Christian Marchal

We use this addendum to indicate a remarkable and simple generalization of a classical property of two-body motions.

Celestial Mechanics has a long history strongly related to human condition and to the successive scientific revolutions. It remains the most accurate science and has seen tremendous progress in the three last centuries. It has led to the discovery of several dissipative phenomena that are in many cases the real factors of evolution. The unsolved questions of Celestial Mechanics may have a decisive impact on cosmology.

At the end of the nineteenth century the triumphant "scientism" left almost no room to consciousness and claimed that it will soon rule everything. The determinism was considered as the main property of scientific facts while freedom, will, free-will were considered by most scientists as illusions.
The danger of this evolution was pointed by Henri Poincaré (1854–1912) who developed many philosophical considerations on the future of science and its relations with mankind. He was also a major scientist opening the gate to the theory of chaos that was for decades considered as an odd singularity and revealed its fundamental importance in the seventies when chaos was acknowledged in most domains of science and technology.
The other main philosophical upheavals of science were of course the intrinsic presence of random, irreducible to determinism, (theory of quanta) and the trouble of scientists confronted with the terrible misuses of science. All this has led to new perspectives on consciousness and freedom while materialism is no more a must.