Orbital mechanics

N-body simulator: pick a preset and watch it run. Drag to pan, scroll to zoom, double-click to fit; Centre on follows one body, and Co-rotating frame rotates the view with the first two bodies (so the Trojan at Jupiter’s L4 point stays put and its libration shows). The readout shows total energy, its relative drift ΔE/|E₀|, and the angular-momentum drift — a direct measure of integrator error.

Integrators: velocity Verlet (kick–drift–kick) is symplectic, so its energy error oscillates but stays bounded over millions of steps. RK4 is fourth-order accurate but not symplectic; over long runs its energy drifts. Raise the time step to see both fail differently.

Hohmann transfer: Δv for the two burns, time of flight, and the transfer ellipse between two circular coplanar orbits, around Earth or the Sun. Enter radii or altitudes; heliocentric transfers also show the synodic period (time between launch windows) and the lead angle the target needs at departure. Plane changes, gravity losses, and the escape/capture hyperbolas at each planet are not included, so interplanetary values are heliocentric Δv only.

Orbit calculator: circular and escape velocity at an altitude, Kepler’s third law (period ↔ semi-major axis, e.g. GEO from a sidereal day), and periapsis/apoapsis speeds for an ellipse from vis-viva.

Elements ↔ state: convert classical elements (a, e, i, Ω, ω, ν) to position and velocity vectors and back.