How does gravity assist work for interplanetary missions?

Gravity assist (slingshot) uses planetary gravity to change spacecraft velocity without propellant. Mechanism: Spacecraft approaches planet on hyperbolic trajectory, Planet's gravity accelerates spacecraft during approach and decelerates during departure, In planet frame, entry and exit speeds are equal, but In Sun frame, velocity changes due to planet's motion. Results: Energy gained (or lost) from planet's orbital energy, Direction changed (plane changes possible), and All without propellant expenditure. Design: Target periapse (closest approach) and approach angle, Flyby altitude limited by atmosphere and planetary moons, and Multiple assists possible (Voyager, Cassini). Limitations: Must wait for favorable planetary alignments, Flyby dates constrained by orbital mechanics, and Navigation accuracy critical. Applications: Outer planet missions, Mercury missions (slow down), and Solar probe missions.