In his book D
ie Signatur der Sphaeren (The
Signature of the Spheres) the author unfolds the astonishing discovery of a complex order in our solar system and puts the ancient idea of a “harmony of the spheres” in an excitingly new perspective. Based on modern
astronomical and mathematical algorithms we witness the facts and figures of an indeed very astonishing order in our cosmic home.
The order and movement of the planets in our solar system corresponds very accurately to simple geometrical figures and musical
intervals, although in a different way than assumed in conventional concepts. One of the keys for an explanation is to be found in the analysis of the harmonical arrangement in the semiminor axes of the elliptical orbits, 
whereas earlier models and calculations were based on the semimajor axes.
The structures presented in The Signature of the Spheres incorporate the distances, the velocities and the periods of conjunction of the planets as well as the rotations of the Sun, Moon and Venus. Numerous graphics illustrate the extraordinary beauty of some of the geometrical forms, that result when the movements of several planets are put in relation.
Moreover the author describes and analyses the most important concepts of a “music of the spheres” from the ancient times until today with a
special consideration of Johannes Kepler's "revolutionary" ideas. Furthermore the current scientific facts about the origin of the universe and the solar system are explained. Thus the reader is invited to an
expedition and will be enabled to take part in a profound - professional and philosophical - discussion of the subject and its importance for the modern, mainly purely scientific view of the cosmos.
The essential discoveries represented in this book - concerning a really stunning geometrical and musical-harmonic order in our solar system - are summarized under the following headlines:
- The “music of the spheres”
- The play of the movements
- The secret of rotations
- The geometrical arrangement of the planets
The results are based on modern astronomical algorithms (VSOP-theory, developed by the Bureau des Longitudes, Paris etc.) In the appendix of the book you will find the mathematical and astronomical methods of calculation and also a detailed discussion of the accuracy and the periods of validity of the used methods.
The graphics on this page show three examples of geometrical forms which result, when the
movements of several planets are placed in relationship to each other over long periods of time:
1.) Jupiter, Saturn, Neptune, 8947 years; 2.) Venus, Mars, Neptune, 195 years; 3.) Venus, Earth,
rotation of the Venus, 240 years. For more details see ‘Play of movements’, ‘Rotations’, resp.
An English translation of
Die Signatur der Sphaeren
(The Signature of the Spheres)
by Hartmut Warm will probably
be published at the end of 2007