My experience with DG to ISS scenario
Hello.
I am a novice to the Orbiter (but not to celestial mechanics). I am a physicist-theoretician and celestial mechanics is my hobby. I calculated many orbits from scratch and it was fun to see how it works in "reality".
I try to explain in two words the idea of orbit synchronization (detals can be found in many manuals). Let's start from some figure. I believe, a figure on the page 98 of the Orbiter User Manual, Edition 2010 is what we need. To be sure that we look at the same figure I describe it. Central body/planet, one circle orbit and one elliptic orbit tangential to the circle orbit in the periapsis. Two vehicles are on the circle orbit: the "ship" and "target" (ahead of the ship). Figure caption is "A transition orbit to intercept the target at the next periapsis passage".
How can ship reach the target? Fire the engine of the space ship oriented prograde until hit the bumper of the front vehicle. Right? Wrong! Well, we are not in a car on a highway
Each firing of the engine CHANGE YOUR ORBIT. This is the main difference between a car and a space ship. If we fire the engine while the "ship" is oriented prograde, we increase it's velocity. This changes "ship's orbit to elliptic tangential to the original circle orbit in the periapsis (how is shown in figure). The bigger semiaxis of the orbit, the bigger the orbital period. This means, that after one revolution along the "ship orbit" (as marked in Figure) we'll be back in the same point, but this will take more time, than if we stayed on the circular orbit. This means, that if we were behind the target (how is shown in the Figure), after one revolution along the elliptic "ship orbit" we will be even more behind the target. If we just slightly behind the target, we need almost double the orbital period to intercept it during the next passage. This takes a lot of fuel. There are two solutions.
1. Intercept the target not on the NEXT pasage, but on the 2nd, 3rd, ... passages. This means that we fire (prograde) the engine and increase our velocity, but not as much as in the case of the next passage intercept. And we'll slightly lag more and more behind the target after each revolution, until at some passage we'll meet.
2. Decrease the velocity. This brings us to the elliptic orbit which is completely inside the original circle orbit (not shown in Figure). The smaller the semiaxis the smaller the orbital period, and we'll catch up with the target! The only downside of this maneuver is that periapsis of the transition orbit can be too low and you'll hit the atmosphere, so I prefer maneuvers with increasing the speed.
Is that crazy?! If we need to catch up we need to SLOW DOWN. If we need to lag behind, we need to SPEED UP.
My experience with the scenario "DG to ISS"
1. The start is scheduled on MJD=51983.6308. If you do this, after aligning orbit planes you'll be behind the ISS approximately 30 degrees. It is too far to catch up by reducing speed (solution 2), because the periapsis drops below the top boundary of the atmosphere. On the other hand, it takes too much fuel to use solution 1.
I already mentioned, that I prefer the first solution of the orbit synchronization, because it is safer, but to make it efficient, the TARGET SHOULD BE BEHIND the ship. We increase the velocity, that increases the semiaxis of the orbit and the orbital period, so we come back to the same point slightly later. We can choose the time lag so that we intercept the target. So, I decided to launch DG to the circle orbit with height of 360 km earlier. I picked MJD=51983.6180, when the ISS was above the north of Canada. After aligning the orbit planes I was about 200 km ahead of the ISS. "Synchronize Orbit" MFD showed that at the 4th pass I intercept the target without any maneuvers. At 4th passage I was at the distance of 15 km (!) with the relative speed of about 45 m/s (!). This was my second try of launching DG.
Hope this helps.
Best regards and good luck!
