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A visit to the Newtonian \(N\)-body problem via elementary complex variables. (English) Zbl 0748.70008

This is an essay on celestial mechanics via elementary complex variables. Some of the material described here is known by experts in celestial mechanics, but, according to the author’s opinion, it does not seem to be well known outside of this community. The study of how \(N\) celestial bodies move under gravitational forces is an old one. With the help of elementary complex variables, the author describes certain selected orbits (Earth, Mars, Mercury). Also, some of the history of the Newtonian \(N\)-body problem is related with an emphasis on the myth that only the two body problem has been solved. By the same way, using elementary complex variales, the theory of the collisions in connection with the spinor transformation, and the Sundman theory regarding the \(N\)-body problem are developed. The paper ends with a historical aside on certain problems from celestial mechanics playing a role in the development of some of the classical results in complex variables.
Reviewer: C.Simirad (Iaşi)

MSC:

70F10 \(n\)-body problems
30C20 Conformal mappings of special domains
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