Energy + angular momentum determine whether an orbit is bound, escaping, or hyperbolic
This demo uses an analytic two-body model (Newtonian gravity). We place the particle at an initial radius and choose its velocity as a multiple of the circular speed. The orbit type is classified using the conserved specific energy ε (per unit mass, in AU²/yr²) and angular momentum h (per unit mass, in AU²/yr). During the animation we advance the particle using the equal-area rule (Kepler’s 2nd law), so it moves faster near periapsis (closest approach) and slower farther away. For escape/hyperbolic orbits, the plotted path is clipped to a finite radius window for visibility; the animation stops at the edge of that window.