# Henri Poincare and the Three Bod Problem

## Henri Poincare and the Three Bod Problem

• Submitted By: preppygirl16
• Date Submitted: 09/07/2008 5:16 PM
• Category: Science
• Words: 597
• Page: 3
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Henri Poincare was born on April 29 1854 in Nancy, France. He came from a very influential family. His father was a Professor of Medicine at the University of Nancy. His Cousin Raymond was the Prime Minister of France. His sister Aline married the spiritualist philosopher Emile Boutroux. In college he studied mining engineering, mathematics and physics. He received a doctorate in Mathematics in 1879. He was appointed to a chair of mathematical physics at Sorbonne in 1881. He held this position until his death on July 17, 1912.
In 1885 Poincare entered a Mathematics contest that was initiated by the King of Sweden. One of the questions in this contest was to show that the solar system as modeled by Newton's equations is dynamically stable. This question was known as the three-body problem. It is viewed as one of the most difficult problems in mathematical physics. He proposed that there is no analytical solution to the three-body problem. He said that we can only obtain approximate answers. For a problem involving three or more interacting bodies there is no closed solution, or simple mathematical expression. Given the law of gravity and the initial positions and velocities of the only three bodies in all of space, the subsequent positions and velocities are fixed so the three-body system is deterministic. However, he found that the evolution of such a system is often chaotic in the sense that a small perturbation in the initial state such as a slight change in one body's initial position might lead to a radically different later state than would be produced by the undisturbed system. If the slight change isn't evident by our measuring instruments, then we won't be able to predict which final state will occur. This research proved that the problem of determinism and the problem of predictability are distinct problems. This approach was viewed as groundbreaking in the world of science and physics. Even though he did not solve the problem he was still...