Poincare's Chaos
Over two hundred years after Newton published his laws of planetary motion the King Oscar II of Sweden and Norway sponsored a most unusual competition that would discover a whole new science.
Competition promised a cash prize to a scientist that would answer this question: ‘How Stable is the Solar System?’. Contestants would basically have to use Newton’s laws of gravitation to mathematically show the stability of our solar system. Applying Newton’s equations was easy for two bodies, say the Sun and Earth, however as soon as one added a third body, say the Moon, the problem would become so complicated that even the best physicists and mathematicians of the time were not able to compute anything. They were not even able to predict the three bodies’ trajectories of motion. This so called ‘three-body problem’ was therefore at the heart of this competition.
The prize was awarded ultimately to Jules Henri Poincare, one of the France’s leading mathematical physicists, even though he did not completely solve the problem and furthermore he showed what everybody was expecting the least. With his elegant math he showed that the three-body system behaved in a complex and totally unpredictable way. The Solar System, or at least his three-body approximation, was not stable at all, it was chaotic! Small changes in the initial conditions (such as planets positions and initial velocities) produced huge and unpredictable outcomes. His findings were ground stones for what we today know as chaos theory.
