Why are the planet's orbits in the form of an ellipse and what is the proof that earth moves in an elliptical path with the sun at its foci? Initially it was thought that earth moved in a circular orbit. Then,how was it discovered that it moves in an ellipse?
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1Very mathematical! http://radio.astro.gla.ac.uk/a1dynamics/ellproof.pdf – Hritik Narayan Jun 08 '15 at 12:37
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2possible duplicate of Why don't planets have Circular orbits? – ACuriousMind Jun 08 '15 at 12:53
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"Initially it was thought that earth moved in a circular orbit" is pretty much completely incorrect. At no point was this the case. You may be thinking of Aristotle and Ptolemy's epicycle system. The only serious heliocentric proposal which involved circular motion was that of Copernicus, which gave way to Kepler's observations of elliptical orbits within a century. In short, though, the proof is: we looked, and it isn't. – Emilio Pisanty Jun 08 '15 at 13:13