# 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:

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:

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:

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:

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:

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:

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

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:
 The same applies to Mercury:

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

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

 Inserting all sizes provides:

## 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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