Rudeyd,
The Earth and sun will not be anywhere near the center of the galaxy at anytime in the future, they are actually far out from the center. There is the idea that the solar system oscillates above and below the plane of the galaxy, but this is very slowly and would certainly not happen on a single day.
The Mayan calendar may turn over in 2012 (how exactly it matches up with our calander is not absolutely certain). But there is no more significance to that than there is to the turnover from Dec. 31, 1999, to January 1, 2000.
The Mayan knew a lot about astronomy - they had a very good calendar, they knew the length of the year and could predict the Venus cycle and eclipses, but there is no evidence that they knew anything about the galaxy.
If you search around BAUT, look for things like 2012 and Mayans and you will find a lot more information.
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At night the stars put on a show for free (Carole King)
One Earth, One Sky - IYA 2009
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