Talk:Tutorial: Gravity Assist
This guide does not adequately explain how gravity assists actually work. For just KSP as it is now, this will suffice. But it is off the mark in explaining technically how they operate, which would be fine, if the authors did not attempt to get technical in their explanation of the physics, even including equations in the diagrams. But since the contributors went there, some corrections or at least clarifications are necessary.
It is not the body's momentum, or trajectory as described here, that generates the assist. It is the body's rotation that does. The trajectory is only important in plotting the correct course to get the assist you want (from rotation) and end up going in the direction you want as you exit the boost.
Why is this important? Well for KSP in current form, it is not important. For real life, or if changes are made in KSP or the upcoming KSP2, then these distinctions will become very important, even crucial in getting these maneuvers right for people who don't understand the mechanics of it.
If a body has a reverse spin as Kerbin, then your description of plotted maneuvers here is also reversed. So everything mentioned here is opposite of the desired outcome. The same is true if the orbit around the star is reverse. Take real life planets in our own solar system, for example. Venus spins in the opposite direction of Earth. In the opposite direction of every other planet in our system, for that matter. Uranus orbits the sun in the opposite direction of every other planet in our system. If you were to perform these maneuvers, as outlined here, against either of these real life bodies, you would be getting a very undesired result.
It is also worth noting that the rotation "pull" against the vessel is strongest at the equator and weakest at the poles. Therefore, maximizing the effect of this maneuver would need to be done as close and as parrelel to the equator as possible.
A gravity assist maneuver, as described here, would have almost no impact at all, if performed in a polar, or near-polar plane, even if going parallel to the body's trajectory. The only thing this maneuver would do, if conducted on a polar plane is throw your vessel wildly off course, gaining very little or no momentum if you want it, perhaps even losing some with sloppy piloting. Or even gaining slight momentum, when you don't want it and are using the maneuver to try and deccelerate.
Think of the gravity well around a body as a whirlpool. If the vessel is flying with the flow of the vortex, it grabs some of that energy and gains momentum. If the vessel is flying against the flow of the vortex, it is losing momentum, like swimming against a tide.
I find it odd that the very most important aspect of this fundamental concept was completely ignored in this article. While the word "trajectory" was used 13 times, "spin" or "rotation" was never even mentioned once. This article depicts that it is the bodies forward motion, its momentum, or as you describe it, simply its trajectory that creates the boost. The planet's trajectory has virtually nothing to do with generating the energy behind the gravity boost.
Again, think of the manipulation of space around a celestial body as a whirlpool. The deeper you go into that whirlpool, the faster the current flow and the more energy you steal with this maneuver. Out near the edges of a whirlpool, water (space, in this case) moves relatively slowly. That is why you get your periapsis as close as safely possible to the body as you can. By doing so, you are going deeper into the whirlpool, where the waters are flowing very fast.
Finally, your diagrams clearly demonstrate this lack of understanding. If drawn properly, they would portray a planet from a polar angle/view (from its axis, to be more precise), looking down at the planet where the equator surrounds the edges of planet. They would include a circular arrow reflecting the direction of the planet's rotation or spin. Your images show us looking at a planet from the equatorial plane. That is like looking at a whirlpool from precisly water level. You wouldn't see it. You can only see a whirlpool from above or below. The best view of the whirlpool is from directionly above, at its axis, 90 degrees up from the water plane.