What would be the best way to reverse orbital direction?

[FancyMouse]

SOI is defined as when Fk=Fm

Not true. The surface that Fk=Fm is not centered at either body. You can see that by looking at degenerate case when two bodies have equal mass. Details here. My point is, if the game currently use an SoI model that is a sphere centered at one body, then it can't have the property that the scalar value of the gravity from two bodies are equal. And the current SoI radius values are actually far from making that equation roughly true for the case when one body has a mass much greater than the other.

[Nich]

actually I used rk of 100km when I should have used 700km (have to add the radius of kerbin)

the real SOI in that example would be 15,652m (at 100,000m altitude) which is still inside the body of Minimus. It would be less closer to Kerbin and more on the opposite side or Minimus away from kerbin. That being said in this situation you would clearly be in the realm of 3 body physics and 2 body physics no longer apply. Because KSP has no bodies this close together you can define the SOI as the boundary when the force from one planet equals the force from another planet/moon

techically https://en.wikipedia.org/wiki/Sphere_of_influence_(astrodynamics) is correct however this leaves large areas where you have to solve the 3 body problem because at some point you will have kerbin and the Mun canceling each other out and Kerbol becomes the main force which KSP does not calculated because it uses a simplier 2 body logic

[FancyMouse]

Has nothing to do with 3-body. You either define SoI to be gravity equality as you did, or define SoI to be a sphere with an arbitrary radius around a body as the game does. You can't get both since they're contradicting.

[cantab]

Method 0: Don't.

In the majority of cases your inclination doesn't matter much. You'll take a small delta-V penalty on an airless landing and on takeoff to the same orbit but that's something your safety margins should cover, and if not you can have the previous stage or the orbiter help with the deorbit and landing burns. And if you aren't even landing then that's irrelevant anyway.

[KerikBalm]

Yea.... as in my eve-gilly example, by inserting on the wrong side, I had a much larger capture burn for gilly, but I doubt it woud be any better if I had put my PE way past gilly...

I intercepted gilly at the AN/DN, and not at its apopasis... I don't think the plane change would have been worth it... at any rate, what I did was faster, and the probe had enough dV to do what was needed, it was a 1 way probe anyway.

[Sharpy]

Plane change near extreme apoapsis is very cheap too. Just make sure to extend it so that DN/AN is near that apoapsis.

I know what I'm talking about. I moved this one from almost-polar retrograde into prograde LKO.