> The LM does return to the CSM before the burn so it is conceivable it was needed for some preparatory step before TEI.
The flight plan makes clear that this is not the case.
> Perhaps a fuel transfer or some guidance calculations or some other maneuvers.
Even without reading the details of the flight plan, the LM was designed to carry just enough fuel to get down to the Moon's surface and back up again, with no extra fuel for other maneuvers; there wasn't any margin for any extra if the mission was to be doable at all. So it doesn't seem plausible that the CSM would have had to depend on getting some fuel transferred back from the LM in order to execute TEI.
As far as guidance calculations, that doesn't seem plausible either. The CSM, having been in a single stable orbit the whole time, would be expected to have much better guidance information than the LM, which had just executed a series of maneuvers, some of which were under manual control.
Sure, that all makes sense, and we know how it worked and that the LM was not needed. I’m just saying that we can’t infer the LM was unneeded for TEI just because it was jettisoned.
The flight plan makes clear that this is not the case.
> Perhaps a fuel transfer or some guidance calculations or some other maneuvers.
Even without reading the details of the flight plan, the LM was designed to carry just enough fuel to get down to the Moon's surface and back up again, with no extra fuel for other maneuvers; there wasn't any margin for any extra if the mission was to be doable at all. So it doesn't seem plausible that the CSM would have had to depend on getting some fuel transferred back from the LM in order to execute TEI.
As far as guidance calculations, that doesn't seem plausible either. The CSM, having been in a single stable orbit the whole time, would be expected to have much better guidance information than the LM, which had just executed a series of maneuvers, some of which were under manual control.