"The aim of this page is to assemble a variety of simple proofs for the wonderful fact, first proved by Isaac Newton, that the orbits of bodies subject to an inverse-square force are conic sections: ellipses, circles, parabolas, hyperbolas or straight lines.
Although conic sections are defined in the first instance as the curves produced when a plane intersects a cone, these curves have a wealth of well-known properties that characterise them equally well. The idea of this page is to explore the relationship between the inverse-square force law and as many of these properties as possible."
5 out of 5
http://www.gregegan.net/SCIENCE/ConicSectionOrbits/ConicSectionOrbits.html
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