I'm curious how people plan an orbital rendezvous. This question explains the basic principles, but not in enough detail for me to understand how it actually works.
From playing Kerbal Space Program, it seems that this is very hard to get right:
- If I try to match the orbit (by adjusting my periapsis/apoapsis and inclination), I invariably end up with a large phase angle from my target.
- If I try to time the launch so that I go straight into my target's orbit, even being a second or two late can mean I end up several kilometers away from the target, but it is very hard to predict how long a launch will take to that accuracy.
- The process is very counter-intuitive, because if I am near my target and I try to thrust towards it, what happens instead is that I warp my orbit on the other side of the planet.
- When I try to manipulate the phase angle by going into a slightly higher orbit, it becomes hard to make predictions because the phase angle doesn't stay constant when my orbit is more eccentric than the target.
- If the phase angle difference is large, I need to either spend a lot of fuel making big adjustments to my orbit, or I need to wait for dozens of orbits to catch up to my target.
All of this seems very error prone and time intensive. KSP doesn't model things like provisions, so the problem is a bit easier. So long as you can create even a tiny difference in phase, you can just crank up the time warp and wait for it to synchronize. But I'm sure that in reality, it wouldn't make sense to send astronauts up and then have the sit in orbit for days or weeks, painstakingly adjusting their phase angle with the ISS.
So, how do space agencies plan their rendezvous missions? Do they have a very precise estimate for the launch, and end up at the right phase when they match orbits? Or is there a good algorithm for optimally synchronizing orbits once you are already in some orbit?