Celestial Mechanics and Dynamical Astronomy

, Volume 50, Issue 1, pp 73–88

The global solution of the N-body problem

  • Wang Qiu-Dong

DOI: 10.1007/BF00048987

Cite this article as:
Qiu-Dong, W. Celestial Mech Dyn Astr (1990) 50: 73. doi:10.1007/BF00048987


The problem of finding a global solution for systems in celestial mechanics was proposed by Weierstrass during the last century. More precisely, the goal is to find a solution of the n-body problem in series expansion which is valid for all time. Sundman solved this problem for the case of n = 3 with non-zero angular momentum a long time ago. Unfortunately, it is impossible to directly generalize this beautiful theory to the case of n > 3 or to n = 3 with zero-angular momentum.

A new ‘blowing up’ transformation, which is a modification of McGehee's transformation, is introduced in this paper. By means of this transformation, a complete answer is given for the global solution problem in the case of n > 3 and n = 3 with zero angular momentum.

Key words

N-body problemblowing up transformationanalytic continuation

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Wang Qiu-Dong
    • 1
  1. 1.Department of Mathematical ScienceUniversity of CincinnatiCincinnatiU.S.A