Letting the calendar cycle for 45 years gives each planet a chance to complete a synodic cycle. //

"By increasing the calendar length to 20 periods of 819-days a pattern emerges in which the synodic periods of all the visible planets commensurate with station points in the larger 819-day calendar," the researchers wrote.

The math appears to bear that out. NASA reckons Mercury's synodic period is 115.88 days, but if we allow the ancient Mayans some leniency due to their lack of advanced scientific instruments and say it's 117 days, you can get exactly seven periods on the calendar.

The other planets visible from Earth and known to the Mayans – Venus, Mars, Jupiter and Saturn – all have similar mathematical matches when the calendar is allowed to make multiple cycles. Mars, which has the longest synodic period at 780 days, takes 21 periods to fit exactly into 20 cycles, both of which have 16,380 days, just shy of 45 years.