V^{2} / 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 / t^{2}
The formula V_{κ}
= 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 insert of relation 2pi. The formula
resolved as for period T, radius r and 2π is become:
Vκ
= 2π r / T →
T = 2π r / Vκ →
r = T × V /
2π → 2 π = Τ ×
Vκ / r
LENGTH OF A ARC
In order to we find
the length of arc that corresponds in each degree on a
perfect circle we use the formula: Arc length =
φ° 2π r /360 (where φ° is the angle
in degrees)
Surface of ball: S = 4πR^{2}
For radius: r =√S/4π
MORE INVESTIGATION WITH
THE FOLLOWING RELATIVE AND KNOWN TYPES
:
Linear speed V=S/t (length
of arc where be 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

CONCISE TABLE OF SAMPLES AROUND
MAX LENGTH S
and TIME T OF THE UNIVERSE
S_{light}
Universe =
1,346954 ×10^{27} m = c^{2}
/ G 
T
Universe =
4,492954
×10^{18} sec
= c / G

S_{mass}
Universe = 6,73477 ×10^{26} m

4,492954 ×10^{18} sec
= 14,237312 ×10^{10} years



R Universe = 2,14374 ×10^{26} m 
T
Universe / 2π = 7,150758 × 10^{17}

S Universe /
2 = 6,73477 ×10^{26} m 
T
Universe x 2 = 8,985908 ×10^{18}

c^{2}
/ S Universe = 6,6725 × 10^{11} =G 
T
Universe x π = 1,41150 ×10^{19}



S Universe^{2}
= 1,814285 × 10^{54} 
T Universe^{2}
= 2,01866 × 10^{37}

1 / S Universe =
0,7424158 × 10^{27} =G/c^{2}

1 / T
Universe = 2,225709 × 10^{19}
=G/c 



S Universe /
T Universe = 2,997925 × 10^{8} =c 
R Universe^{2}
= 4,59562 × 10^{52} 
1/ R Universe =
4,66474479 × 10^{27} 
D Universe^{2}
= 1,838257 × 10^{53} 
1/ D Universe =
2,33237 × 10^{27} 


For S_{mass}
Universe = 6,73477 ×10^{26} m
Length of arc per degree =
1,87076 ×10^{24} m 
For S_{light}
Universe = 1,346954 ×10^{27} m
Length of arc per degree =
3,74153 ×10^{24} m 



1st
PUBLICATION
www.kosmologia.gr ©200910
ISBN 9789609324311 

WILL BECOME CORRECTIONS
AND WILL BE CONTINUED...
Now, it is not privilege of few leading physicists to speak 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 student! Because the Universe has constant min and max
limits... forever and everywhere. 
