Final answer:
Kepler discovered his second law by analyzing Tycho Brahe's detailed astronomical data on Mars, which led him to realize that a planet moves faster when near the Sun and slower when farther away, sweeping out equal areas in equal time intervals in its elliptical orbit.
Step-by-step explanation:
How Kepler Discovered His Second Law
Johannes Kepler figured out his second law, which deals with the orbital speed of planets, by analyzing the meticulous observations made by Tycho Brahe. Brahe's detailed records of Mars' movements provided Kepler with the data necessary to determine that planets move faster when they are closer to the Sun and slower when they are further away. Kepler envisioned a straight, elastic line connecting the Sun and Mars and noticed that as Mars moved in its elliptical orbit, the line swept out equal areas in equal time intervals. This observation led to the formation of Kepler's second law, sometimes described as the 'law of equal areas.'
Kepler's analysis of the motions of planets was crucial in developing his laws of planetary motion, which were published in 1609 in The New Astronomy. These discoveries were significant in advancing the scientific understanding of our solar system and laid the groundwork for Newton's later work on gravitational forces.