It has long been known – possibly since the time of the Babylonians – that the relation of the movements of the planets Venus and Earth is geometrically structured according to the number five. When we continually plot the movement of Venus from a geocentric view we obtain a fivefold loop figure. If we connect the subsequent positions of conjunction of both the planets by lines this leads to a nearly exact pentagram. As shown in Fig. 2.1, one pentagram which forms in an 8-year period is turned only by 2.4 degrees compared to the preceding one. Figure 2.1 Venus/Earth-loops as seen from Venus over a period of 15.987 years (including 10 conjunctions). The pentagrams show the positions of the conjunctions and oppositions (on the outside). A view from Earth yields the same figure, only turned by 180 degrees.

In the representation of the linklines or  ‚Raumgeraden‘, (i.e. the imaginary connecting lines between two planets within a fixed period), a concept developed by the author, it can be seen that the geometrical formative principle repeats itself in the heliocentric view. After about eight years we witness the full blossom of a fivefold starflower shown in Figure 2.2. Figure 2.2. Linklines between Venus and Earth, continually plotted, stepping interval 3 days (1000 times). Scale in millions of km. Sun in the centre of the co-ordinate plane. © Keplerstern Verlag

The evenness of these figures results from the very exact 13/8 proportion of the periods of revolution of both planets (and is independent of the chosen 3-day interval). Ratios of small integers of this type are called resonances in celestial mechanics. In the long term they can influence the stability of the orbits of planets or asteroids. This influence can have a reinforcing but also a destabilising effect, depending on the gravitational interaction between the celestial bodies, caused by the build-up of resonance. The graphics of movements shown here, give an overall impression of these influences. Up to the number 12 there is only one more geometrically distinct resonance among the relations of any two planets within our solar system, as shown in Fig. 2.3. (Why the number 12 serves as the upper limit the planets will explain "for themselves" shortly). Figure 2.3 Linklines between Jupiter and Uranus, continually plotted, stepping interval 60.78 days (1000 times), total space of time 166.4 years. © Keplerstern Verlag

Strangely enough the pentagram, which has been associated with the human being since ancient times, manifests itself in the inner solar system, in the relation of Earth and Venus, the goddess of love. In outer regions, on the other hand, we see the hexagram, a symbol for the permeation of two polar principles, which constitute the order of the material world. To delve more deeply into the symbolic language, which seems to be incorporated in our cosmic home, we now have to consider other planets, i.e. the constellations of three of them at a time. As already mentioned the Venus/Earth pentagram forms, when we plot the positions of their conjunctions continually and draw lines between them (in geocentric as well as in heliocentric view). If we plot the position of Mars after each complete formation of a pentagram and connect the various points, we obtain an almost fully resonant square. It is just slightly distorted, due to the relatively high eccentricity of the Mars revolution (compare Figure 2.4). Figure 2.4 Mars in relation to Venus/Earth-pentagrams (150 times); from inside to outside: orbits of Venus, Earth and Mars over a total period of approx. 1195 years. The Venus/Earth pentagram is noted only once in each orbit. © Keplerstern Verlag.

The symbol of the human being is thus placed into a quadrangle; one could also say, man is nailed to the cross of the world or of the god of war. A cross arises if one connects the opposite corners of the square, but it materialises also in other diagrams, or patterns, of planetary movement, but this goes beyond the scope of this summary. Even without this interpretation the geometrical constellation between our home planet and its two cosmic neighbours is so remarkable, that you have to wonder, why it has never been mentioned in any relevant literature on the planetary system.  ... ...