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Kepler's Laws

Interactive two-body simulation of planetary motion

Orbit Setup

Playback

Display

Presets

Controls

Space Play / Pause
R Reset simulation
Drag to pan view
Scroll to zoom

Orbit Setup

Speed < 1 vc → tighter ellipse
Speed = 1 vc → circular orbit
Speed > √2 vc → Escape
Angle tilts initial velocity

Law Tabs

I — Watch r₁+r₂ = const
II — Equal-area wedges
III — Click canvas to add orbits at different distances. Scroll down for the T² vs a³ chart.
e 0.000 a 1.000 AU T 1.000 yr E -19.74
How to Use

Kepler's First Law: Planets orbit in ellipses with the star at one focus. Watch the traced orbit match the computed ellipse. The sum r₁+r₂ stays constant.

Kepler's Second Law: A line from the star to the planet sweeps equal areas in equal times. The colored sectors all have the same area—they are short and wide near perihelion (fast), long and thin near aphelion (slow).

Kepler's Third Law: T² ∝ a³. Add multiple orbits and watch them all fall on the same line in the T² vs a³ chart. Click on the canvas to quickly add circular orbits at different distances.

Controls: Adjust sliders to change the orbit. Use presets for common configurations. Toggle display options to show velocity/acceleration vectors and grid.