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  2. Eccentricity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Eccentricity_(mathematics)

    The eccentricity of an ellipse is strictly less than 1. When circles (which have eccentricity 0) are counted as ellipses, the eccentricity of an ellipse is greater than or equal to 0; if circles are given a special category and are excluded from the category of ellipses, then the eccentricity of an ellipse is strictly greater than 0.

  3. Ellipse - Wikipedia

    en.wikipedia.org/wiki/Ellipse

    An ellipse (red) obtained as the intersection of a cone with an inclined plane. 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.

  4. Conic constant - Wikipedia

    en.wikipedia.org/wiki/Conic_constant

    In geometry, the conic constant (or Schwarzschild constant, [1] after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by K = − e 2 , {\displaystyle K=-e^{2},} where e is the eccentricity of the conic section.

  5. Elliptic orbit - Wikipedia

    en.wikipedia.org/wiki/Elliptic_orbit

    A radial trajectory can be a double line segment, which is a degenerate ellipse with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1, this is not a parabolic orbit. Most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed.

  6. Flattening - Wikipedia

    en.wikipedia.org/wiki/Flattening

    Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution respectively. Other terms used are ellipticity , or oblateness . The usual notation for flattening is f {\displaystyle f} and its definition in terms of the semi-axes a {\displaystyle a} and b {\displaystyle b} of ...

  7. File:Ellipse Properties.svg - Wikipedia

    en.wikipedia.org/wiki/File:Ellipse_Properties.svg

    The distance from a point, P, on the ellipse to a focus is always proportional to the distance to a vertical line, D, called the directrix. The constant of proportionality is the eccentricity, e. The eccentricity is always between 0 and 1. At zero, the ellispe becomes a circle, at 1 the ellipse becomes a parabola. Greater than one, it is a ...

  8. Conic section - Wikipedia

    en.wikipedia.org/wiki/Conic_section

    the eccentricity can be written as a function of the coefficients of the quadratic equation. [18] If 4AC = B 2 the conic is a parabola and its eccentricity equals 1 (provided it is non-degenerate). Otherwise, assuming the equation represents either a non-degenerate hyperbola or ellipse, the eccentricity is given by

  9. Angular eccentricity - Wikipedia

    en.wikipedia.org/wiki/Angular_eccentricity

    Angular eccentricity α (alpha) and linear eccentricity (ε). Note that OA=BF=a. 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 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 ...