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Eccentricity
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Eccentricity ($\epsilon$ or $e$) is a dimensionless parameter that quantifies the deviation of a geometric curve, most commonly a conic section, from being perfectly circular. In mathematics, it is a fundamental measure of how "squashed" or elongated a curve is. Formally, eccentricity relates the distance between the two foci of the conic section to the length of its major axis.
Historically, the concept was deeply embedded in pre-Newtonian celestial mechanics, particularly in the Ptolemaic system, where it referred to the of… -
Epicycles
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An epicycle (from the Ancient Greek: $\varepsilon\pi\acute{\iota}\chi\upsilon\varkappa\lambda o\varsigma$, epíkyklos, meaning "upon a circle") is a geometric construction used in the history of astronomy to explain the apparent retrograde motion of the planets, the Sun, and the Moon relative to the fixed stars. Developed primarily within the framework of the Ptolemaic system, the epicycle is a small circle whose center moves around a larger circle, known as the deferent, which is centered on the Earth. While conc…