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I know it can't be a perfect ellipse or smooth orbit due to all the matter in every direction, and our Sun could be affected by a gravity assist of sorts if it passes close enough to another massive star. I also know that galaxy orbits are different than Solar System orbits because most of the mass is in the dark matter halo and as a result, the outer stars orbit faster than in a standard orbit, so there's a number of variables.
But, if we ignore gravity assists, is the sun mostly in a standard, or lightly inclined orbit around the center of the Milky way or more sinusoidal?
Reason I'm asking - see (attached and in my opinion, bad) article, and picture included.
I've seen pictures like this before that suggests that the Solar System moves in a kind of sine wave motion. I've seen estimates between 26 and 32 million years with the solar-system, rising above then below the plane of the Milky way with consistency (and perhaps, mass extinctions tied to this movement).
I can kind of see that happening, as the sun rises above it might have more gravitational pull below it drawing it back down and you kind of have a horizontal velocity to displacement cycle creating a sine wave in the orbit. That makes logical sense, but I'm wondering if that 26-32 million year sine wave type of movement is generally accepted or more somebody's imagination. Is anything definitive known about stars' orbits within galaxies?