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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.
Since the eccentricity of a hyperbola is always greater than one, the center B must lie outside of the reciprocating circle C. This definition implies that the hyperbola is both the locus of the poles of the tangent lines to the circle B, as well as the envelope of the polar lines of the points on B.
With eccentricity just over 1 the hyperbola is a sharp "v" shape. At = the asymptotes are at right angles. With > the asymptotes are more than 120° apart, and the periapsis distance is greater than the semi major axis. As eccentricity increases further the motion approaches a straight line.
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
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 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section.
Note that non-elliptic trajectories also exist, but are not closed, and are thus not orbits. If the eccentricity is greater than one, the trajectory is a hyperbola. If the eccentricity is equal to one, the trajectory is a parabola. Regardless of eccentricity, the orbit degenerates to a radial trajectory if the angular momentum equals zero.
For an attractive force (α < 0), the orbit is an ellipse, a hyperbola or parabola, depending on whether u 1 is positive, negative, or zero, respectively; this corresponds to an eccentricity e less than one, greater than one, or equal to one.
Conversely, if the energy is positive (unbound orbits, also called "scattered orbits" [1]), the eccentricity is greater than one and the orbit is a hyperbola. [1] Finally, if the energy is exactly zero, the eccentricity is one and the orbit is a parabola. [1]