As our solar system performs its +-230 million year lap around the Milky Way, is the orientation of the ecliptic plane preserved independent of the center of our galaxy, or does the plane perserve its orientation (ie is gravitationally tied) to the center of our galaxy?
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1$\begingroup$ See: astronomy.stackexchange.com/questions/43208/… and astronomy.stackexchange.com/questions/34365/… $\endgroup$– Nilay GhoshCommented Oct 5, 2023 at 0:24
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Conservation of angular momentum keeps the solar system's overall axis of rotation pointing in a fixed direction as it revolves around the galaxy, just as the earth consistently points at Polaris over the course of an orbit. Tidal forces do cause the earth's axis to precess on a 25,000-year timescale, but tidal forces of the galaxy on the sun are much weaker. See this Q&A for a discussion of whether the sun's axis precesses like the earth's does.
Even if the entire system's plane does change over time under the effect (perhaps) of nearby stars, you would not expect it to be synchronized with its orbit around the center of the galaxy.
