PiMath.de Planetary Systems of the Earth 1
Classisc Systems
 
     
  Copyright © Klaus Piontzik  
     
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8.2.1 - The planetary orbits

Our solar system also has a concentric structure with its planetary orbits. The distances in astronomical units (AU) for the first 8 planets are compiled from the common literature. The individual planets are arranged and numbered according to their distance.

 

Planet Nr Distance ln(Distance)
    (AU)  
       

Mercury

0

0,3871

-0,94907222

Venus

1

0,723

-0,32434606

Earth

2

1

0

Mars

3

1,524

0,42133846

Jupiter

4

5,203

1,64923538

Saturn

5

9,582

2,25988634

Uranus

6

19,201

2,95496236

Neptune

7

30,047

3,40276282

 

AU = astronomical unit = 149,597,870 km = distance Earth - Sun

The table gives the following function y for the logarithms of the distances:

Logarithmic planetary orbits

Illustration 8.2.1 – Logarithmic planetary orbits

 

The dashed line in the diagram represents an approximate straight line.

As can be seen, there is already good linearity of the values.
Only Earth and Mars deviate from the approximation line. Point 3 (Earth) is therefore pushed to point 1.5 and point 3 (Mars) becomes point 2. The linearized function now looks like this:

 Linearization

Illustration 8.2.2 – Linearization

 

The parameters of the approximation line are determined using the same procedure as described for the sun shells.

The equation for the approximation line is: y = 0.62169 x 0,94907

The following applies to the planetary orbits: Distance = 0.3871 e0.62169x [AU]

This results in the following values:

 

Planet Nr Distance Distance
    [AU] [AU]
      calculated
       

Mercury

0

0,3871

0,3871

Venus

1

0,723

0,7208087

Earth

1,5

1

0,98359983

Mars

2

1,524

1,34219887

Jupiter

4

5,203

4,65383058

Saturn

5

9,582

8,66577519

Uranus

6

19,201

16,1363114

Neptune

7

30,047

30,047

The entire situation for the planetary orbits then looks like this:

Planetary orbits as an e-function

Illustration 8.2.3 – Planetary orbits as an e-function

 

The gap for n = 3 is remarkable. The distance to it is 2.5 AU.
The asteroid belt extends from 2.0 to 3.4 AE. The average is 2.7 AU.

The model therefore corresponds very well to real events. And it shows that the asteroid belt is part of the oscillation system of the planets.

And it also shows that the procedure of logarithmization and linearization is not an arbitrary act, but rather reveals the harmonic structures of a system.

 

Planet Nr Distance ln(Distance)
    (AU)  
       

Mercury

0

0,3871

-0,94907222

Venus

1

0,723

-0,32434606

Earth

2

1

0

Mars

3

1,524

0,42133846

Asteroid belt

4

2,7

0,99325177

Jupiter

5

5,203

1,64923538

Saturn

6

9,582

2,25988634

Uranus

7

19,201

2,95496236

Neptune

8

30,047

3,40276282

Pluto

9

39,482

3,67584487

The table gives the following function for the logarithms of the distances:

Logarithmic planetary orbits

Illustration 8.2.4 – Logarithmic planetary orbits

 

The dashed line in the diagram again represents an approximation straight line. As can be seen, there is already a very good linearity behavior of the values. The values ??are linearized and result in the following diagram:

 

Linearization

Illustration 8.2.5 – Linearization

 

The equation for the approximation line is: y = 0.52856 x 0.94907

The following applies to the planetary orbits: Distance = 0.3871 e0.52856 x[AU]

This results in the following values:

 

Planet Nr Distance
  new [AU]
     

Mercury

0

0,3871

Venus

1,3

0,723

Earth

1,9

1

Mars

2,6

1,524

Asteroid belt

3,75

2,7

Jupiter

5

5,203

Saturn

6,1

9,582

Uranus

7,5

19,201

Neptune

8,25

30,047

Pluto

8,75

39,482

 

The new situation for the planetary orbits then looks like this:

Planetary orbits as an e-function

Illustration 8.2.6 – Planetary orbits as an e-function

 

There is still the possibility of better adjustment for the numbering values. Based on the previous linearization, exact numbers can be calculated, just as was already seen with the sun shells.
The table below shows the calculated numbering values ??as well as the approximate numbers and the initial numbers.

 

Planet Nr Distance Nr Nr
  alt [AU] calculated approximately
         

Mercury

0

0,3871

0

0

Venus

1

0,723

1,3

1,182

Earth

2

1

1,9

1,796

Mars

3

1,524

2,6

2,593

Asteroid belt

4

2,7

3,75

3,675

Jupiter

5

5,203

5

4,916

Saturn

6

9,582

6,1

6,071

Uranus

7

19,201

7,5

7,386

Neptune

8

30,047

8,25

8,233

Pluto

9

39,482

8,75

8,750

 

The more precise function for the planetary orbits is shown in the following illustration 8.2.7

Planetary orbits

Illustration 8.2.7 – Planetary orbits

 

There is a mathematical relationship between orbital radii and orbital times for the planets that also allows the orbital times to be represented as an e-function


8.2.2 - The orbital periods of the planets

There is a mathematical relationship between the orbital radii and orbital times of the planets, which Johannes Kepler (*Dec. 27, 1571 - ?Nov. 15, 1630) discovered at the beginning of the 17th century, a German natural philosopher, mathematician, and astronomer. It also allows the circulation times to be represented as an e-function.
 
The general rule is:

Path radii and circulation times

   
The same applies to Mercury:

Path radii and circulation times

By rearranging, the equation for the orbital periods of the planets results:

Circulation times

The following applies: r/r0 = eax und x = calculated numbering


Inserting all sizes provides:

Circulation times as an e-function

 

 

8.2.3 - The tenth planet

In 2005, US astronomers discovered a new planet behind Pluto made of ice and rock. It is the tenth planet in our solar system.

Based on the existing model, the distance to the sun can be determined.

The following applies to the planetary orbits: Distance = 0.3871 e0.52856x[AU]


The following applies: x = 10. Based on the previous values, a tolerance of ±0.25 is assumed. This gives the range for the distance of the tenth planet between 67 AU und 87 AU.
DThe exact value for x = 10 is 76,44 AE.


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Der Autor - Klaus Piontzik