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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 ...
Roundness is the measure of how closely the shape of an object approaches that of a mathematically perfect circle.Roundness applies in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft or a cylindrical roller for a bearing.
For an ellipse 0 < ε < 1 ; in the limiting case ε = 0, the orbit is a circle with the Sun at the centre (i.e. where there is zero eccentricity). At θ = 0°, perihelion, the distance is minimum = + At θ = 90° and at θ = 270° the distance is equal to .
where e (the eccentricity), and θ 0 (the phase offset) are constants of integration. This is the general formula for a conic section that has one focus at the origin; e = 0 corresponds to a circle, 0 < e < 1 corresponds to an ellipse, e = 1 corresponds to a parabola, and e > 1 corresponds to a hyperbola.
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