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Eratosthenes measured the size of the round Earth using the Sun (240 B.C.). This was important because he was not far off from the actual measurement, he made his measurements in a time everyone thought the Earth was flat , and his discovery paved the way for future scientists.
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Ptolemy developed the theory of a geocentric universe (127 AD). Although this theory was incorrect, it was important because it led other scientists to research it and eventually come to correct conclusions.
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Copernicus published a work in 1543 that explained why Ptolemy's geocentric theory was incorrect, and how a heliocentric universe is more accurate. It was important because he was the first one to bring up the theory during the Renaissance period.
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Tycho Brahe attempted to prove that the Earth was in the center of the universe, and is credited with having the most accurate observations made by the naked eye (1564-1597). He also managed to measure to one minute of arc. This was important because Kepler used his observations to come up with the planetary laws of motion.
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Kepler discovered that the planets' orbits are ellipses (1609) and came up with three laws of planetary motion. These discoveries were important because it helped astronomers get an accurate picture of what the universe looks like and how it works.
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Newton came up with three laws of motion (1686), which was important because before him, scientists didn't know about the force of gravity. Understanding gravity unlocked the doors to many more discoveries.
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Einstein is known for coming up with the theory of relativity (1905). This was important because it is so essential to modern physics that it is known as one of its two pillars. This discovery also was important because Albert Einstein made the claim that the laws of physics were the same throughout the universe.