Hyperbolic

You get (approximately) elliptic trajectories are realized in Newtonian central force problems: if 2D phase space whenever you shoot are close to a rock toward the sun, but it doesn't hitnondegenerate stable equilibrium. This is one way to explain why harmonic oscillators are so universal. Similarly, then its trajectory forms either you get hyperbolic trajectories when you are close to a stable orbit (elliptic), nondegenerate unstable equilibrium. The standard example is a critical escape (parabolic), ball on top of a smooth frictionless hill or an honest escape (hyperbolic). The outcome is determined by how upside-down pendulum, in the ratio limit of initial kinetic energy to initial gravitational potential energy compares to -1 (where zero potential energy is at infinity)small deviations.

Hyperbolic trajectories are realized in Newtonian central force problems: if you shoot a rock toward the sun, but it doesn't hit, then its trajectory forms either a stable orbit (elliptic), a critical escape (parabolic), or an honest escape (hyperbolic). The outcome is determined by how the ratio of initial kinetic energy to initial gravitational potential energy compares to -1 (where zero potential energy is at infinity).