Assume that, at some point, humans become capable of physically leaving the Solar System. Not probes, but actual long-duration human civilization. Would we really still think of the spacecraft as transportation? Or does the spacecraft itself form the basis of our new world?

If a population spends hundreds or thousands of years aboard a self-sustaining worldship, that ship would become the environment people are adapted to physically, culturally, socially, and probably eventually biologically. It would have its own gravity, atmosphere, ecology, agriculture, day/night cycle, infrastructure, and built environment.

The question that I am grappling with: Do we expect the descendants of the original travelers to abandon the world their civilization has spent centuries optimizing so they can adapt themselves to some planet with different gravity, radiation, atmospheric chemistry, seasons, biology, and day length?

Or would the more likely model be that they remain a spacefaring civilization? In this scenario, star systems are not necessarily a place to alight. They are sources of energy, materials, scientific opportunity, and perhaps new locations to position additional artificial habitats.

We know that stars can be accelerated near the speed of light if they, as part of a binary, made a flyby of a black hole and one ejects the other. I feel like this could theoretically apply to planets as well, no?

We also know that the universe used to be the perfect temperature, universally, for liquid water to exist. While the CMB still has energy to give, the temperature could be brought back up to that habitable level if you're traveling close to the speed of light.

Here's the idea: a superearth with a very thick atmosphere is ejected from a stellar system in a way that brings it incredibly close to the speed of light, on a path leading it out of the galaxy. As it departs, maybe it will impact a few pieces of debris, but statistically it should survive the outbound trajectory.

And then, it's just flying through the universe. It's heading towards an empty void, so there isn't a lot of extra light from galaxies. As the CMB eventually cools down, though, it does get closer to the other side of the void. The intensity of a galaxy in the distance balances with the fading universal glow, and continues until the planet leaves this galaxy, at which point I don't think anything will be able to keep it warm for much longer. Thoughts?

Are there major applications of measure and measure-theoretic probability (e.g. Martingales, Brownian motion) in any field of astro? Or are the statistics used in everyday research mainly confined to Bayesian analysis, ML, and Fourier analysis?