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But here's the good news: the work of Laskar and Gastineau - and also another team - shows that nothing dramatic should happen to the planets' orbits for the next billion years. So we can worry about other things. (9/n)
In the *really* long term, most of the stars in the Milky Way will be ejected. Through random encounters, individual stars will pick up enough speed to reach escape velocity. The whole Galaxy will slowly "boil away". It will dissipate in about 10^19 years. (10/n, n = 10)
That's only if it doesn't accrete other galaxies/clusters/dust/gas to offset losses, right? It's a little like the ship of Theseus. Is it still the Milky Way if all the present stars are replaced by new ones?
I believe all the accretion of other galaxies, dust and gas will be done long before 10^19 years. 10^19 years is a long time from now. Andromeda is expected to merge with our galaxy in just 5 x 10^9 years, even before the Sun becomes a red giant.
Nice thread! Maybe what is missing is some account of KAM theory, that was motivated by these stability problems in Celestial Mechanics but had an important impact in modern mathematics, and some rigorous results for a solar system with small planet masses (Arnold, Herman, etc)
KAM theory is great - but according to Laskar the existing results don't apply to our Solar system. Fun article: http://www.scholarpedia.org/article/Stability_of_the_solar_system … In 1966 Henon argued that the masses of the planets needed to be smaller than 10^{−320} the Sun's mass to apply KAM theory.
How about when humans starts mining nearby bodies, would that change how fast things will change?
Since we're talking about millions and billions of years, it's hard to tell. The amount of mining we can do in the next few hundred years is negligible. But in a thousand or million or billion years.... it's very hard to predict!
What fraction will enter the black hole at the galaxy's center before ejection?
I don't know any attempts to estimate that. I bet someone has tried, though!
When the Soviets discovered the Dzhanibekov effect also made a jump on the chair since they thought this could cause the Earth suddenly flip. It was demonstrated later that this cannot happen https://en.wikipedia.org/wiki/Tennis_racket_theorem …
Now I don't feel so bad about the star orbit simulator I wrote where this happened every time.
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