A recent question asks why the Apollo lunar module wasn't routinely brought back when returning from the Moon, so it could be used as an Apollo 13 style lifeboat. The answers correctly state that after ascent from the Moon, the LM is essentially depleted of supplies and therefore would not be helpful. However, there is also an implication (particularly in the comments) that there was not enough fuel to bring back the added mass of the LM ascent stage.
I suspect that some missions actually did have enough fuel (or at least had capacity to add enough fuel) to bring back their ascent stage. Remember, the service module was designed for a "direct mode" mission, without a lunar module. The CSM was to land on the Moon atop a descent stage; the CSM would then take off from the Moon and return to Earth. When the mode was changed to lunar orbit rendezvous, the SM therefore had excess delta-v capability, particularly for Apollo 10-14. This excess capability was taken advantage of during Apollo 15-17 to add the service module experiment bay, a lunar rover, supplies for more days and more EVAs, and more moon rocks brought back.
Did some of the Apollo missions have enough fuel left to bring back the ascent stage?
- Consider Apollo 10-12 and 14-17. We know it worked for 13. The other missions either had no crew, did not go to the Moon, or did not have a LM. Apollo 10 could have performed the lifeboat scenario, even if it didn't get all the way to the lunar surface.
- Assume that the mission has already landed the LM on the Moon, performed its EVAs, launched from the Moon, and rendezvoused in lunar orbit.
- The mass to return should include the CM, SM, LM ascent stage, whatever residual propellants exist in these three modules, the 3 astronauts, and the lunar samples.
- There needs to be enough propellant to perform the trans-Earth injection. Your choice if you also want to consider any correction burns. Your choice if you want to burn the residual propellant in the ascent stage.
- Please use the actual statistics of the individual missions (available in Apollo by the Numbers), rather than the nominal or theoretical statistics of Apollo hardware.
- Don't worry about why you would do this (that's the purview of the previous question), just whether it is simply possible.