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This is a fair reflection - there are some really great detailed simulations of Andromeda swirling through MW - thousands of stars all moving by Newtons nearly-400-year-old laws.
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Gemini 3 FAST - I simplified it for non geeks:
The Milky Way, positive spin vector points toward the South Galactic Pole (SGP).
This vector is tilted 62.9° away from Earth’s South Pole (or 117.1° away from Earth's North Pole).
Andromeda's positive spin vector is tilted 77° away from the Milky Way's positive spin vector.
This means these spin axes are nearly perpendicular (not quite, but closer to 90° than to being parallel). They are effectively spinning on different planes as they rush toward each other.
When these two galaxies merge in roughly 4.5 billion years, these near-perpendicular spin vectors will cause a chaotic "settling" period. Because they are not aligned, they won't simply merge into a larger spiral; the angular momentum will cancel out in various directions, eventually resulting in a giant elliptical galaxy (often nicknamed "Milkomeda").