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| a small circle whose center moved uniformly around Earth on a second and larger circle |
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| a construct of the geocentric model of the solar system which was needed to explain observed planetary motions |
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| the observed motions of the planets made it impossible to assume that they moved on a simple circular paths around Earth |
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| The full Ptolemaic required |
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| a series of no fewer than 80 distinct circles |
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| Tycho maintained meticulous and accurate records of |
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| stars, planets, and other noteworthy celestial events |
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| the shape of each planet's orbit by triangulation from Tycho Brahe |
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| The orbital paths of the planets are |
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| elliptical, with the Sun at focus |
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| one of two special points within an ellipse, whose separation from each other indicates the eccentricity |
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| an imaginary line connecting the Sun to any planet |
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| sweeps out equal areas of the ellipse in equal intervals of time |
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| the coolest approach to the Sun of any object in orbit about it |
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| the point on the elliptical path of an object in orbit about the Sun that is most distant from the Sun |
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| The square of a planet's orbital period is proportional to the cube of its |
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| essentially the average distance between Earth and the Sun |
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| the "average" position of all the matter making up the two bodies |
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| attain enough speed to escape our planet's gravity and move away from Earth forever |
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| orbital and distance; The square of a planet’s orbital period (measured in years) is equal to the cube of its semi-major axis (average distance from the Sun) measured in A.U. |
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