@lizarddan: Your situation is exactly the same I was in during my first career, trying to learn how to do an orbital rendezvous to rescue Jeb from high orbit. Like you, I also had no RCS parts yet. In reality, it's a pretty simple procedure once you get the hang of it. Here's how to save your kerbal: Once in orbit in the chase ship, target the stranded ship. Maneuver and burn so that your orbit lines up roughly with your target's orbit, but is not identical to it. If the ships are in identical orbits, they'll never catch up with each other. At either the ascending or descending node on your map, place a maneuver node and tweak the purple arrows until your orbital inclination matches the target's. Burn as required. The orbits should now be "flat" relative to each other. Congratulations, you've removed one whole dimension from the equation. Find the marker for "intercept 1" on your map. Place a maneuver node at that location and tweak it (playing with prograde/retrograde should be all that's required) so that the markers for intercept 1 and target position at intercept 1 line up as close as possible. That's where you'll intercept your target. Note the separation; you want it to be a kilometer or less ideally. To save fuel, you may want to wait a few orbits before doing this, letting the ships get closer together. Execute the maneuver. Afterward, you should now be on course to intercept your target. When you reach the intercept point, you'll need to kill your relative velocity quickly or risk overshooting. Click the top of your navball where it gives your speed, until it reads "target". This shows you your velocity relative to your target, and changes the prograde and retrograde markers on your navball to correspond to the target ship. That last part is crucial. Point your ship at the retrograde () marker and burn your main engine. By thrusting in the opposite direction of the target's motion relative to you, you reduce your relative velocity. Keep it up until your velocity reads as 0.0. If you overshoot, just turn the ship around and burn in the other direction. You are now stationary. And now the fun part. Unless you've been very exact, it won't stay at 0.0 for long. The ships will gradually begin drifting apart unless their orbits are exactly the same. So it's time for a walk. Switch back to the other ship and say goodbye (for now) to your stranded vessel, then jump out and head for the chase ship using your jetpack. Good luck!