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Johannes Kepler
In 1596, Johannes Kepler published his Mysterium Cosmographicum which argued that the structure of the universe was based on five Platonic solids enclosed inside a sphere that represented the orbit of Saturn. The five shapes of the Platonic solids were tetrahedron(four faces), cube or hexagon (six faces, octahedron (eight faces), dodecahedron (twelve faces), and icosahedron(twenty faces). In 1609 Kepler published his book Nova Astronomia which argued heliocentrism and ellipses for planetary orbits instead of circles modified by epicycles in which Copernicus used. Nova Astronomia presented the first two laws of planetary motion by Kepler, but the laws would not have been formulated without the careful observations of Tycho Brahe. Tycho's observations allowed Kepler to prove that planets traveled in ellipses, and that the sun does not sit directly in the center of the orbit but off to the side. Kepler's second law was proven when he realized planets did travel in ellipses at different velocities, but still covered an equal amount of area over the same amount of time. In 1619 Kepler published his third and final law which showed the relationship between two planets instead of a single planets movement.

Kepler's laws of planetary motion

 * Indented line 1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.


 * Indented line 2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.


 * Indented line 3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit.

Galileo
In 1610, Galileo Galilei used his telescope to observe the phases of Venus as well as the moons of Jupiter. His observations upheld the opinions predicted by Copernicus. In addition, he showed that the theory of the anomalous orbit of the Moon was not unique. Using these facts, Galileo defended the heliocentric model in Dialogue Concerning the Two Chief World Systems in 1632. This led to his trial by the Inquisition and ultimate house arrest.