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This is important because most people believed the Earth was flat until then.
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A few of the things in this were a catalog of 48 constellations and a geocentric model of the solar system. Although it was wrong, it's an important part of Greek history.
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came up with an early model of the solar system where the Earth revolves around the sun. This is important because many thought the Earth was at the center before. His model was more accurate to today
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Discovered that Jupiter and Saturn pass very close to each other, that contradicted information about planetary motion during the time. Brahe decided he could do a better, more accurate observation and dedicated his studies to proving so. This is connected to Kepler's Law, and is important because we wouldn't know what we do today without him
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came up with three laws of planetary motion based on Tycho's observations. He was one of the first to state that motion is in terms with a force from the sun - this is important because it later led to Newton's law, which we are all familiar with
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established his three laws of gravity, which altered the way we see science and led to numerous other discoveries. He was also influential because he invented calculus and investigated common things such as chemistry, theology, etc.
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He stated that energy and matter are the same thing in different forms, physics are the same everywhere, space and time are linked, etc. He discovered many things over the course of his life, but many important observations took place in 1905. He is important because his studies went beyond understanding and introduced something new.