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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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The N-body problem

The N-body problem

(p.119) 13 The N-body problem
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter discusses the N-body problem. In 1886, Karl Weierstrass submitted the following question to the scientific community on the occasion of a mathematical competition to mark the 60th birthday of King Oscar II of Sweden. Weierstrass asked that, ‘given a system of arbitrarily many mass points that attract each other according to Newton’s laws, try to find, under the assumption that no two points ever collide, a representation of the coordinates of each point as a series in a variable which is some known function of time and for all of whose values the series converges uniformly’. Henri Poincaré showed that the equations of motion for more than two gravitational bodies are not in general integrable and won the competition. However, the jury awarded the prize to Poincaré not for solving the problem, but for coming up with the first ideas of what later became known as chaos theory.

Keywords:   N-body problem, Laplace effect, restricted three-body problem, Gauss equations of perturbations, gravitational bodies, chaos theory

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