It's not Rocket (limited super)Science

[jeff_wilson]

Originally Posted by Fred Brackin

Maybe, maybe not, unless slingshot maneuvers work the way they do in Star Trek. If they did you probably wouldn't need reaction mass.

Some technically don't need reaction mass, but a little is often used to adjust the trajectory for maximum effect.

It's the physics of conservation of energy and momentum. The spaceship loses gravitational potential energy as it gains velocity and momentum by falling closer to the planet. Assuming it avoids an inelastic collision with the planet itself or its atmosphere or any satellites, it will then continue around and fall away from the planet, trading back velocity and momentum for potential energy as it slows due to the planet's gravity. It arrives and leaves with the same speed at the same distance, measured relative to the planet.

However, it is not the direction or the same speed relative to the sun, since the planet is orbiting the sun at numerous miles per second itself, and it is not the same speed relative to the other planets which have their own speeds and orbits of course, so the slingshot maneuver can effectively add or subtract as much as twice the difference in speeds between the slinging planet and the other planets, or the sun. The velocity change of the spaceship can be considerable, but since the mass is so much smaller than the planet, conservation of momentum makes some invisibly small alteration in the planet's orbit that will be lost in the noise of everything else zipping past it.