Abstract
In the half-dozen or so years leading up to the publication of the Principia, Isaac Newton observed the comets of 1680 and 1682 and wrestled with the extent to which his law of gravitation could be applied. In time, he would see the connections between the four possible orbits of a satellite (circular, elliptical, parabolic, and hyperbolic) and the four curves produced by the careful carving of a cone. But if we look a little further into the conic sections, we find some interesting connections among the natural orbit of a satellite, ancient mathematics, and the roots of familiar words. Illuminating these connections for introductory physics students may help them to better understand the role of language and mathematics in the descriptions of science.
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