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One computer simulation that should give a general notion:

Most stars and matter will become part of the fused galaxy, "Milkomeda" is one proposed name. Some will be flung int intergallactic space.

The Sun will have entered its white dwarf phase. Earth will either be a cinder, or have been subsumed by or possibly be nova ejecta of the Sun.

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Wow, thanks. That's such strange dynamics... their separation seems to follow a square wave more than a sine wave! Any idea why?

This is an entirely uneducated guess, but look closer at the spin over time, and consider the objects low density. Think timeline of a highly elliptical orbit, but with energy and work concentrated on angular momentum.

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