00:00The two-body problem is an important theoretical model in mechanics, whether classical or quantum, in which
00:05The movements of two bodies, considered as material points A, in mutual interaction, are studied in a conservative manner; the global system
00:12being considered as isolated, B.
00:14This article will only address the two-body problem in classical mechanics; see, for example, the article on the atom.
00:21hydrogen for an example in quantum mechanics, first in the general case of an attractive potential, then in
00:27the very important special case where the two bodies are in gravitational interaction, or KE motion with acute accent, which
00:34is an important topic in celestial mechanics.
00:36The importance of this problem stems primarily from its exactly integrable nature, unlike the three-body problem.
00:42and more.
00:43Indeed, the two-body problem, which a priori has six degrees of freedom, can in fact be reduced to
00:49to the resolution of a one-body problem with a single degree of freedom, c.
00:53Furthermore, the results obtained make it possible to account for the trajectories of the planets in the solar system, in the frame of reference
01:00heliocentric, as well as those of their natural or artificial satellites, at least as a first approximation.
01:06We then find Kepler's laws, highlighted by the analysis of astronomical observations from the beginning of the
01:1217th century.
01:13Thus, the situation under consideration is far from being purely academic.
01:17The first solution to this problem was presented by Newton, who stated the fundamental law of mechanics.
01:23classically, the result is announced in propositions 57 to 65 of his principias.
01:28This article aims to present and provide a general treatment of the two-body problem, including the proof of the
01:34Kepler's laws and the detailed study of the different types of trajectories that could be considered.
01:39The question of determining the orbital elements, as well as Kepler's and Barker's equations and their
01:44Applications are covered in separate articles.
01:46See the articles on Keplerian acute accent movements, Kepler's equations and orbital elements.
01:52Let's go!
01:52Let's go!
01:52Let's go!
