I stand corrected. Regardless, there was no means of reconnecting the CSM to the S-IVB, and no intention to ever reuse the stage.
There were proposals for various on-orbit tugs and Lunar shuttles that would take command vehicles to and from the Moon but always remain in space, but as far as I’m aware these all used some variation of the Apollo Docking Mechanism. There was also a proposal (or actually several) for the use of an up-sized Gemini ('Big Gemini) for various orbital operations including the Air Force Manned Orbiting Laboratory (MOL) but nothing ever went past the study phase.
If the TLI burn did not get the CSM-LM stack to a high enough orbit to get caught by the moon’s gravity, what was the point (if any) where the SPS could get them there
I’m not sure I understand the question. Are you asking whether the Service Module main propulsion system could perform translunar injection? No, it didn’t have nearly enough impulse to send the CSM-LM to Lunar orbit. It barely had enough to inject and circularize a near equatorial Lunar orbit, and then send the CSM back to Earth intercept with a few minor correction burns if necessary.
Sorry, I was not clear, I am aware that without the SIV-B they were not going anywhere out of Earth orbit.
Per Apollo abort modes, if the SIVB failed during launch, the SM engine could still burn and get them into Earth orbit, I was wondering that if the* SIVB failed during TLI,* was there any possibility of them using the SPS to get to the moon? Maybe contingents on when exactly did it fail (say three-quarters of the way through the burn as opposed to almost immediately ) or if they were placed in a lower than expected orbit after TLI.
I guess it would depend on when and how the S-IVB failed. By dumping the LM they might have enough impulse to make a roundabout to the Moon, but remember, it isn’t just the distance they have to cover; they also have to be able to return to the Earth in the right position and at the right vector in order to reenter. Without running a trajectory simulation I can’t say for certain, but my off-the-cuff answer is that it is unlikely they could get to the moon and return on a trajectory that would be within the operational life of the CSM.
There is no way to answer that without specifics of the trajectory. If it failed before TLI, I think it is very likely. After, it’s not so good. And if the S-IVB explodes or ruptures and damages the Service Module, they may be SOLregardless.
In general there was always an available abort trajectory for all Apollo mission phases, except for the trans-earth injection burn to return home. Even for the lunar ascent there were some limited abort options where the CSM could dip to a low orbit to rescue a LM which had a premature engine cutoff.
On the TLI burn if the S-IVB shut down early or late it would be a mission abort, the only question is what mode. The CSM did not have enough delta V to complete the normal mission without a full duration S-IVB burn.
The CSM had about 2,804 meter per sec total delta V. The S-IVB trans-lunar injection burn was about 3,100 meters per second.
For an S-IVB shutdown early in the TLI burn, the SPS could do a direct abort, cancel that velocity and come back. For a shutdown late in the TLI burn, a direct abort was not possible using the main SPS engine so the CSM would do a short burn to change trajectory to an Apollo-13-style slingshot around the moon and come back.
In theory a direct abort might have been possible at any point after TLI by sequentially burning both SPS then the LM descent stage. I think the 2,804 m/s delta V figure was the CSM by itself; if they kept the LM attached the velocity change would be lower but the total delta V from burning both engines was probably higher. I don’t know if that was a practiced contingency.