ON THE PROBLEM OF BERTRAND AND THE LAWS OF KEPLER
Keywords:
the problem of Bertrand, laws of Kepler, hypothesisAbstract
In the article are presented results from historic research and a new interpretation of historical material. Joseph Bertrand offers the following problem: If you know that the planets describe conics without suggesting anything more, to find the expression of the components of the force from which they depend as a function of the coordinates of the application point. Another solution to this problem is given, which is based on the works of Darboux. Only two laws satisfy the necessary conditions: First law where force varies inversely with the square of the distance, and this is the law of Newton and second law where the attraction is proportional to the distance. The hypothesis is that the natural laws of the Universe depend on the scale of the phenomena. Within a galaxy is probably the only valid law of Newton. However, in the extra-galactic space of colossally longer distances, the other law is probably valid, where the attracting power is proportional to the distance.
References
•Bertrand, J. Théorème relatif au mouvement d’un point attire vers un centre fixe. C. R. Acad. Sci. Paris, 1873, 77, p. 849.•Bertrand, J. Sur la possibilite de deduire d'une seule des lois de Kepler le principe de l'attraction. C. R. Acad. Sci.Paris, 1877a, 84, pp. 671-674.•Bertrand, J. Note sur un Problème de Mécanique. C. R. Acad. Sci. Paris, 1877b, Vol. 84, pp. 731-732.
•Darboux, G.Study of a question on the motion of a point on a surface of revolution. Bulletin of the Mathematical Society of France, 1877a,5, pp. 100-113.•Darboux, G. Recherche de la Loi que Doit Suivre une Force Centrale pour que laTrajectoire qu’elle Détermine Soit Toujours une Conique.C. R. Acad. Sci. Paris, 1877b, Vol. 84, pp. 760-762; pp. 936-938.
•Darboux,G. Sur un probleme de mecanique, Cours de mecanique, T. Despeyrous, Vol. 2, Note XIV, Herman, 1866, Paris, pp. 461–466.•Glaisher, J.W.L. On the Law of Force toany Point in the Plane of Motion, so thatthe Orbit may be always a Conic, Monthly Notices of the Royal Astronomical Society, 1878, Vol. 39,pp. 77-91.
•Halphen, G-H.Sur les Lois de Kepler. C. R. Acad. Sci. Paris, 1877a, Vol. 84, pp. 939-941.•Halphen,G-H. Darboux's Notes to Despeyrous' Mecanique. C. R. Acad. Sci., 1877b,Paris, 8.
•Kepler,J., AstronomiaNova. 1609.•Kepler,J., Harmonices Mundi. 1619.•Moulton, F.R., An introduction to Celestial Mechanics. MacMillan Co., New York., 1914.
•Newton,I.,Philosophiae naturalis principia Mathematica. 1687.•Villarceau, Y.,Memoires et Notes sur les Etoiles Doubles, Paris, Bachelier, 1850.•Bonev N., Theoretical Astronomy. Nauka i Izkustvo, Sofia, p. 466, 1961. (In Bulgarian).
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
CC BY-ND
A work licensed in this way allows the following:
1. The freedom to use and perform the work: The licensee must be allowed to make any use, private or public, of the work.
2. The freedom to study the work and apply the information: The licensee must be allowed to examine the work and to use the knowledge gained from the work in any way. The license may not, for example, restrict "reverse engineering."
2. The freedom to redistribute copies: Copies may be sold, swapped or given away for free, in the same form as the original.
