Everyone from the Greeks to Copernicus assumed the orbits of the planet had to be circular. In 1571, German mathematician Johannes Kepler shattered that assumption with his great discovery.
If calculus were developed at that time, the calculation of planets’ orbit would be rather easy. However, astronomers at that time did not have this power mathematical tool. Thus, Kepler had to improvise ways to compute circular orbit of Mars. The work was tedious. Kepler wrote that he was almost driven to madness considering in calculating the matter.
His calculations began to reveal that the accepted notion of planet moving in circles simply did not work, and to get a self-consistent picture, he found that an ellipse was the path rather than a circle. With this finding, Kepler predicted when the planet Mercury would pass across the front of the Sun. At that time nobody else’s theory could do that.