Re: Movement of the Sun?
Its motion through the galaxy has been explained already, but there are also local dynamics in play. The Sun doesn't actually sit still at the center of the Solar System: it has its own orbit as well.
In the two body problem, each body orbits the common center of gravity (the barycenter). Jupiter is large enough that the Sun actually orbits a point slightly above its own surface. The Earth makes it wobble a tiny amount too (a few hundred kms I think), as do the other planets, but Jupiter's effect probably accounts for >99% of the Sun's wobble.
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