What path shape results if a celestial object's eccentricity ($e$) is 1 or greater?
Answer
An unbound parabola or hyperbola.
The value of eccentricity determines the nature of the trajectory relative to the gravitational center. When the eccentricity ($e$) is strictly less than one ($0 < e < 1$), the object is gravitationally bound to the central star, tracing a closed curve like an ellipse. However, if $e$ reaches 1 or surpasses it, the resulting path is an open, unbound conic section—either a parabola ($e=1$) or a hyperbola ($e>1$). In these unbound scenarios, the object gains enough velocity to overcome the central star's pull entirely, meaning it will pass by once and never return to complete a revolution around the star.
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