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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 of an ellipse which is not a circle is between 0 and 1. The eccentricity of a parabola is 1. The eccentricity of a hyperbola is greater than 1. The eccentricity of a pair of lines is ; Two conic sections with the same eccentricity are similar.
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.
where e is the eccentricity and l is the semi-latus rectum. As above, for e = 0, the graph is a circle, for 0 < e < 1 the graph is an ellipse, for e = 1 a parabola, and for e > 1 a hyperbola. The polar form of the equation of a conic is often used in dynamics; for instance, determining the orbits of objects revolving about the Sun. [20]
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.
A bi-elliptic transfer can require less energy than the Hohmann transfer, if the ratio of orbits is 11.94 or greater, [5] but comes at the cost of increased trip time over the Hohmann transfer. Faster transfers may use any orbit that intersects both the original and destination orbits, at the cost of higher delta-v.
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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.