I am new to the game. In Career mode, I am now trying to orbital rescue missions were I must get close enough to a craft/Kerbal to transfer between the vehicules, and re-enter the atmosphere.
I know the orbital basics and how to create maneuver nodes. So far I have managed to capture one Kerbin, but luck played a bit part.
Once I have a stable orbit at approximately the same altitude as the target craft, I don't understand how I can catch up (or get caught up) with it with a range small enough that I can RCS my relative velocity out.
I can set basic intercepts but by playing around I can mainly only get my closest intercept to ~20km, or waste so much fuel that I am left with none, or I can cross the path but only extremely briefly.
The orbits are also very close to Kerbin which makes it difficult to distinguish the paths clearly in the Orbital Map view (by zooming to the maximum, I can see paths are made up of straight sections for display).
I have found this thread about orbital maneuvers:
I understand the gist of it, but am mostly still stuck in the very same orbits as my targets, but with a phase angle.
Additionally I have found this thread, where user Iodestar provided an example of a calculation for adjusting and out of phase orbit, but I am missing important intermediate steps and cannot reproduce the calculations.
Any help would be appreciated. Stock game, Career mode, some elements of the 90 level tech tree unlocked.