ARCHITECTONICS

Dr. Hossam Aboulfotouh

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* 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

The following are the primary assumptions concerning the spin of orbiters and nuclei of basic systems that we will prove it when discussing in details the spin of plants, satellites, and the sun of our solar system.

In unloaded Bs, but may carry the nucleus of other Bs, the orbiter of the first should thus be in the ready state for being able to carry that nucleus and transfer its load to the thrust X of its system. The orbiter runs actually on the thrust X, however, due to the harmonic process of load transfer between two basic systems, it will carry a Bs 's nucleus that is located imaginary at the limit of zero-load of its system. This means, the orbiter will transfer the orbital force of the moment that has been generated by the load vector R_Z of the carried system to the thrust X of its system. This orbital force is, in fact, a thrust that matches the perimeter of zero-load P_Z of the carrier system; its perimeter equals 2pR_Z and T_b is its time, i.e., the thrust X and the orbital moment (P_Z) have, imaginary, the same angular velocity. The orbiter is then free to jump to the P_Z of its system in the proper time in order to carry the other Bs's nucleus and together return to such thrust that has a load equal to the load it carries (e.g., in this case it will be X). Then, the load of X will be the total moment that applies on the carrier system's nucleus.

Further, we may imagine as said earlier, geometrically, in Bs, the actual carrying load of any of its thrusts is the travel length that any point on these thrusts performs in T_b. Thus, the orbiter achieves its carrying workability via, any point on the orbiter's equatorial thrust P_o (its domain and steering thrust) should travel a distance in T_b equal to P_Z that represents the load length it carried, and it was ready to carry. Accordingly, before and after carrying, the orbiter that is steered by its domain-thrust P_o performs several cycles a, in T_b, in order to transfer the load length P_Z to its thrust-X; then and only then it will be ready for carrying. The orbiter's spin a is thus a mechanism for load transfer in T_b. Then, a*P_o=2pR_Z=2pX=P_Z. Since, w_b=X=R_Z of P_Z, we may say that the orbiter conserves w_b in its carrying workability. Moreover, we may imagine that X of Bs is a P_Z of a minor thrust P_M, where its perimeter P_M equals R. During the ready state, if the orbiter runs on P_M, it carries only the load X and thus its spin in T_b will be S where S*P_o=X and a=2pS.

Besides, an orbiter shall spin with the same rate, according to its carrying load despite the tilting angle of its equatorial plane may change in relation to the equatorial plane of its Bs, as the load will not change. The law of tilting-phases according to the applied load is outside the scope of this work. We will publish it in another paper as it needs as much as the text of the work in hand, as it concerns the array of the system's tectonic coordinates particularly if it was a Cs.

Further, in unloaded Bs that is being carried by another system, and is being in a condition that, it does not carry any thing but itself, its orbiter will become in the state of rest or in the sleeping mood. In this case, the orbiter will not spin, and thus it will have a fixed orientation in relation to the system's nucleus while orbiting it like any point of the thrust-X.

Moreover, since both orbiter and pillar are equally stressed, the pillar carries also the orbital moment that is represented by P_Z during the ready state; thus, its spin a_p is given by a_p*P_p=P_Z, where P_p is the perimeter of the pillar's domain equatorial thrust. The nucleus of unloaded Bs carries, in the ready state, the mean orbital load of the system, i.e., the orbital moment at the radius that has the mean frequency equal to 0.5w_b, which equals 0.5X; thus, the nucleus carries pX. Then, its spin a_n in T_b is given by a_n*P_n=pX, where P_n is the perimeter of the nucleus's domain equatorial thrust.

In Cs, the case is more complex but amazingly organized and needs the following extended explanations and assumptions as a base for establishing the spin equations of actually loaded orbiters of Cs₂₄₊₄. Following Plato's definitions2, in Cs₂₄₊₄, the perimeter of any of the inner rings' thrusts (or the thrusts of combined rings or parts of rings) will be called hereafter "the perimeter of the diverse" (P_d). The perimeter of the outer ring's thrust will be called "the perimeter of the same" (P_X) where w_x is the frequency of its radius. The thrust P_X may be a circle and matches the perimeter of zero-load P_Zc, if the difference between the frequencies of the inner and outer radii of its ring approaches but not equals zero. Imagine that the diatone ofthe system's outer-most ring is divided into micro-tones where P_X is the thrust of the outermost micro-tonal ring.

Besides, any point on P_X performs one orbiting cycle in T_X, and any point on P_d performs one orbiting cycle in P_d 's local time T_d. The orbiters run only on P_d s based on conserving w_x of Cs₂₄₊₄ 's R_Zc, which means that, the orbiter that is orbiting the system's nucleus at any P_d should conserve the condition as if being carried on P_X. Thus, it should perform several orbiting cycles K_Vd in T_X in order to travel a distance equal to P_X, i.e., P_X=K_Vd*P_d. This means, at any P_d, the orbiter's velocity V_d per T_X is constant, while its V_d will have different quantities per T_d of each P_d. Moreover, each P_d of Cs₂₄₊₄ is like X of Bs that has its own P_Z; i.e., P_Zd=2pP_d. In Cs₂₄₊₄, P_Zd of any P_d is imaginary the product of single motion; however, P_Zc or P_X is the product of the four directional motions. Besides, there will be a diverse thrust P_dM that its P_Zd matches P_Zc or P_X of Cs₂₄₊₄. Thus, P_dM will be the outermost median-thrust (load) between such perihelion and such aphelion for Cs₂₄₊₄ 's orbiters. Accordingly, in our solar system, its radius R_dM is about 30.5 AU.

Since Cs₂₄₊₄ is not isolated from the rest of the cosmic enclosure, some of its orbiters may carry the nuclei of other systems. We may classify them in two types: system-carrier-orbiter that carries Bs_n or ion-carrier-orbiter that carries only Bs₁'s base. Any orbiter of Cs₂₄₊₄ should conserve w_x in its spin, i.e., the spin a of all orbiter conserves the condition that any point on the orbiter's steering thrust travels a distance equal to P_Zc (or P_X) in T_X. However, as we will see, each orbiter achieves this condition according to its type of loading or carrying workability.

We presume the observed motion of a system-carrier-orbiter running on a P_d is, at most, the product of seven motions (6 + the motion of P_X) that may be divided into two groups of four motions, since the motion of P_d is participating with both groups. Group-1, we will call it the "steering mechanism" that links the spinning motion of an orbiter with the motion of its P_d. Group-2, we will call it the "harmonization mechanism" that links the motion of a P_d with the motion of P_X, which conserves the condition P_X=K_Vd*P_d. When taking into our consideration that, the motion of P_X is the product of the four directional motions of Cs₂₄₊₄, the observed motion of a system-carrier-orbiter is then the product of ten motions at most. In section-4, we will add another one that makes them eleven motions at most.

Group-1, as shown in fig-8, is composed of a P_d and one or two levels of steering-thrusts that have the same center, which is the center of the orbiter; i.e., they are carried on a P_d. Although we are speaking about semi-elliptic thrusts, each has only one center, which is the center of an imaginary sub-circular-ring through which the thrust passes within its harmonic middle third HMT. We may observe the steering mechanism of any system-carrier-orbiter as a multiple levels of thrust-contours that each level is composed from the three typical thrusts of a Bs: P_Z, X and P_M. The outer contour-level is P_Z3, P₃ and P_M3 and the second inner level is P_Z2, P₂ and P_M2, where the perimeter of any thrust of such level is equal to S times its comparable thrust in the contour level below it, i.e., P_Z3=S*P_Z2 and so on. It is similar to the relation between X and P_o in Bs; besides, in this case both have the same center.

Click picture to see high resolution  

The geometric perimeter of any of these thrusts is given by Eq.1; however, for simplicity we will put them hereafter as Pz₃=2pRz₃, P₃=2pR₃ and P_M3=2pR_M3, where Rz₃, R₃ and R_M3 are their mean radii respectively, and similarly for the second inner level. As we will see, in most cases of our solar system, the loaded orbiter may take either P_M3 or P_M2 as a domain-thrust for the nucleus it carries, depending on the radius's frequency of the P_d it chooses. However, in all cases, P₃ is the steering-thrust that to which the observed spin belongs. If P_M3 was the domain-thrust, the inner contour-levels take place inside the carried nucleus, e.g., the planet.

Since, the orbiter is a foundation for other system 's nucleus; we presume it has a working radius R_W. In a solar system, R_W is the mean observed radius of the planet's equator. R_W may equal to the radius of the planet's domain-thrust (R_M3 or R_M2) or deviate from it with a ratio Y; i.e., R_M3=Y₃*R_W or R_M2=Y₂*R_W, where Y indicates the location of the planet 's domain-thrust in relation to its actual working thrust P_W. If Y=1, the planet's P_W is the same as its domain-thrust, and then the planet's observed size follows the norm of Cs₂₄₊₄. However, if Y<1, the planet's domain-thrust is below its P_W and if Y>1, the planet's domain-thrust is above its P_W.

The steering mechanism achieves the condition that any point on the planet 's working but equatorial thrust (P_W) travels a distance equal to P_d in T_d. We presume that, P_d and the steering thrusts P₃ and P₂ are similar to the thrust-X of Bs, where Pz_d, Pz₃ and Pz₂ are their perimeters of zero-load or their perimeters of the same. Accordingly, we imagine that the steering mechanism works based on the following four conditions.

First, P₃ performs a cycles in T_d in order that any point on it travels a distance equal to P_Zd, where a=2pS, and S*P₃=P_d. Thus,

a * P₃=2p * P_d (7)

Second, for the orbiter that takes P_M3 as a domain thrust for the nucleus (planet) it carries.

P₃ = 2p * P_M3 (8)

Third, for the orbiter that takes P_M2 as a domain-thrust for the nucleus (planet) it carries, P₂ performs a cycles in T_d, similar to P₃ 's cycles, in order that any point on P₂ travels a distance equal to P_Z3, where a=2pS, and S=P₃/P₂=P_d/P₃. Thus,

a * P₂=2p* P₃ (9)

Fourth,

P₂ = 2p* P_M2 (10)

Then, by substituting the quantity of P₃ from Eq.9 in Eq.7 we get,

a²* P₂= (2p)² * P_d (11)

In addition, by substituting the quantity of P₃ from Eq.8 in Eq.7 and substituting the quantity of P_M2 from Eq.10 in Eq.11 we get Eq.12 and Eq.13 respectively.

a * P_M3 = P_d (12)

a² * P_M2= 2p* P_d (13)

Then, if we inserted the ratio Y in Eqs.11, 12, and 13 and put the approximate quantities of P_d, P₂ and P_M2, we get the spin equations for Cs₂₄₊₄ 's system-carrier-orbiters.

a * Y₃ * R_W = R_d (14)

a²* Y₂ * R_W = (2p)² * R_d (15)

a²* Y₂ * R_W = 2p* R_d (16)

Based on NASA's planetary fact sheets of our solar system16b, we found that Eq.15 matches the case of Pluto where its Y₂=1. Eq.14 matches the case of Jupiter, Saturn, Uranus and Neptune, where Y₃ is nearly 1.0 for Jupiter and Saturn, Y₃=2.63 for Uranus and Y₃=2.0 for Neptune. Eq.16 matches the case of both Earth and Mars, where Y₂ is 1.1 for Earth and is 0.9 for Mars.

For Earth, a =365.25 c/T_d, where T_X=K_Vd*T_d, and its S=58.13 c/T_d. Since, a =2pS, Eq.16 may be put in the form: (2p*S²*Y*P_W=P_d), where 2pS²= Ka ; and where Ka is the cycles that the thrust P_M2 performs in T_d, i.e., P_d=Ka*P_M2. Further, since, P₃ is the major steering thrust; the observed spin is only a; the motion of both P_M2 and P₂ is unobserved. The time of all steering thrusts is T_d, and the velocity of any point on any of them is constant and equals V_d of P_d of the planet.

Group-2, or the harmonization mechanism, links the motion of a P_d with the motion of P_X. In between P_X and P_d there are two thrusts: P_E and P_F. Their mean radii are R_E and R_F respectively. In group-2, P_d, P_E and P_F are like P_M2, P₂ and P₃ in group-1 respectively; and P_X in group-2 is like P_d in group-1. Similarly, in group-2, V_d, S_d and K_Vd are like a, S and Ka in group-1 respectively; thus, in group-2, V_d=2pS_d and K_Vd=2pS_d², i.e., V_d²=2pK_Vd. Group-2 has only one possible condition; the relation between the motions of P_X and a P_d will be similar to Eq.16 of group-1, thus, in group-2, we imagine that P_X (or P_Zc) is like X of a Bs that has P_Z, which is P_ZX that equals 2pP_X. In our solar system, P_ZX equals 1,205 AU. Thus, the Eqs.17, 18, and 19 represent the first, the third, and the fourth condition of group-1 respectively,

V_d* P_F = 2pP_X (17)

V_d* P_E = 2pP_F (18)

P_E = 2pP_d (19)

Then, by substituting the quantity of P_E from Eq.19 in Eq.18 and then from the resulted equation substituting the quantity of P_F in Eq.17 we get,

V_d² * P_d = 2pP_X (20)

Then, we get,

V_d² * R_d = 2pR_X (21)

If we substitute each quantity of R_d from the Eqs.14, 15, and 16, in Eq.21 and since V_d²=2p*K_Vd, we get the three orbiting-spin-equations of the system-carrier-orbiters in Cs₂₄₊₄ and as we previously identified for the planets of our solar system, they respectively are:

K_Vd * a * Y₃* R_W = R_X (22)

K_Vd * a²* Y₂* R_W = (2p)²R_X (23)

K_Vd * a²* Y₂ * R_W = 2pR_X (24)

Where, K_Vd is the orbiting cycles that each of these orbiters (or the points of any P_d) performs, in T_X, in order to travel a distance equal to P_X of Cs₂₄₊₄, and thus it conserves w_x of the system. For Earth, K_Vd is about 192 cycles; accordingly, T_X of our solar system is 192 Earth-years.

For ion-carrier-orbiters, like the case of Venus and Mercury, their spin-equation may be established as follows. Since, V_d²=2p*K_Vd, we may write Eq.20 in the form,

K_Vd²*2pP_d = P_X (25)

If we imagine that the ion-carrier orbiters are in the ready state like the orbiters of a Bs, before the moment of carrying, then,

a* P_o = 2pP_d (26)

Then, we may substitute the quantity (2pPd) in Eq.25 with the left side of Eq.26. Besides, when these orbiters become actually loaded with a base of a Bs (ion), their domain and steering thrust becomes X of the orbiter-less Bs instead of P_o; thus, the orbiting-spin-equation for the ion-carrier orbiters of Cs₂₄₊₄ is as follows,

K_Vd²* a* X = P_X (27)

Eq.27, shows that the ion-carrier-orbiters also conserve w_x in their motions; besides, as K_Vd*P_d=P_X, X=2pR, and P_d=2pR_d thus,

Px * a * X = P_d² (28)

Then, the spin equation for the ion-carrier orbiters of Cs₂₄₊₄ is as follows,

Rx * a * R = R_d² (29)

We know from section-2 that R_X (or R_Zc) of our solar system equals 28,689 million km. Based on NASA's planetary fact sheets16b, R_d for Venus and Mercury is 108.21 and 57.9 million km. respectively. Their observed a is 1.924 and 0.5 c/T_d respectively, i.e., a of these two planets is taken equal to the result of subdividing the "tropical orbit period" by the "length of day." Then, by Eq.29, R for Venus and Mercury is 0.212 and 0.234 million km respectively and accordingly their X equals 1.33 and 1.47 million km respectively, taking in consideration that each of these planet has its own X that differs form X of our solar system and should be less than it. Thus, X of our solar system equals 5.88 million km for M_b equals 1.0 million km. Accordingly, in relation to T_X, the T_b of X of our solar system is about 14.3 Earth-day. Besides, X of a Bs may take any quantity, denoting a musical note; X for Venus and Mercury is equivalent to 0.01 the frequency of the note Do₂=C₂ and Re₂=D₂ respectively, while, X of our solar system is 0.01 the frequency of the note Re₄= D₄. If the spin data of these two planets were incorrect and their X were the same as X of our solar system, we may say that these two planets might be part of the surplus HESBs of the Bs₂s that have not yet being released out of the system.

Concerning the spin of the Sun, as said earlier, the system's nucleus carries the mean orbital moment that applies on the system during the ready state, i.e., it carries the load length of the thrust that the frequency of its mean radius equals half w_x of the system. Then, for our solar system half w_x= 0.5* 5.88=2.94 c/T_X. Then, by Eq.6, R_d for that different frequency w_d is equal to 1,793*10⁶ km. Thus, the spin of the sun a_n in T_X (192 Earth-years) equals the result of subdividing the perimeter of that median thrust by the equatorial-thrust's perimeter of the Sun, i.e., a_n=2p(1,793*10⁶)/2p (696*10³) = 2576.14 c/T_X; then, (2,576.14)/192 gives 13.41 c/Earth-year. Then, each cycle is about 27.22 Earth-days, which matches the observed spin of the Sun16b.

We observe satellites (like Moon and Titan) as orbiters of such carried Bs; and thus they will not participate with other basic systems for assembling such Cs. They are, therefore, in the sleeping mood and accordingly they do not spin. Due to that, each has a fixed orientation towards its system's nucleus (planet), and as known the day of each is equal to its orbiting period. We may observe the system of the Earth and its Moon as a Bs₁ that is carried on one of the orbiters of Cs₂₄₊₄ (our solar system). Thus, our planet Earth may be a HESB and our Moon may be the orbiter of that Bs₁.

 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. Mar, , Kuiper Belt,NASA, (200) 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-4: Gravitation and the Music of the Spheres. 

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