Sorry for the delay on replying to this, I haven't had time to go online the last few days.
In the case of "Home Direct" we need to adjust O-E's TEj because we changed our orbit (the circularisation burn) after we set up our plan in P-A, thus changing the time when we reach the ejection point. While this step isn't crucial for a lunar return, it does increase the fuel efficiency.
When making an Orbit Escape burn (which is also the transfer burn) it is most efficient if the burn vector is aligned with the prograde velocity vector. This is the case when your burn is centered around the point where the planned course is tangent to the current orbit (assuming the plane is aligned). Burning before that point means some thrust is used to redirect the ship inward of it's current orbit, burning after means some some of the thrust is used to redirect the ship outward. Changing directions is very expensive in terms of delta-v, and inward/outward changes are as fuel expensive as plane changes. We want as much of the dV as possible applied to changing the amount of our velocity, not the direction.
Let's consider our flight to have three separate "stages"; Launch, Eject, and Transfer. As usual in spaceflight, it's best to work "backwards" so we'll consider the Transfer stage first.
For a moon-earth transfer, the window is pretty much open ended. The dV needed for the transfer if made today is about the same as it will be tomorrow, or next week, or even next month, so we don't need to worry about when we actually make the transfer. There will be slight variations in the required dV since the moon's orbit isn't perfectly circular and stable, but the difference will be considerably less than 100 m/s, and only an issue in a vessel with an extremely tight dV budget. For an interplanetary flight, the Transfer window is obviously much more important, although a couple hours one way or the other is usually insignificant. Adjusting the values in IMFD's Course program to attain the lowest dV finds the best Transfer window, but that's not possible (or needed) for a moon-earth transfer using Planet Approach.
For a moon-earth transfer the Eject window is much more important. Changing the direction is much more expensive than changing the velocity, so we want to minimise any inward/outward velocity change (also any plane change velocity, so being in the correct plane before ejecting is also important - more on that later). This means we want our Ejection burn vector to be as closely aligned with our prograde velocity vector as possible. This means our ejection burn should be centered around the point where our planned transfer orbit is tangent to our pre-ejection orbit. That's what we accomplish by adjusting the TEj in IMFD's Orbit Eject program.
The Launch window is chosen to put us in the desired pre-ejection orbit as efficiently as possible. Ideally, we would launch from the specific location that allows us to enter our desired ejection plane using a 90 degree launch heading (assuming the body we are leaving rotates in a prograde direction), at the specific time that puts us at the ejection point at the exact time indicated by the TEj in the Course (or Planet Approach) program. This is rarely possible, since we can only launch from certain places (can't launch from the side of a mountain or the middle of a densely populated urban area, etc), so we choose a launch time that allows us to reach our desired plane using as close to a 90 degree launch as possible. It's important to be in the correct orbital plane before making the ejection burn to minimize the dV needed for the ejection burn (since it's also the Transfer burn). For a lunar return it's a bit simpler - since the moon rotates so slowly using a 90 degree launch heading isn't as important. We chose our launch time and heading so that we can get into our ejection plane without needing any plane changes once in orbit.
A few hours difference between the TEj in the Planet Approach (or Course) program and the Orbit Eject program is pretty insignificant, as Jarmonik pointed out. The closer they are, the more accurate the flight will be (minimising mid-course corrections) but we're talking about a very small difference, usually less than 100 m/s difference in our MCC burn. For a vessel with an extremely tight delta-V budget it may pay to match the TEj's, but keep in mind that IMFD's Course and Planet Approach programs have limited accuracy, so the deviation from the plan caused by a slight difference in TEj's is less than the deviation caused by IMFD's inaccuracy. In some cases the deviation caused by the difference in TEj's may cancel out some of the deviation caused by IMFD's inaccuracy, and it's rarely worth trying to make the TEj's match perfectly.
For a moon-earth transfer matching the TEj's won't result in any noticeable difference in the dV required, and you can use IMFD's Map program (which is much more accurate than Planet Approach or Course) to fine tune your course with just a few seconds of translational RCS almost immediately after the ejection burn.
Also, in "Home Direct" we needed to adjust our arrival time (PeT in IMFD) so that we would place our Pe in the correct place for the direct re-entry, and adjusting the PeT had an effect on the required dV. Optimally, we could have planned out launch and eject times to create a more efficient transfer if we calculated the optimal "time of flight", and subtracted that from our required PeT to get our TEj.
I hope I've explained this understandably, it's a complex subject and if you have difficulties understanding it's likely due to my not explaining it well enough. Feel free to ask more questions if you have any and I'll do my best to make the answers understandable.
Tommy
) plotting a course to Jupiter. I didn't have enough time to eject before History, but after reviewing what I did and looking at the "Home Direct" tutorial, I have a question. When I set the course TEj, then set the Orbit Eject TEj, aren't they supposed to be the same? In Home Direct, the Orbit Eject TEj is changed to find a lower Dv solution. I thought the TEj set in the course was the time the ship is supposed to eject from the source which would be changed when you changed in the Orbit Eject display.
