Does the star move?

"moving away from us" is sort of misleading, it's more just a case of us and whatever object moving away from one another, because we don't know which one is doing the moving.
It doesn't matter which is moving. Only that the distance beween the two is increasing.

We are not motionless in space. The Sun revolves around the center of the Miky Way once every 250 million years and drags the rest of our Solar System with it.

The Milky Way, the rest of the Local Group, and all other galaxies that are part of the Hubble Flow are moving towards the Great Attractor, 47-79 Mega parsecs (150-250 Million Light-years) from the Milky Way, in the direction of the Hydra and Centaurus constellations. Variations in the redshifts of the galaxies in the Hubble Flow are sufficient to reveal the existence of the anomaly we call the Great Attractor. The first indications of the G. A. came in 1973, it's not a new discovery.

The parsec is a unit of linear measure equal to the length of the adjacent side of an imaginary right triangle in space. The two dimensions that form this triangle are the paralax angle (defined as 1 arcsecond) and the opposite side (which is defined as 1 astronomical unit (AU)) the distance from the Earth to the Sun. So a parsec is approximately 3.26 light years.
 
Holy crap. This thread sure turned into a giant pissing contest of everyone trying to sounds smarter than everyone else. Well done, guys.
 

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