Never, the plane of the ecliptic is inclined about 63 degrees to the plane of the galaxy and the center of the galaxy is not at one of the nodes, therefore they will never be in a straight line.
The center of our galaxy is in the constellation Sagattarius. So if you want to know when it comes closest, just get a star wheel, or use other means to determine what time of year Sagattarius is on the meridian at midnight or noon.
Well Giving that the top and bottom replys are true and that the 63 degrees difference doesn't count for much due to the size difference between the Earth and sun vs the sun and the center then where in sagattarius is the center? Would that be if the center of the gallaxy is in the center of sagattarius and why the meridian. I'm not a student and I don't have a star wheel. Will some one bring the question up to one of there teachers and find the andswer out for me. I will be very thankful for that help
There are a number of shareware planetarium programs out there, but according to Starry Night (it also has a shareware version), the galactic center makes its closest pass to the sun on about December 20 -- at about 6 degrees of separation.
Hmmm - looks like the trial of Starry Night isn't offered anymore. But I found this via google: http://www.maa.mhn.de/Tools/tools.html Some are pretty old, though. You could just google "planetarium software download" or "planetarium software shareware"