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This page refers to eccentricity in astrodynamics. For other uses, see the disambiguation page eccentricity. In astrodynamics, under standard assumptions any orbit must be of conic section shape. The eccentricity of this conic section, the orbit's eccentricity, is an important parameter of the orbit that defines its absolute shape. Eccentricity may be interpreted as a measure of how much this shape deviates from a circle. Under standard assumptions eccentricity () is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values: For elliptical orbits, a simple proof shows that sin−1 yields the projection angle of a perfect circle to an ellipse of eccentricity . So to view the eccentricity of, say, the planet Mercury (0.2056), simply calculate the inverse sine to find the projection angle of 11.86 degrees. Then tilt any circular object (such as a coffee mug viewed from the top) by that angle and the apparent ellipse projected to your eye will be of that same eccentricity. Calculation Eccentricity of an orbit can be calculated from orbital state vectors as a magnitude of eccentricity vector: ight | where: ---- For elliptic orbits it can also be calculated from distance at periapsis and apoapsis: where: Examples For example, the eccentricity of the Earth's orbit today is 0.0167. Through time, the eccentricity of the Earth's orbit slowly changes from nearly 0 to almost 0.05 as a result of gravitational attractions between the planets (see graph *). In other values, Mercury (with an eccentricity of 0.2056) holds the title as the largest value among the planets of the Solar System. Prior to the redefinition of its planetary status, the dwarf planet Pluto held this title with an eccentricity of about 0.248. The Moon also holds a notable value at 0.0554. For the values for all planets in one table, see Table of planets in the solar system. Climatic Effect
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