The Mayans and the Greeks and the Egyptians and the Indians, and maybe the Chinese, knew that the Earth orbits the Sun, they just used the geo-centric model for astrological purposes. In the Mayan long-count calender the wobble of the sun is mapped out exactly day by day. This is what the whole tonal system is in their astrology. Although people have known that the Earth orbits the sun, it isn't practical for astrological purposes to map it that way. The Christians in the dark ages suppressed this knowledge.
As for the Mayans calling planets stars, semantics lost in translation. They did this all without telescopes. So did the Greeks. So did the Egyptians and the Indians. The Eskimos have 100 words for snow. We know that there are different kinds of snows, but we just call it 'snow'. The Mayans knew that the Sun was different than the Moon. It can be forgiven if people call some asteroids 'planets', even Pluto is no longer a planet, but if we call it a planet that doesn't mean that we are ignorant. It is just a word. The word translated to 'star' may literally mean 'celestial body' for all we know. The Mayans knew there was gravity. Sure, they didn't have Newton's law, but they observed the Sun's wobble and apparently figured it out via some unknown science. It is all mapped out in the tonal. Day by day. The evidence that they knew this is right there on their calendar. They used this information to predict the weather. Their calendar was also a weather forecast! I wonder if you guys have actually looked at their calendars. They had many, not just the one that we are talking about here. These different calendars served different purposes. The ones that the average people used was very basic, but still much more sophisticated than our modern one.
I saw a video on google videos of an astronomy conference that took place in 2001 and an astronomer from Hawaii was claiming that the sun wobbled and he had a slideshow showing how it does it. Apparently he was the one who discovered this. I agree that it makes sense that everybody should know this, and maybe now everybody does. The wobble of the sun also affects the orbit of the Earth, it is all interconnected, of course.
Edit: apparently they do measure the wobble of stars to determine if there are planets around them, but many times they are wrong and find only asteroids or 'planetoids'. This may also be semantics.