How does the search to explain planetary orbits exemplify the scientific method and the use of models

Since antiquity, people have made observations about the way the stars and planets move. Up until newton, no one thought they had elliptical orbits, everyone assumed they were perfect circles (circles were "perfect" and they assumed the heavens were perfect), even when their models they made didn't work to explain their movements. Gradually, people would make maps of the orbits that added circles on circles on circles, and could never really explain the ways the planets moved well. In fairness to them, they lacked the math to explain it, it wasn't until newton invented calculus that we could have understood and calculated planetary orbits to any accuracy. People used their observations to say that the orbits looked kind of like circles, they developed their models and did the math, and their hypothesizes were wrong, so they kept going back to the drawing board (usually with the same trick of adding more and more circles) until newton came along and tried to match a model that used elliptical orbits and invented the math that allowed him to make predictions with it, and it turned out his model worked for most planets. Mercury for instance had a very strange orbit that wasn't fully explained until Einstein's theory of General Relativity. Scientists and Astronomers made hypothesizes that there was another planet orbiting too close to the sun to see with telescopes, called Vulcan, that explained mercury's wayward orbit before Einstein's theory, even long after we had telescopes good enough to see if there was a planet orbiting closer to the sun than mercury.