physics

Orbital Mechanics

The physics of orbits, transfers, and space travel — from Kepler's laws to gravity assists and Lagrange points.

orbitsKeplerHohmann transferLagrange pointsgravity assistastrodynamics

Orbital mechanics is the physics of motion in gravitational fields. Founded by Johannes Kepler (1609–1619) who discovered the three laws of planetary motion, and formalized by Isaac Newton (1687) who showed that gravity's inverse-square law explains all orbits, it is the science that makes space travel possible.

Every spacecraft trajectory — from Apollo's lunar transfers to Voyager's Grand Tour of the outer planets — is computed using these principles. Hohmann transfers provide the most fuel-efficient way to move between orbits. Lagrange points are gravitational sweet spots where spacecraft can park with minimal fuel. Gravity assists use a planet's motion to boost a spacecraft's velocity for free.

These simulations let you design orbital maneuvers: draw Kepler orbits with different eccentricities, plan Hohmann transfer burns, find the five Lagrange points, and see how gravity assists bend trajectories to reach the outer solar system.

4 interactive simulations

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Gravity Assist Simulator

Visualize how spacecraft gain or lose speed by flying past planets, using the gravitational slingshot effect

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Hohmann Transfer Orbit Calculator

Simulate the most fuel-efficient two-impulse maneuver to transfer between circular orbits, with animated spacecraft trajectory

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Kepler Orbit Simulator

Interactive simulation of elliptical planetary orbits using Kepler's laws, showing equal-area sweeps and velocity changes

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Lagrange Points Visualizer

Explore the five equilibrium points of the restricted three-body problem with an interactive effective potential map