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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.
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.
A hyperbolic asteroid is any sort of asteroid or non-cometary astronomical object observed to have an orbit not bound to the Sun and will have an orbital eccentricity greater than 1 when near perihelion. [1] Unlike hyperbolic comets, they have not been seen out-gassing light elements, and therefore have no cometary coma. Most of these objects ...
With eccentricity just over 1 the hyperbola is a sharp "v" shape. At e = 2 {\displaystyle e={\sqrt {2}}} the asymptotes are at right angles. With e > 2 {\displaystyle e>2} the asymptotes are more than 120° apart, and the periapsis distance is greater than the semi major axis.
An e greater than 1 will be hyperbolic and still be unbound to the Solar System. Although it describes how "unbound" an object's orbit is, eccentricity does not necessarily reflect how high an incoming velocity said object had before entering the Solar System (a parameter known as V infinity, or V inf).
This is an elliptic orbit with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1, this is not a parabolic orbit. Radial parabolic orbit: An open parabolic orbit where the object is moving at the escape velocity. Radial hyperbolic orbit: An open hyperbolic orbit where the object is moving at greater than the escape ...
Prior to finding a well-determined orbit for comets, the JPL Small-Body Database and the Minor Planet Center list comet orbits as having an assumed eccentricity of 1.0. (This is the eccentricity of a parabolic trajectory; hyperbolics will be those with eccentricity greater than 1.0.)
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]