What integration method does this simulator use?

It uses the Velocity Verlet (leapfrog) symplectic integrator, which conserves the Hamiltonian energy over long periods far better than standard Runge-Kutta schemes, making it ideal for orbital mechanics simulations.

How does the Kepler second law sweep work?

Click 'Show Sweep' and select a planet. The shaded sector shows the area swept by the planet's radius vector from the focus (Sun) over equal time intervals — Kepler's second law states these areas are always equal, reflecting conservation of angular momentum.

What is the vis-viva equation?

The vis-viva equation v² = GM(2/r − 1/a) relates the speed v of an orbiting body to its distance r from the focus, the central mass M, and the semi-major axis a. It is derived directly from conservation of energy and is used to compute orbital elements in the stats panel.

What is the figure-8 choreography?

The figure-8 choreography (Chenciner & Montgomery, 2000) is a periodic solution to the three-body problem in which three equal masses mutually chase each other along a figure-of-eight curve. It requires very precise initial conditions and a symplectic integrator to maintain stability.

Home▸Physics & Mechanics▸Orbital Mechanics Simulator: Kepler's Laws and N-Body Gravity

🧪 Orbital Mechanics Simulator: Kepler's Laws and N-Body Gravity

Simulate planetary orbits and Kepler's laws interactively. Leapfrog N-body integrator, vis-viva equation, orbital elements (a, e, T), Kepler 2nd law area sweep, 5 presets including figure-8 choreography and Trojan asteroids.

Physics & Mechanics2DModerate60 FPS

⚙ Under the hood

This simulation allows users to explore orbital mechanics by simulating the motion of celestial bodies governed by Kepler’s laws and Newton’s law of universal gravitation. It provides a hands-on way to understand orbital dynamics.

N-BodyGravityOrbital Mechanics

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install