Conservation Laws: Orbit Shapes

Energy + angular momentum determine whether an orbit is bound, escaping, or hyperbolic

Model note (teaching model)

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.

Orbit type
circular
 
Eccentricity ()
0.00
 
Specific energy ()
0
AU²/yr²
Angular momentum ()
0
AU²/yr
Speed (, instantaneous)
0
km/s
Kinetic ()
0
AU²/yr²
Potential ()
0
AU²/yr²
Periapsis ()
0
AU
Semi-major axis ()
0
AU
Central mass
Log scale: 0.1 – 10 M☉
Initial conditions
Log scale: 0.1 – 10 AU
Escape at √2 ≈ 1.414
0° tangential; ±85° near-radial