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Parabolic and Hyperbolic Orbits

Parabolic orbits occur when ε = 1, which means that E = 0.

Figure %: Potential graph for parabolic and hyperbolic orbits.
Hyperbolic orbits occur when ε > 1, which means that E > 0. In both cases the particle will go off to infinity. In the parabolic case the particle barely has enough energy to make it to infinity, but the hyperbolic orbit makes it with energy to spare. In the parabolic orbit this equation simplifies to y2 = ±2x. This is an equation for a parabola with its vertex at (, 0).

Figure %: Shapes of various orbits.
Shows the shapes and locations of the circular, elliptical and parabolic orbits.

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