Newton's nightmare?
Newton’s laws seem to promise that we may ‘know’ everything we might care to about systems that obey the laws of classical mechanics... and, in particlular, the solar system.
The promise is empty: in practice the future of many such systems cannot be inferred from their present state because it (the future) depends extremely sensitively upon
- what the present state actually is
- external influences
We find this phenemenon in surprisingly simple systems, Thus, for example, a satellite moving under the influence of two planets can exhbit a wildly evolving path, which seems never to repeat itself.
The accompanying figure shows the results of a computer simulation of the variation of the eccentricity of the solar orbit of Mercury over the last 400 million years. You can find out more about this here. |
As you may know, this takes us back to ‘chaos’ and butterflies.