Open problems on the eve of the next millennium
This paper contains some interesting opinions of the author on some open problems in the field of celestial mechanics for the next century. It must be noticed that Prof. Szebehely is a well-known authority in this field, particularly in the restricted problem of three bodies, and consequently his opinions have a special value. The paper starts with some historical remarks on the evolution of celestial mechanics from Copernicus up to the present century. Then the author comments briefly on the open problems which pose the non-integrable systems in this field by introducing an illustrative example which shows how the reduction techniques allow to gain insight into the properties of the flow and also into the underlying field of forces. Finally, he points out that, taking into account the increasing improvements of computer technologies, it is expected that new numerical techniques will allow to have a better knowledge of many problems of celestial mechanics and, on the other hand, with the help of statistical mechanics the statistical approach will gain importance in the future.
scientific article; zbMATH DE number 1051508