Slingshot (Gravity Assist): A spacecraft approaches Jupiter on a hyperbolic path. Jupiter's gravity bends the trajectory and, in the Sun's frame, the spacecraft picks up heliocentric speed — exchanging momentum with the planet. Switch to the co-rotating (Jupiter) frame to see the classic symmetric flyby hyperbola. Voyager-1 and Voyager-2 used multiple gravity assists to reach the outer solar system.

Free Return (Apollo): A trajectory that loops around the Moon and returns to Earth without any engine burn. Requires precise translunar injection (TLI) Δv and timing. Apollo 8 proved the figure-8 shape works; Apollo 13 used it as an emergency abort after losing its main engine.

Hohmann Transfer: The minimum-Δv two-burn transfer between two coplanar circular orbits. First burn adds energy to enter an elliptical transfer orbit whose aphelion touches the target orbit. Second burn circularizes. Earth → Mars requires roughly 5.6 km/s total Δv and ~8.5 months.

Patched-Conic (Earth → Mars): Launch phase angle is critical — Mars must be at the right position when you launch so it meets you at aphelion. The "Hohmann window" occurs when Mars leads Earth by about 44°. Too early and Mars isn't there yet; too late and you overshoot. All three bodies (Sun, Earth, Mars) gravitate the spacecraft in this simulation.

Controls: Space to play/pause, R to reset, mouse wheel to zoom, drag to pan. Select a preset to jump to a known scenario.