text: how does the slingshot effect (or gravity assist) work to change the orbit of a spacecraft?   when a space probe passes around a planet the orbital energy of the spacecraft relative to the planet will remain constant and so from the point of view of the planet the spacecraft will not be moving any faster on the way out as it was on the way in.  but the planet orbits the sun and when one looks at the trajectory from a sun centered point of view then the momentum of the spacecraft is greater on the way out then it is on the way in.  for conservation of momentum to hold the planet must lose the same amount of momentum as the spacecraft gained.  of course since planets are typically many orders of magnitude heavier than space probes the change in the orbit of the planet is so small that we can't detect it.