How can a planetary flyby change a spacecraft’s speed around the Sun?

A spacecraft can leave a planetary flyby moving faster around the Sun without firing its main engine during the encounter. Gravity bends its path, and the planet's orbital motion makes that direction change an energy exchange. Comparing planet-centered and Sun-centered velocities explains how the same encounter can preserve one speed while changing another.

In an ideal planet-centered encounter, the spacecraft speeds up on approach as gravitational potential energy becomes kinetic energy. It slows again on departure. Far before and after the encounter, at comparable distances, its planet-relative speed can be nearly unchanged. Its velocity has nevertheless changed because velocity includes direction as well as speed.

To describe the same motion relative to the Sun, add the planet’s orbital velocity to the spacecraft’s velocity relative to the planet. Suppose the incoming relative motion points largely across the planet’s motion and the outgoing relative motion points more along it. Adding the same planet-motion arrow to each produces different resultant lengths: the more aligned combination has greater Sun-relative speed.

The diagram’s vector additions make this change of direction visible. Other encounter geometry can turn the relative motion against the planet’s travel and reduce the spacecraft’s Sun-relative speed instead. The planet-centered equality of speeds and the Sun-centered change are compatible because a moving reference frame changes the energy comparison.

The spacecraft exchanges energy and momentum with the planet, whose much larger mass makes its response extremely small. No energy is created by the field. Real assists require carefully timed trajectories so the planet is in the right place and the departure direction is useful; the invented vector geometry explains the exchange without representing a mission trajectory.