The question is, "Why stop at EML1?" Assuming the command and service module for the Earth-return has been loitering at EML1, could it let the lunar ascender fly past and then execute its own burn to match velocities for a rendezvous that takes place during the Trans-Earth cruise phase?A superficial analysis seems to show a primary advantage in fuel savings. Fuel for the ascender rendezvous burn is eliminated, and this also eliminates the descent fuel required to soft-land the rendezvous fuel on the lunar surface.
What happens if something goes wrong?
You can probably get to EML1 even if you don't get it exactly right the first time. If your navigation is a bit off, or if the burn gets cut short for some reason, you can try again.
If the CSM is waiting at L1 for the LM to fly by and it misses the departure burn by an hour, or the departure burn gets cut short by 100 m/s, everyone is screwed.
We're agreed the safety concern dictates that for a rendezvous, the spacecraft making the burn must be able to execute a correction burn as required. In the suggested TER scenario the spacecraft with that capability is the CSM. The lunar ascender takes the role of passive target. Is that inherently more dangerous for the crew aboard the ascender?
I think corrections in trans-earth cruise are going to be more difficult than around EML1. The wrong halo orbit will still stay around EML1, but an incorrect trans-earth injection will steadily drift away from the desired course.
Minimising total delta-v is not the only consideration.
I'm slowly upgrading my still very limited orbital mechanics fu and I haven't reached libration orbits yet. What are the advantages of halo orbits over Lissajous orbits?
We will start with the computation of the Lissajous trajectories (two dimensional tori) and the halo orbits (one dimensional tori) using the Lindstedt-Poincar´e method.
Anyone interested in an online study group for this?