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Eratosthenes discovered the circumference of the earth. This is still used today for several things including GPS, traveling, and much more.
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Claudius Ptolemy believed that the earth was at the center of the solar system. This was important to astronomy because he had the basics right, that planets are orbiting around something in the solar system, so he gave other astronomers something to work off of.
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Copernicus discovered that the sun is in the center of the solar system. It is important because it has completely changed the way astronomers see the solar system whether it be on a macro or micro level.
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Tycho Brahe discovered a star in the Cassiopeia formation. Brahe also discovered that comets were objects moving through space and not just objects in the earths atmosphere. He also created several instruments which have paved the way for instruments used in astronomy today.
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Kepler discovered the three laws of planetary motion. this is important because it has changed the way we know how our plants orbit the sun. He discovered that the planets orbit is an ellipse and not a perfect circle.
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Isaac Newton discovered several very important things. He discovered the laws of gravity and motion which astronomers use almost every day, and he also discovered calculus which is also used daily by many and has supported many theories.
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Albert Einstein found the equivalence of mass and energy, space relativity with the speed of light, and gave astronomers a much better idea of how gravity works. Einstein's discoveries are still used today by astronomers.