I am given equatorial coordinates and I need to transform them into a coordinate system that is at rest relative to the center of the galaxy. The closest thing I could find is galactic coordinates which seems like they are fixed with the sun at the center. Wouldn't this meant that they are moving with the same velocity as the sun and they are rotating?
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$\begingroup$ These are related and you may find them helpful as well: Where is the center of the Milky Way located? and also can you translate a GPS coordinate to a Galactic coordinate? and also How was the galactic plane established? $\endgroup$– uhohFeb 15, 2020 at 2:07
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$\begingroup$ aanda.org/articles/aa/full_html/2011/02/aa14961-10/… may or may not be helpful. $\endgroup$– user21Feb 17, 2020 at 15:53
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Galactic coordinates are sun centred with a zero longitude chosen to align with the centre of the galaxy when the measurements were made in 1958.
As defined, the galactic coordinates don't rotate, and so the position of Sag A* is very slowly drifting. Currently Sag A* is about 4 arc-minutes from the defined zero longitude, but decreasing by 5.7 milli-arcseconds per year (a tiny amount)
The task is ill defined, You can convert between different coordinate systems of the sky, but they all must be centred on the solar system.
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$\begingroup$ Okay, just to clarify, the galactic coordinate system is moving with the same velocity as the sun, right? Or can it be taken as stationary relative to the galactic center? $\endgroup$ Feb 14, 2020 at 22:57
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$\begingroup$ It is centred on the sun, so moving with the sun, $\endgroup$– James KFeb 14, 2020 at 23:26