Lyapounov Time

The Lyapounov time (L) is a parameter that measures the speed rate at which orbits diverge (or, in other words, it measures how much chaotic an orbit is). L is the period of time for the distance between two near possible orbits to increase of a factor e. The bigger this value is, the more stable is the orbit (L has typical values of a few years for chaotic asteroids, upt to 5 million years for the inner planets and hundred million years for the external planets).

For a non chaotic orbit (above picture) the distance between two near orbits that have similar initial conditions, is a linear function of time. The two orbits diverge slowly, and their distance can be expressed as a linear function of time:

For chaotic orbits, the distance between two near orbits can be expressed as an exponential function of time with the formula:

This formula means that after a period of 2 L, the 2 orbits will be at a distance of , meaning that this distance varies exponentially with time.

 

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