From Jupiter's point of view, the situation is similar to a bicyclist speeding up going downhill into a valley, then slowing down again on the uphill part of the road.

In the vector diagram at left, the situation is simplified to two dimensions. You can see the magnitude and direction of the spacecraft's velocity on its way in towards Jupiter in the lower right. At the upper left, you can see that the accelerating force of Jupiter's gravitation has made a significant change in the direction of the spacecraft's velocity, but not in its magnitude. (These represent velocity at "infinity," from Jupiter, that is, before and after being noticeably changed by Jupiter's presence.) Near the middle of the diagram, the long arrow shows that there's a significant, but temporary, increase in the magnitude (speed). Note these speeds are all with respect to Jupiter.

To look at the same phenomenon in terms of a cyclist, V_IN shows the cyclist approaching a downhill grade into a canyon. V_OUT shows that the cyclist slowed down again at the top of the ensuing uphill grade (of course this cycling analogy asks us to ignore air friction and vehicle friction, etc., which are virtually absent in the spacecraft's case). Indeed, after negotiating the canyon, the cyclist's direction has changed, but in the end s/he has not made a lasting change in speed (unless you don't ignore all that friction etc.).

The planet's own motion is a key. A gravity assist with Jupiter involves not a stationary planet as considered above, but a planet with enormous angular momentum as it revolves around the Sun. In the diagram at right, Jupiter's motion along its solar orbit has been illustrated with a vector colored red (simplified, of course: Jupiter revolves along an arc, not a straight line. Imagine the Sun situated below the bottom of the diagram). The spacecraft acquires this Sun-relative vector, or a significant portion of it, during its interaction with Jupiter.

You can see how the red vector is added to V_IN and V_OUT. The resulting vector shows how the spacecraft's velocity, relative to the Sun, takes on a nice boost from Jupiter. Notice how rotation of the vector from V_IN to V_OUT (the bending of the spacecraft's path by the planet's gravity) helps increase the result. This trajectory bending is the other key.

The spacecraft is a physical mass, so it has its own gravitation. That's how the spacecraft can tug on Jupiter and actually decrease the planet's orbital momentum by a tiny amount. In the exchange, the spacecraft acquires momentum from Jupiter – a significant amount, compared to the momentum the spacecraft already had.

We were at this time no more than some sixty-five thousand miles from the moon's surface. The Planetara presently would swing upon her direct course for Mars. There was nothing that would cause passenger comment in this close passing of the moon; normally we used the satellite's attraction to give us additional starting speed.