A gravity-assist "slingshot" trades a tiny bit of a planet's orbital momentum for a large boost to a probe's heliocentric speed, without burning any propellant.
v_probe' = v_probe + 2 * v_planet * cos(θ/2) (in the planet's frame)
Δv_max ∝ v_planet, larger for closer, faster flybys
- Approach velocity — the probe's incoming speed relative to the planet; it sets how sharply the trajectory bends.
- Periapsis distance — how close the flyby passes to the planet; a closer pass bends the trajectory more and yields a bigger speed boost (but risks atmosphere/rings).
- Planet mass — scales the planet's gravitational pull and its own orbital velocity, both of which feed the slingshot boost.
Watch the trailing path line bend sharply around the planet; the escape-velocity-gain stat reports how much faster the probe leaves than it arrived — real missions like Voyager 2 and New Horizons used exactly this trick to reach the outer solar system.