I don't know that Venus was much help in creating a 360 day calendar, which is obviously based on an Earth orbit.

Venus orbits the sun in 225 days and, when combined with the Earth's orbit, becomes very interestingly complex to predict morning and evening positions long into the future. The Mayans were some smart cookies, however, and Venus is incredibly bright and obviously important, so (without more research), I wouldn't be surprised at all if their astronomers figured it out and incorporated the motion of Venus into their calendar or, more likely, were able to predict Venus' motion with their very sophisticated long and short calendar rounds (or whatever they called them).

Time range of the Mayan calendar is a different question. From what I understand they had a short one and a long one. Of course, now everyone is getting all excited about the end of the long one.

Synodic time is related to the phases of the moon, no? Got nothing to do with the universe as a whole.
Source(s):
http://inkido.indiana.edu/a100/earthmoon4.html

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