What did johannes kepler use to discover that the orbit of mars is an oval

Kepler believed in the Copernican system and sought the key to reconciling Tycho’s observations with a heliocentric model for the solar system. In addition to his mathematical genius, his philosophical contribution was huge - as described by Einstein: "[Kepler] had to realize clearly that logical-mathematical theorizing, no matter how lucid, could not guarantee truth by itself; that the most beautiful logical theory means nothing in natural science without comparison with the exactest experience. Without this philosophical attitude, his work would not have been possible." (from the introduction Einstein wrote for Baumgard & Callan's 'Johannes Kepler: Life and Letters' (1953)). Kepler's focus on fitting the exact observations from Tycho led him to abandon the idea that the planets had to move on combinations of circles, a bit of logical-mathematical theorizing that had held sway for 1800 years!

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