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This question already has an answer here:

I'm curious; does the Sun actually move? The concept behind the question is that if you wear a shirt and you move, does the shirt actually move? The Solar System orbits around the Milky Way, but does the Sun move?

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marked as duplicate by TildalWave, Mitch Goshorn, called2voyage Jul 8 '15 at 19:49

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    $\begingroup$ If you're wearing a shirt and you move, then of course the shirt moves. I think your confusion stems from the fact that motion doesn't make sense without (at least implicit) reference to something else to compare it to. You don't move with respect to yourself, and the shirt doesn't move with respect to you. ... You should specify something the Sun may or may not be moving with respect to (the Milky Way center, the Earth, etc.). If you don't, the question is just silly. $\endgroup$ – Stan Liou Jul 3 '15 at 10:23
  • $\begingroup$ One possible answer to this question: yes, the sun accelerates and is NOT in an inertial reference frame: en.wikipedia.org/wiki/Inertial_frame_of_reference In other words, if you yourself were not accelerating (meaning you ARE in an inertial reference frame), you would see the sun accelerate (move at a non-constant velocity). $\endgroup$ – barrycarter Jul 4 '15 at 18:20
  • $\begingroup$ This question is not a perfect duplicate of the linked question, but the answer lies either in the linked question or in What is in the center of the universe? that Tildal linked to. $\endgroup$ – called2voyage Jul 8 '15 at 19:50
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The Sun orbits in the Galactic potential. The motion is quite complex; it takes about 230 million years to make a circuit (meaning an orbital speed of around 220 km/s), but at the same time it oscillates up and down with respect to the Galactic plane every $\sim 70$ million years and also wobbles in and out every $\sim 150$ million years (this called epicyclic motion).

One can also measure how the Sun moves with respect to the average motion of the stars in the solar vicinity - the so-called local standard of rest. Estimates of the Sun's motion with respect to the LSR vary a little. According to Dehnen (Walter!) & Binney 1998 the Sun moves at 10 km/s inwards, at about 5 km/s faster than the average star tangentially to the Galactic centre and at about 7 km/s upwards out of the Galactic plane. Though as I mentioned previously, these motions are of an oscillatory nature around the mean value.

We could cast our net wider and ask how fast Sun moves with respect to the standard of rest defined by the cosmic microwave background - the local cosmological rest frame. The Sun moves at about 370 km/s relative to the CMB in the direction of the constellation Leo (as revealed by the dipole-like anisotropy in the CMB temperatures).

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Yes. No. It depends on your perspective. Suppose you're in a plane, flying from New York to Los Angeles. If you stay in your seat all the way, you haven't moved (from your seat). On the other hand, you clearly have moved, since you were in New York and now you're in Los Angeles. Motion is relative to some reference point, and you can always pick a reference point that makes something stationary. However, some reference points are easier to use than others; that's why the geocentric model of the universe isn't used any more: cycles and epicycles and so on are just too complicated, and using the sun or the the center of the galaxy makes it much easier to visualize and calculate what's going on.

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