They used to study the star relative to earths position.
But I guess they stumbled upon a problem in their calender program like Microsoft windows with the year 2000 date problem ( apparently in 90s microsoft machines were programmed with 31/12/1999 as the last date and there was a lot of panic caused with that error which was finally solved)
They were at a great location to view the sky, many hundred metres above sea level. They also had many people who believed what they said and they produced some of the most amazing sky charts that became used by many of the European astronomers. Although the Mayans did believe the world was going to end in 2012!
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