Which eccentricity value ($e$) is associated with an orbit classified as a parabola?
Answer
$e = 1$
The categorization of orbital paths based on eccentricity defines distinct geometric shapes. When the eccentricity ($e$) is exactly equal to one, the path taken by the object is mathematically defined as a parabola. This shape signifies a trajectory where the object possesses exactly the escape velocity needed to break free from the central body's gravitational influence but no more. Orbits with $e=1$ (parabolas) and $e>1$ (hyperbolas) are generally categorized as escape trajectories, as opposed to elliptical orbits where $e$ is strictly less than one, which represent bound orbits where the object remains gravitationally tethered to the central mass.
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