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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.
Conic sections of varying eccentricity sharing a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated pair of lines.
The constant is given by =, where e is the eccentricity of the conic section. The equation for a conic section with apex at the origin and tangent to the y axis is y 2 − 2 R x + ( K + 1 ) x 2 = 0 {\displaystyle y^{2}-2Rx+(K+1)x^{2}=0}
Unwrap the cone to a plane. Then the curve in the plane to which the conic section of eccentricity λ is unwrapped is a generalized conic with polar equation as specified in the definition. In the special case when k < 1, the generalized conic cannot be obtained by unwrapping a conic section. In this case there is another interpretation.
Neptune's and Venus's have even lower eccentricities of 0.008 6 and 0.006 8 respectively, the latter being the least orbital eccentricity of any planet in the Solar System. Over hundreds of thousands of years, the eccentricity of the Earth's orbit varies from nearly 0.003 4 to almost 0.058 as a result of gravitational attractions among the planets.
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The second theorem is that for any conic section, the distance from a fixed point (the focus) is proportional to the distance from a fixed line (the directrix), the constant of proportionality being called the eccentricity. [6] A conic section has one Dandelin sphere for each focus.