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In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: The eccentricity of a circle is 0. The eccentricity of an ellipse which is not a circle is between 0 and 1.
The mean eccentricity of an object is the average eccentricity as a result of perturbations over a given time period. Neptune currently has an instant (current epoch ) eccentricity of 0.011 3 , [ 11 ] but from 1800 to 2050 has a mean eccentricity of 0.008 59 .
Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It is denoted here by α (alpha). It may be defined in terms of the eccentricity , e , or the aspect ratio, b/a (the ratio of the semi-minor axis and the semi-major axis ):
Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same.
The eccentricity e is defined as: = . From Pythagoras's theorem applied to the triangle with r (a distance FP) as hypotenuse: = + () = () + ( + ) = + = () Thus, the radius (distance from the focus to point P) is related to the eccentric anomaly by the formula
This corresponds to the formula for a conic section of eccentricity e = (+ ) where the eccentricity = | | and C is a constant. [ 1 ] Taking the dot product of A with itself yields an equation involving the total energy E , [ 1 ] A 2 = m 2 k 2 + 2 m E L 2 , {\displaystyle A^{2}=m^{2}k^{2}+2mEL^{2},} which may be rewritten in terms of the ...
Note that at low eccentricity (left-hand side of the graph), the series does not need to be carried to high order to produce accurate results. Series-expanded equation of the center as a function of mean anomaly for various eccentricities , with the equation of the center truncated at e 7 for all curves.
the eccentricity of the Earth's orbit around the Sun, which is about 0.0167. The equation of time vanishes only for a planet with zero axial tilt and zero orbital eccentricity. [5] Two examples of planets with large equations of time are Mars and Uranus.