# How can the life time of a multiple star system, such as for example the trinary system PSR J0337+1715 be derived?

As for example explained at the beginning of this blog post, the trinary system consists of a millisecond pulsar ($1.438$ times the mass of the sun) orbited by two white dwarfs. One of the white dwarfs ( $0.198$ solar masses) is very close to the pulsar and has an orbit period of $1.6$ d, whereas the other one ($0.410$ solar masses) is farther away and and needs about a year ($327$ d) to orbit the central pulsar.

Such a three-body system is in principle expected to show a chaotic behavior sooner or later, which means that collisions between these three celestial bodies can be expected and a finit life time of the system can be assumed.

Making some in my opinion way too hand-waving arguments, the blog post further explains that the collisions can not be expected too soon however, by taking into account that the distant white dwarf "sees" the inner white dwarf and the pulsar as a single central body and the relative motion of the inner white dwarf around the pulsar is rather stable and eliptic too.

Thinking about such multiple star systems as chaotic dynamical systems, another approach to estimate the liftime could be to make use of some chaos-theoretic methods which could for example involve the Lyapunov Exponent of the system, such that a large exponent would mean that the collisions happen soon and the stellar system has a rather short life time, whereas the converse would be true if the Lyapunov exponent is small (which is what I would expect for the system in my question).

So in short my question is: how can the liftime of a multiple star system be calculated in a not just hand-waving way?

This question is interestingly related to my issue, but it does not yet answer it...

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One place to look at is Kozai mechanism, which describes the effect of a third body on the parameters of the binary. It can potentially make the WD and NS collide with each other. – Alexey Bobrick Jan 10 '14 at 18:10