Gravitation · Interactive

Orbits & Kepler's Laws

Launch a satellite sideways past a star and let gravity do the rest. The path bends into a circle, an ellipse, or an escaping curve depending only on how fast you throw it. Watch the shaded wedges: sweep out equal areas in equal times — Kepler's second law, live.

→ Velocity ◍ Equal-area sweeps Central star · satellite launched straight up

Setup

Launch distance r 2.00 units
Launch speed v 1.00 × v_circ
Central mass M 1.00 × M
Circle
Orbit type
1.00
speed (× v_circ)
0.00
eccentricity e
6.28
period T (arb)
2.00
semi-major a
v_circ = √(GM/r) v_esc = √2·v_circ T² ∝ a³ equal areas / equal time

Playback

Try this: set speed to 1.00× for a perfect circle; nudge to 1.41× and it just escapes on a hyperbola; drop to 0.70× for a stretched ellipse that races through periapsis and crawls at apoapsis — yet every shaded wedge has the same area.