Illustration 1.0 – the earth
© Klaus Piontzik, Claude Bärtels 2014
Planetary Systems - Volume 1
Production and publishing:
BoD – Books on Demand GmbH, Norderstedt
ISBN 978-3-7357-2783-1
SUMMARY
This book is the essence and progression of two presentations, the author K. Piontzik has held on 3/14/2009 to the association for the support of the geobiology in Brügge and on the spring conference of the research group for geobiology in 4/24/2009 in Eberbach.
The present material represents a progression and completion of the book "Gitterstrukturen des Erdmagnetfeldes". The basic material (about 60%) of the book "Gitterstrukturen des Erdmagnetfeldes" is also on the Internet in English accessible at: www.pimath.eu.
Seen from today's perspective „lattice structures of the earth magnetic field“ delivers a collection of facts and basic informations. A closed homogeneous model is recognizable in attempts, but the golden threat is still missing.
Now in cooperation with the biophysicist Dr. Claude Bärtels the new work „Planetary systems“ forms a closed uniform working hypothesis, with that the physical layer structures of the earth (geologic bowls, atmospheric layers, earth magnetic field, electric earth field) can be explained.
This book is a working hypothesis, which can be falsified after the today's epistemology by Popper.
From it the information of a physical measuring method occurs which represent the experimentum crucis for this working hypothesis.
Overall, the model shown here, represents a holistic approach on an oscillation base that explains several structures of the earth.
What is valid on the earth, must be valid also "in" the earth and with it is valid both on the large and small scale. What means for the authors that the macroscopic oscillation structures have her correspondences also in the (sub) microscopic (atomic) area.
The course of the development in the last both years has shown, that the whole themes about stratifications, oscillations and grids can be attributed to a central concept with which all phenomena can be explained: it is the concept of the planetary system.
The question which raises here is: What is to be understood by a planetary system? In addition the concept must be examined such closer.
Planetary means a global earth phenomenon. And the concept system implies that a certain order exists.
Planetary systems are so global or earth-enforcement structures. Two systems are recognised in the following picture: the earth's surface even with her lying underneath geologic bowls and the atmosphere with her stratifications.
Illustration 1.0 – the earth
Earth System
= All energy and matter that is present in the area of planet Earth and its neighbourhood.
The neighbourhood of the planet Earth can be explained by a spherical space with a radius of 2 or 3 Earth radii. Here, the concept of neighbourhood is reminiscent of the definition from the topology.
Planetary System
= a global elementary subsystem of the earth system with a geometrical structuralisation.
The geometrical structure would have to be defined even closer. This happens in the following chapters.
In the following we will have a look at the listed systems.
Illustration 1.1.1 – geologic layers
The geometrical structuralisation of the geologic bowls exists as concentric balls in the earth.
Illustration 1.1.2 – atmospheric layers
The geometrical structuralisation of the atmospheric layers exists as concentric balls round the earth.
Illustration 1.1.3 – magnetic field of the earth
The geometrical structuralisation exists (simplisticly) as concentric balls in the earth and round the earth. Polar (north south pole) and radial structures (magnetic flux density) still appear.
Illustration 1.1.4 – electric field of the earth
The geometrical structure exists as concentric spheres round the earth. Polar (plus minus poles) and radial structures (electric field strength) still appear.
Geologic spheres, atmospheric layers, earth magnetic field and the electric field own a geometrical structuralisation which exists of concentric spheres.
The geologic bowls lie within the earth. The atmospheric layers and the electric field lie outside, around the earth.
The earth magnetic field exists in the earth as well as round the earth. With magnetic field and electric field radial and polar structures still appear.
At the end of the 19th century the geologists W.L. Green and A. de Lapparent compared the shape of the earth with a tetrahedron.
A similar comparison did in the sixties of the twentieth century B.L. Litschkow and N.N. Schafranowski with an octahedron. Litschkow published a little later the model of a dodecahedron and an icosahedron for the earth shape.
In 1974 Nikolai F. Gontscharow, Wjatscheslaw S. Morosow and Walerij A Makarow published in the Russian magazine "Chimi-ja i Zisn" (chemistry and life, No. 3, March) the model of a dodecahedron of the earth.
Tetrahedron
end of 19. century
W.L. Green
A. de Lapparent
Octahedron
in the 60. years of 20. century
B.L. Litschkow
N.N. Schafranowski
Illustration 1.2.1 – polyhedron models of the earth
Icosahedron
In the 60. years of 20. century
Litschkow
Dodecahedron
1974
Nikolai F. Gontscharow
Wjatscheslaw S. Morosow
Walerij A. Makarow
1999 – S. Prumbach
Illustration 1.2.2 – polyhedron models of the earth
These polyhedron models of the earth were developed primarily by geologists. There is only one body missing to receive a certain set from bodies.
There is only the cube missing to complete the Platonic solids.
Platonic solids are regular bodies which are built up from regular bases. There exist only five Platonic solids as shown here.
Illustration 1.2.3 – cube
The corner points of the polyhedrons lie on the infolding sphere. All edges are transferred to the ball surface. In contrast to all other planetary systems lines with finite lengths occur here, due to the structure of the polyhedron.
Illustration 1.2.4 – polyhedron in cross section
You can project the edges or corners of the polyhedron on the enveloping ball.
The best way is to depict all corners of a polyhedron as intersections of circle of latitude and meridians, such like the geographical system.
Illustration 1.2.5 – Gitterbildung
The points of intersection of the resulting grid correspond to the corners of the polyhedron. And the edges of the polyhedron are usually on the circles of latitude or meridians.
The octahedron is the only platonic solid in which all edges of the polyhedron and grid lines fully match. The grid is used by three, each perpendicular on each other standing circles formed. As a result, the spherical surface is decomposed into eight equal parts.
The cube has a decomposition which is formed by four circles and also forms a symmetrical grid. All horizontal edges of the cube are identical with the circles of latitude. All vertical edges of the cube are included with the meridians as parts.
The tetrahedron has the same separation as the cube, a tetrahedron can be represented as an inside body of a cube. Edges of the polyhedron occur but they are not directly represented in the coordinate system.
Another possibility for the tetrahedron is to see this as a triangular pyramid. So one would get three meridians, and a parallel, but also an irregular grid.
Also the icosahedron provides a regular grid with five meridians and two circles of latitude. Edges of the polyhedron occur, but that are not directly represented in the coordinate system.
Only the dodecahedron builds irregular distances with five meridians and four circles of latitude.
All together the following statement can be formulated:
Polyhedron ⇔ Grid
Polyhedrons are equivalent to grids on a ball surface.
For the systems to be looked exist, according to 1.1 and 1.2, following geometrical structuralisations:
ball shape, concentricity
north-south poles plus-minus poles
magnetic flux density electric field strength
Polyhedrons
Oscillation structure
= A system of patterns of vibration or oscillating structures that are related to each other.
This vibration structure form usually spatial structures, whose basic patterns include geometric solids, both have harmonical ratios to each other.
According to definition 1.0.2 is valid:
Planetary system = a global elementary subsystem of the earth system with a geometrical structuralisation.
The aim of this chapter is the description of basic mathematical and physical terms and conditions, that serve the development of an equation for an oscillation structure and allow a quantification of the model. The approach is based on oscillations around a ball.
Examples for oscillation possibilities:
sine
cosine
Illustration 2.0.1 – oscillations
sine or cosine = oscillation = wave
Applies to physical oscillations:
(Frequency multiplied with wavelength is equal to speed of light)
How to get vibrations around a ball? - Analogous to the Bohr model of the atom, if it contains the surrounding Electron as a wave by de Broglie:
Illustration 2.0.2 – oscillations around a ball
It fits only an integer number of oscillations around the globe.
NThe wavelength is proportional to the circle angle alpha:
Illustration 2.0.3 – wave length and circle angle
Condition for n vibrations around a globe:
NTheoretically, the following form is possible:
NHere, the oscillation circle does not close after one revolution, but only take m turns.
A standing wave around a sphere can be interpreted as a stationary state. Thus, each state of a wave is spatially fixed. The question now is: how many waves fit around a globe?
In classical mechanics, degrees of freedom is the number of freely selectable, independent movements of a system
A rigid body in space has a degree of freedom f = 6, because you can move the body in three independent directions and rotate in three independent planes.
Because a sphere is rotationally symmetric, so rotations are irrelevant. A ball has therefore 3 freedoms regarding a wave propagation. Therefore, three independent waves around the globe are possible.
Due to the spherical shape, the three freedoms can be represented as spherical coordinates.
Example earth:
There exists a mathematical concept namely for the first two examples, that is suitable for a representation - the spherical harmonics.
Standing waves on the surface of a sphere can be treated as spherical harmonics. There are 3 types:
Zonal spherical harmonics only depend on the latitude.
sinϕ
cosϕ
Illustration 2.1.1 – zonal spherical harmonic
Sectorial spherical harmonics depend only by the degree of longitude.
sinλ
cosλ
Illustration 2.1.2 – sectorial spherical harmonic
Tesseral spherical harmonics depend of the latitude and the longitude.
sinϕ · sinλ
sinϕ · cosλ
cosϕ · sinλ
cosϕ · cosλ
Illustration 2.1.3 – tesseral spherical harmonic
tesseral spherical harmonic
= product of two oscillations
= 2 perpendicular standing waves
= grid
A complete route in terms of square grid on a sphere can not materialize. Only grid systems are developed, which are designed as the geographic grid system. There are always two poles. The corresponding "meridians" and "circle of latitude" then make the grid.