spin-gravity-S2-music-spheres

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ARCHITECTONICS

From Cosmic Theories to Urban Development

Dr. Hossam Aboulfotouh

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Determining Planetary Spin and Musical Gravitation in the Spheres of Cosmic Systems of Perfect Numbers

Hossam M. K. Aboulfotouh, PhD*

* Lecturer, Architectonic Cosmic Theories and Development, Department of Architecture, Faculty of Fine Arts, Minia University, and Director, WPAHR-V, International Union of Architects-UIA. fotouh@mail.com

Section-2: THE LAW OF MUSIC OF THE SPHERES.

Imagine that each Bs has a module of rotation; it is the smallest thrust in the system's ring. It takes place within the system's nucleus, since the ring starts actually from the center of the system, like a disk. Its perimeter M_b is the system's measurement unit. As a general condition, for reasons will be discussed in section-3, any point on any thrust that is less than X in the system's ring travels the same distance X in T_b. Then, while the orbiters, or any point on the thrust X, perform(s) one simultaneous cycle in T_b, the module M_b performs several cycles, i.e., M_b as the smallest thrust is the cyclic unit of X. Thus, the imaginary cyclic frequency w_b of such Bs is given by:

(3)

Since the applied compression forces are perpetual, w_bis harmonic and since M_b is the system's unity, w_b equals X. In unloaded Bs that carries only the external compression forces, its semi-elliptical thrust-X represents geometrically the actual load that the system's nucleus carries. If the thrust-X is being transformed into one concentrated load that applies directly on the system's nucleus, it will represent a load vector R_Z that equals in magnitude and travel length to that thrust-X. If R_Z is observed as a radius, it identifies the circular perimeter P_Z of the system's limit of zero-load, fig-4. Under any circumstance, the nucleus of unloaded Bs does not carry any external loads beyond this limit. Since the load vector R_Z equals X, we may also observe w_b as the cyclic frequency of R_Z. Eq.3 may also be used to get the cyclic frequencies for different load vectors less than R_Z in Bs, presuming that any of them is X of a separate system having the same M_bsize. Thus, the lower the radius the lower its frequency. However, due to that any lower load vector is still part of the whole system, the lower the radius the higher the load and accordingly the higher the orbiting velocity. Imagine that R_Z is a high-rise building, where its foundation is the system's nucleus; then, the load on a column in the third floor is more than a similar column in the thirteenth floor and the load will be zero at the roof of this building. Thus, w_b as an imaginary cyclic frequency indicates the harmonic level that upon which the load will be identified.

Click picture to see high resolution

Figure-4: The main tectonic components of a basic system. The thrust-X in an abstract circular shape and the load vector R_Z that equals X and identifies the perimeter limit of zero-load of a basic system.

In complex systems, the case is quit different. If the 64 orbiters of Cs₂₄₊₄ performed simultaneously in T_b one cycle around their nuclei, due to the four directional motions of Cs₂₄₊₄'s sub-basic-systems, the actual collective load vector R_Zcthat applies on the nucleus of the system's base"Bs₄" is given by:

R_Zc= X * 2X * 3X * 4X =24X⁴ (4)

Eq.4 is based on that R_Z of each Bs has been observed as a force generating a moment on the nucleus of the Bs that caries it. Imagine that the nuclei of Bs₁, Bs₂ and Bs₃ are carried on the limits of zero-loads of Bs₂, Bs₃ and Bs₄ respectively, fig-5. Then, R_Z of Bs₁ will generate a moment equal to X² on Bs₂'s nucleus. This moment is like an orbital thrust around Bs₂ 's nucleus. It represents the actual load that applies on it. This load may be transformed into a load vector that generates a moment equal to X³ on Bs₃ 's nucleus. Similarly, the load vector of the moment X³ generates a moment equal to X⁴ on Bs₄ 's nucleus. For the 24 wings of the system, the collective load vector R_Zc equals 24X⁴; R_Zc as a radius identifies the perimeter limit of zero-load P_Zc of Cs₂₄₊₄.

Click picture to see high resolution

Figure-5: The carrying workability of one of the 24 wings of Cs₂₄₊₄. It shows the generated orbital moments X², X³ and X⁴around the nuclei of Bs₂, Bs₃ and Bs₄ respectively during one cycle per the periodic time T_b of Bs.

In other words, geometrically, as shown in fig-6, repeating X during the system's four directional motions generates R_Zc, where it is the total sum of thrusts' images that coded itself in multi cross-sections of the cosmic enclosure. For each Bs₁, repeating its X along Bs₂ 's X gives X², then repeating X² along Bs₃ 's X gives X³ and finally repeating each unite layer of X³ (each like X²) along Bs₄ 's X gives X⁴. For the 24 wings, the total sum of repeated images will be 24X⁴. Moreover, the quantity 24X⁴ is the real coded volume of Cs₂₄₊₄ 's topological structure that its observed volume is equal to only 48X³.

Click picture to see high resolution

Figure-6: The linear model of the coded images of thrusts for one-wing of Cs₂₄₊₄that will be generated during one cycle/T_b. The observed volume of one isonly 2X³ however itsreal coded volume is X⁴. For the 24 wings oCs₂₄₊₄, the observed volume will be 48X³ and the real coded volume is 24X⁴.

Since basic systems, of the same X size, generate Cs, the imaginary cyclic frequency w_x of Cs₂₄₊₄'s limit of zero-load R_Zc will also be X, where M_b is its module and that from Eq.4 is given by:

(5)

Unlike Eq.3 that deals with w_b as the product of a single directional motion of Bs, Eq.5 deals with w_x as the product of the four directional motions of Cs₂₄₊₄'s sub-basic systems. Since, w_b of basic systems is harmonic, w_x is also harmonic.

Eq.5 may also be used to get the frequencies of different radii or load vectors less than R_Zc in Cs₂₄₊₄. Thus, we may put it in the form:

(6)

Where, R_d is any radius in Cs₂₄₊₄that differs from R_Zc, and w_d is the imaginary harmonic frequency that corresponds to that different radius.

Moreover, right after the joining process, we presume the topological structure of Cs₂₄₊₄ will transform into a multi-ringed-system with one nucleus and multiple protecting rings around it. This transformation will take place within the system's limit of zero-load P_Zc=2pR_Zc, while conserving its cyclic frequency w_x that represents its main intrinsic property. Then, P_Zc will be the circumference of the system's outer most ring.

We presume that Cs₂₄₊₄'s rings will be 46 in total. We think they have the following order from the nucleus: 4 rings correspond to Bs₄, one ring gap, 12 rings correspond to Bs₃s, one ring gap, 24 rings correspond to Bs₂s and 4 rings as a cover for the system since it has a fourth order base. Bs₁s will not build rings, as their orbiters will swim within the rings of Bs₂s.

Due to the harmonic property of the system, we presume the two-limits of each of the 46 rings will match the limits of diatones (half tones). Taking w_d of the mean radius of the system's nucleus as the primary musical tone for the diatones of the system's rings, the musical tone "w_x" of R_Zc will denote the system's musical name. Moreover, since the musical octave contains 12 diatones22a,b and its second harmonic is twice its first harmonic14, the ratio l between the frequencies of two successive diatones is 2^-12, i.e., l =1.059463094 approximately.

In music, the typical musical octave starts from the note C = Do22a; however, a musical octave may start from any note22b, e.g., from "A₂" or La₂=110 cycles/second to its second harmonic La₃ = 220 cycles/second. The symbols of the 12 musical notes of an octave are A, A#, B, C, C#, D, D#, E, F, F#, G, and G# that means La, La#, Si, Do, Do#, Re, Re#, Mi, Fa, Fa#, Sol, and Sol#, respectively. The symbol # means major.

If M_b of our solar system is the decameter, based on NASA's planetary fact sheets16a our Sun's radius equals 0.695*10⁸ Decameter. Then, by Eq.6, w_d of our Sun's radius equals 41.25 cycles per T_b of X of our solar system. Accordingly, w_x of R_Zc of our solar system equals 41.25*(l ⁴⁶)= 588 cycles/T_b, which is equivalent to the note "D₄" or Re₄; it is the third harmonic22 of D₂ =147 c/s. By Eq.4, R_Zc of our solar system is equal to 28,689*10⁸ decameter (about 192 AU). Since w_xequals X, it denotes the size of basic systems that constructed our solar system, which is based on the assumption of M_b 's quantity. Using the multiple 10⁴ to increase M_b 's quantity, if M_b of our solar system is set as 10⁴or 10⁸of a decameter,the corresponding frequencies will be 0.1 or 0.01of the mentioned notes respectively, while the size of X increases proportionally. In section-3, we will identify the exact size of X of our solar system.

Similarly, we can get the equivalent musical tone of any radius in our solar system. The equivalent musical tone of Mercury 's perihelion is close to La₂# =117 c/T_b. Venus 's aphelion is close to Re₂ =147 c/T_b. Earth's perihelion has a tone Re₂# =157 c/T_b. Mars's perihelion is close to Fa₂ =172 c/T_b. Jupiter's perihelion is close to La₃# =234 c/T_b. There is nearly one octave between Mercury's perihelion and Jupiter's perihelion; it is the first of the two musical octaves of Bs₂'s rings of our solar system.

If we imagine that the 46 rings are forming one combined ring (like a disk), the major thrust of the system will have a perihelion and aphelion at the inner and outer limits of the middle third of the combined ring. At these two limits, the two resultants of the fluctuated compressive stress digram²³ those apply on the cross section of the ring take place, fig-7. In our solar system, the inner limit matches the median circle of the asteroid belt at w_d= 588/3= 196 c/T_b and that by Eq.4 gives a radius equals 354*10⁸ decameter (354*10⁶ km). The outer limit matches the median circle of the Kuiper belt at w_d=588*(2/3)=392 c/T_b and that by Eq.4 has a radius equals 5,667*10⁸ decameter (about 38 AU). These distances coincide with the published data of both belts16^,17^,18. Another reason that makes the asteroid belt, the major disposal for Cs₂₄₊₄'s debris will be discussed in the following section.

Click picture to see high resolution

Figure-7: The two main resultants of the fluctuated compressive stress in Cs₂₄₊₄ 's combined ring. For the maximum permissible load, due to that the ring is being under only compressive stress, the stress diagram for any of its cross sections will be only in the compression side. The resultant of each stress diagram for any cross section will denote the location of the thrust at that cross section. At the aphelion-point, the maximum compressive stress will apply on the outer limit of the ring with zero stress in the system's center. At the perihelion-point, the maximum compressive stress will apply on the center of the system, with zero stress in the outer limit of the ring. Due to that the combined ring has multiple major-thrusts in its middle third, its outer and inner circular-limits contain the array of the perihelion and aphelion points of these multiple thrusts. Thus the two resultants are in continues revolution and apply on any cross section of the combined ring denoting the two limits of its middle third. The compressive stress diagram of the ring's cross-section(s) is not linear, due to the harmonic distribution of loads.

REFERENCES.

1. Peder, Olaf, Early Physics and Astronomy, A Historical Introduction, Cambridge University press, p53 & p120 (1993).

2. Plato, Timaeus, (330 BC.). part1-paragraph-6 http://psychclassics.yorku.ca/Plato/Timaeus

3. O'connor, J J & Ropertson, E F, Perfect numbers, (2001).

Http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Perfect_numbers.html

4. McLeish, John, Numbers: From Ancient Civilizations to the Computer, Flamingo, HarperCollins, London, chapter 6, 1992.

5. Euclid, Elements, Book IX, Proposition 36, (150 AD.).

http://www.educa.fmf.uni-lj.si/java/pck/ELEMENTS/bookIX.html

6. Einstein, Albert, Relativity: The Special and General Theory, Methuen & Co. Ltd., (1924). Http://www.marxists.org/reference/archive/einstein/index.htm

7. Samuel, Eugenie, If the Universe is Spinning, Here's How to Feel it, New Scientist, p17, (July 13, 2002).

8. Mewhinney, Mike, Huge Mars-size Rocks May Have Caused Earth's Rapid Spin, News release 93-03ar, NASA Ames Research Center (Jan. 15, 1993) http://amesnews.arc.nasa.gov/pages/releasearchive.html

9. Brick Industry Association, Technical Notes on Brick Construction, Structural Design of Brick Masonry Arches. (Oct. 1967) http://www.brickinfo.org/BIN/technotes/t31a.htm

10. Leontovich, Valerian, Frames and Arches, M.S., McGraw hill, (1959).

11. Hawking, Stephen, The Universe in a Nutshell, Bantam Books, New York (2001)

12. Davies, Paul, About Time, Simon & Schuster, New York, chapters 1, 2 &4 (1995)

13. Schwarz, Patricia, the official "Super String " web site http://superstringtheory.com

14. Yavorsky, B & Detlaf, A, Handbook of Physics, Mir Publications, Moscow, p996, p680,& p101 (1997)

15. Rogers, Melissa J.B, Vogt, G L & Vargo, M, The Mathematics of Micro Gravity, NASA, p11-12 (1997). http://www.hq.nasa.gov/education

16. Williams, David R., Planetary fact Sheets, NASA Goddard Space Flight Center, (June 2002)

a. http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html ,

b. http://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html ,

c. http://nssdc.gsfc.nasa.gov/planetary/factsheet/galileanfact_table.html , and

d. http://nssdc.gsfc.nasa.gov/planetary/factsheet/asteroidfact.html

17. Jewitt, David, Kuiper Belt, http://www.ifa.hawaii.edu/faculty/jewitt/kb.html

18. Martin, David, Kuiper Belt, NASA, (2003) http://solarsystem.nasa.gov/planets/profile.cfm?Object=KBOs

19. Vygodsky, M., Mathematical Handbook: Higher Mathematics, Mir Publications, Moscow, p810, (1971).

20. Gioia, A. Anthony, The Theory of Numbers: An Introduction, Markham Publication Company, Chicago, p25, (1970).

21. Serway, R.A., Physics for Scientists and Engineers: With Modern Physics, fourth edition, Saunders, p1367, (2002).

22. Frequencies of Musical Notes,

a. http://www.phy.mtu.edu/~suits/notefreqs.html

b. http://www.techlib.com/references/musical_notes_frequincies.htm

23. Oulsnam S R & Brothers, B G, Mechanics of Materials and Engineers, B I Publications, Bombay, p99-106, (1962).

Introduction

Section-1: The Law of Numbers

Section-2: The Law of Music of the Spheres.

Section-3: The Law of the Spinning Motion.

Section-4: Gravitation and the Music of the Spheres.

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