What are Kepler's three laws? Why are they significant?
Kepler's first law states that the planets travel around the sun in elliptical orbits with the sun located at one focus. This was significant because, until Kepler, it had been firmly believed that the planets traveled in circular orbits. No one was pleased with the aesthetically distasteful idea of ellipses. The second law, which Kepler discovered first, states that as the planets travel around their orbits, they sweep out the same amount of area per unit of time, no matter where they are on the orbit. Like Kepler's first law, this second law destroyed a long-held belief. Astronomers had always assumed that the planets traveled with a uniform speed – Kepler proved that the speed varied as the planets traveled around the orbits. It was only the area covered that remained uniform. Finally, the third law states that the cube of the distance a planet's orbit is from the sun is directly proportional to the square of the period, or time it takes the planet to travel around the sun. This was the first time anyone had thought to question the relationship between a planet's distance from and speed around the sun. The equation was nothing more than an interesting mathematical relationship to Kepler; it wasn't until Newton created the theory of universal gravitation that the meaning of this relationship became clear.
What was Kepler's theory of the perfect solids?
In 1595, Kepler had an epiphany. He was searching for a rationale for the number and spacing of the planets, and he believed he had found it in the perfect solids. A perfect solid is a three dimensional figure, such as a cube, whose sides are all identical. There are only five perfect solids, each of which can be inscribed in and circumscribed around a sphere. Kepler believed that the orbits of the six known planets could be fit around the five regular solids. He felt he had seen into the mind of God and finally understood the structure of the universe. He described this theory in his first book, the Mysterium Cosmographicum. Kepler's theory was incorrect, but developing this idea became his motivation for a lifetime of astronomical study.
What role did Tycho de Brahe play in Kepler's life?
Had Kepler not crossed paths with the famous astronomer Tycho, he may never have formulated any of his three laws. Kepler needed Tycho's incredibly accurate and comprehensive astronomical observations in order to fully develop his own system. In 1600, Kepler traveled to Prague to work in Tycho's lab. Although he was there for only a year before Tycho died, that year marked a turning point in Kepler's life. Tycho was a tyrannical boss, but he provided Kepler with the two tools Kepler would need to revolutionize astronomy: detailed observations and the orbit of Mars. Tycho assigned Kepler to figure out the shape of the orbit of Mars. The thorny problem would take him over half a decade to solve, but the struggle was worth it. Only in the irregular orbit of Mars could Kepler have discovered the fundamental properties of the planetary orbits. Once Tycho died, Kepler took his astronomical observations from the laboratory and went to work on the Mars problem. Eight years later, he published his results in the Astronomia Nova. Tycho had hoped that Kepler would apply his theories to the Tychonic system of the universe, but Kepler stayed true to the Copernican system. Kepler used the Copernican system to develop the Astronomia Nova.