Gravity Assist Maneuver: Hyperbolic Flyby Lab (2D)

This 2D companion strips the maneuver down to the physics that actually drives a gravity assist: a spacecraft on a hyperbolic path around a fixed planet, integrated with RK4 under real inverse-square gravity. The impact parameter sets how sharply the trajectory bends, the planet-mass slider sets the pull, and the "planet orbital speed" control shows why the same flyby that looks like a simple turn in the planet's frame becomes a real speed gain (or loss) once you add the planet's own motion back in — the actual mechanism NASA uses for Voyager- and Cassini-style slingshots.