In a circle, the semimajor axis would be the radius. Kepler had studied astronomy long before he met Tycho; he favored the Copernican world-view that said the planets orbited the Sun. He also worked on problems in optics, and in particular, invented a better version of the refracting telescope.
Kepler also corresponded with Galileo about his observations and conclusions. Check Your Learning What would be the orbital period of an asteroid a rocky chunk between Mars and Jupiter with a semimajor axis of 3 AU?
Speed is greatest at the point in the orbit closest to the Earth, called perigee, and is slowest at the point farthest from the Earth, called apogee.
His discovery of the basic laws that describe planetary motion placed the heliocentric cosmology of Copernicus on a firm mathematical basis. The shape roundness of an ellipse depends on how close together the two foci are, compared with the major axis. All matter exerts a force, which he called gravity, that pulls all other matter towards its center.
From this realization, he concluded that the orbit of Mars was elliptical, not circular. By unifying all motion, Newton shifted the scientific perspective to a search for large, unifying patterns in nature.
Brahe was the last and greatest of the pre-telescopic observers in Europe.