What astronomical cycle takes 52 years to coincide with the Mayan calendar century?

Its not so much to do with an astronomical cycle, though the 365 days for the earth to rotate the sun does come into it.

The tzolk'in calendar has 20 day names which then cycle 13 times to make 260 unique days. A normal year has 365 days, so to the two calenders are out of sync. It takes 52 years for the days to match up again, for the cycle to restart.