## Abstract

Based on McGehee's transformation f = I^{-1}q; g = I^{ 1 2p};, dt dt′ = I^{ 3 2}, I introduce the transformtion X = (g^{T}M^{-1}g) ^{ 1 2}, h ≥ 0X = (g^{T}M^{-1}g) - 2Ih)^{ 1 2}, h≤0, u = IX^{-2}; F = X^{2}f; G = X^{-1}g; dt′ dt = X^{-3}. I prove that these variables may be continued to every point of the new time axis t for any initial value, and the whole axis corresponds to the "time interval of existence of the global solution". Also, F, G, u are O(e^{Bτ}). I then obtain a region H on the complex plane τ, |Im(τ)| < A exp (B Re τ^{2}), over which F and G are analytic. Here, A, B, C are constants related only to the masses and the initial value. Lastly, a conformal mapping is established which maps a subregion of H, H, onto the unit circle of the new complex variable, thus obtaining a global solution of the n-body problem. The convergence of my power series is admittedly unsatisfactory and so the present result is of limited value for practical calculation.

Original language | English (US) |
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Pages (from-to) | 135-142 |

Number of pages | 8 |

Journal | Chinese Astronomy and Astrophysics |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1986 |

Externally published | Yes |

## ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science