Tom, making observations and predictions based on observational periods is not a model. Tycho Brahe, who was brilliant at observation, never did generate a model that accurately fit with his own observations. That didn't happen until Kepler who was Brahe's student. Secondly, the naked eye is unable to resolve angular diameter smaller than one arc minute. Galileo was first to notice the changing angular diameter of Mars via a telescope. That didn't happen until the early 1600s. Your statement that we have been able to to predict the change in angular diameter of Mars for 1000's of years is absolutely false.
You seem to be struggling with the concept of a model. Observations are not models. Periodic observations over hundreds of years are not models. Models are explanations for the historical observations. A model is tested for its accuracy by using it to make predictions. If the predictions do not line up with the periodic observations then it needs to be adjusted. The models of Aristotle, Ptolemy, Copernicus, and Brahe all had errors. Some large and some small. It wasn't until Kepler proposed elliptical orbits that the modeling began to accurately fit with the periodic observations.
Lastly, are you able to look at the Java Script for the predictions for the upcoming eclipse? If you are, you will see that it's not pulling from a historical record.