How can someone obtain such vector, for stars in the Milky Way?
Input should be star data (from a catalog, eg: Hipparcos) and Julian Date.
Output should be a Vector Position (in pc) in relation to the galactic center.
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EDIT: It turns out a major problem with galaxy-center-based coordinates is that we don't actually know how far from us the center of the galaxy actually is. According to https://en.wikipedia.org/wiki/Galactic_Center estimates vary between 24,800 and 28,400 light years. You could arbitrarily choose a value, but the results would be off by at least 2,000 light years in some cases.
I was surprised that I couldn't find something like this online directly. The closest I found is the file "heasarc_tycho2.tdat.gz" on http://heasarc.nasa.gov/FTP/heasarc/dbase/dump/
The format is explained on http://heasarc.nasa.gov/W3Browse/all/tycho2.html and it includes the galactic latitude and longitude which are explained here:
Using this information, you'd still have to compute the positions yourself, but at least all of the data is there.
Of course, as others have noted, you can take any star catalog with any set of coordinates and convert it to the format you need. The catalog I list above just makes it a little easier, since they're precomputed some of the steps for you.
As you mention above, SIMBAD also includes galactic coordinates, but I couldn't find an easy way to download the entire catalog.