Kepler's Laws - Cosmic Playground

Kepler's Laws Sandbox

Explore orbital mechanics: empirical patterns and physical laws.

Controls

Keyboard shortcuts Space, arrows, presets

Semi-major axis $a$

1.00 AU

0.3 AU $\rightarrow$ 40 AU (log scale)

Eccentricity $e$

0.017

0 (circle) $\rightarrow$ 0.99

Orbital phase

0.00 / 1.00 yr

Speed (yr/s)

Presets

Solar system

Extreme orbits

Overlays

Foci Apsides Equal areas

Readouts

Distance $r$

1.00

Speed $v$

29.8

km/s

Acceleration

5.93

mm/s^2

Period $P$

1.00

Conservation laws energy + angular momentum

Kinetic ($v^2/2$)

AU^2/yr^2

Potential ($-\mu/r$)

AU^2/yr^2

Total $\varepsilon$

AU^2/yr^2

Angular momentum $h$

AU^2/yr

Areal velocity ($dA/dt$)

AU^2/yr

What to notice 3 bullets

Model note (teaching model) AU / yr / M_sun

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.
Teaching normalization: $G = 4\pi^2\,\frac{\mathrm{AU}^3}{\mathrm{yr}^2\,M_{\odot}}$.
Kepler 3: $P^2 = \frac{a^3}{M}$.
The time slider advances mean anomaly uniformly; position is solved from Kepler's equation.