Gravity Assist Flyby Delta-V Calculator
Interplanetary astrodynamics: Model hyperbolic flybys (swingbys), turning angle δ, hyperbolic excess velocity v_∞, and heliocentric velocity boost ΔV.
Encounter Planet & Approach Geometry
Trajectory Bending & Heliocentric Boost
Recommended Tools & Equipment
Tested hardware and components for high reliability
Frequently Asked Questions
Where does the energy come from during a planetary gravity assist?
The energy gained by the spacecraft is stolen directly from the orbital momentum of the flyby planet around the Sun. In the planet's reference frame, the spacecraft's departure speed equals its arrival speed (v_inf = constant); the planet only bends its direction. But in the heliocentric (Sun) frame, adding the planet's massive orbital velocity (e.g. 13 km/s for Jupiter, 30 km/s for Earth) boosts the spacecraft while slowing down the planet by an unmeasurable fraction of a millimeter over billions of years.
What is the difference between a trailing-edge and leading-edge flyby?
Passing behind a planet's trailing edge pulls the spacecraft along in the direction of the planet's orbital travel, accelerating the spacecraft and pumping energy into its heliocentric orbit (e.g. Voyager 1 & 2 escaping the solar system). Passing in front of a planet's leading edge decelerates the spacecraft, dumping orbital energy to drop closer to the Sun (e.g. MESSENGER and BepiColombo slowing down to enter Mercury orbit).
What is a powered flyby (Oberth maneuver)?
If a spacecraft fires its rocket engines at the closest approach point (periapsis) during a gravity assist, it exploits the Oberth effect. Because kinetic energy scales with the square of velocity (E = 0.5 * m * v²), burning propellant when the spacecraft is moving fastest deep in the planet's gravity well converts chemical energy into orbital mechanical energy far more efficiently than burning in deep space.