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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 eccentricity of a circle is defined to be zero and its focus is the center of the circle, but its directrix can only be taken as the line at infinity in the projective plane. [2] The eccentricity of an ellipse can be seen as a measure of how far the ellipse deviates from being circular. [3]
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit , values between 0 and 1 form an elliptic orbit , 1 is a parabolic escape orbit (or capture orbit), and greater than ...
and the formula for the area A of a circular sector of radius r and with central angle of measure 𝜃 is = ... A circle is an ellipse with an eccentricity of zero ...
Having a constant diameter, measured at varying angles around the shape, is often considered to be a simple measurement of roundness.This is misleading. [3]Although constant diameter is a necessary condition for roundness, it is not a sufficient condition for roundness: shapes exist that have constant diameter but are far from round.
A circle of radius a compressed to an ellipse. A sphere of radius a compressed to an oblate ellipsoid of revolution. 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.
For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle. The length of the semi-major axis a of an ellipse is related to the semi-minor axis's length b through the eccentricity e and the semi-latus rectum ℓ {\displaystyle \ell } , as follows:
Mathematically, an ellipse can be represented by the formula: r = p 1 + ε cos θ , {\displaystyle r={\frac {p}{1+\varepsilon \,\cos \theta }},} where p {\displaystyle p} is the semi-latus rectum , ε is the eccentricity of the ellipse, r is the distance from the Sun to the planet, and θ is the angle to the planet's current position from ...