 # THE CIRCULAR MOTION AND FINITE FREE SPACE

with a limit in 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 (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 cross-correlation 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/sec2

1ly = 9,46073 ×1015 m

1 Mpc = 106 pc ≈ 3,2615 ×106 ly × 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 ? It's 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 inerval T=4,49295 ×1018 sec, in other units 14,2372994125 ×1010 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 × 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

0,673475432 ×1027 m / 3,086333 ×1016 = 2,1821216 ×1010 pc

Also, if we multiply time T= 4,49295 ×1018 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 ×1018 sec of the 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 ( 0,673475432 ×1027 m × 2 )= 1,346952 ×1027 m (Theorem Merton about the speed until a limit in the increase).

 Dividing time T = Vc / amin = 4,49295×1018 sec by 2π we find : T / 2π = 0,449295 ×1019 sec / 6,2831852 = 0,07150752 × 1019 sec   (0,07150752 × 1019 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 [-]

1 year = 365,25 days ×24hours ×60minutes ×60sec =31,5576 ×106 sec (31 557 600 sec)

1 sec = 1/ 31,5576 ×106 = 3,168808781 ×10-8 earthly years

1 light year (ly) = 31,5576 ×106 sec × 2,9979245 ×108 m/sec = 9,46073 × 1015 m

1 parsec = 3,2615 ly = 3,0857 ×1016 m

1Mpc = 106 pc = 3,2615 ly ×106 × 9,46073 ×1015 m = 3,0857 ×1022 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

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 mass. The mass however in 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 formula 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 insert of relation 2pi. The formula resolved as for period T, radius r and is become:

Vκ = 2π r / TT = 2π r / Vκ r = T × V / 2π2 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 = 4πR2   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

 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 = 14,237312 ×1010 years R Universe = 2,14374 ×1026 m T Universe / 2π = 7,150758 × 1017 S Universe / 2 = 6,73477 ×1026 m T Universe x 2 = 8,985908 ×1018 c2 / S Universe = 6,6725 × 10-11 =G T Universe x 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

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

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.

#### THAT DIRECT RIGHTLY THE RESEARCH  In physical 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 a close relation of nuclear force with the dynamic connection that material things  have in a minimal distance from the free space and immediately 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, 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 limits did not exist. They are exist limits in the Universe, as roughly we have determined them and for this reason, we have the advantage to detect these limits through observations of the most microscopic processes.

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