Kepler's Laws Sandbox

Explore orbital mechanics: empirical patterns and physical laws

Station Card (PDF)
Model note (teaching model)

This simulation is a simplified, planar (2D) two-body model. It ignores perturbations and treats the planet as negligible-mass in Newton mode. The animation speed is a teaching scale (years per second), not real time.

Keyboard shortcuts
  • Space: Play/Pause
  • Home / End: Perihelion / Aphelion
  • ← / →: Move along orbit (Shift = fine)
  • K / N: Kepler / Newton mode
  • 1–6: Presets
Focus (Star) Perihelion Aphelion r = 1.00 AU
Distance (r)
1.00
AU
Velocity (v)
29.8
km/s
Acceleration
5.93
mm/s²
Period (P)
1.00
years
Conservation laws (energy & angular momentum)

These are specific (per unit mass) quantities. In 101 mode we show them in AU²/yr² and AU²/yr (“code units”). In 201 mode we show the same quantities in CGS (cm²/s² and cm²/s).

Kinetic (v²/2)
0
AU²/yr²
Potential (−μ/r)
0
AU²/yr²
Total ε
0
AU²/yr²
Angular momentum (h)
0
AU²/yr
Areal velocity (dA/dt)
0
AU²/yr
Orbital Phase 0.00 / 1.00 yr
Perihelion Aphelion Perihelion
Semi-major Axis (a) 1.00 AU
0.3 AU 40 AU
Eccentricity (e) 0.017
0 (circle) 0.99
Presets
Solar System
Extreme Orbits

Kepler's Laws (1609–1619)

Empirical patterns discovered from Tycho Brahe's observations:

Law 1: Planets orbit in ellipses with the Sun at one focus.

Law 2: A line from Sun to planet sweeps equal areas in equal times.

Law 3: (years, AU)

These are descriptions of what we observe. But why? Toggle to Newton Mode to find out →