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In case the Apollo Lunar module had approached the landing site at way too high velocity, could the ascent stage have separated and returned to the command module before a crash? Thus performing a task similar to a launch abort tower. One challenge would be to synch with the orbit of the command module.

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Did you consider googling "apollo lm abort" before asking this question? – Russell Borogove Feb 22 at 0:34
I believe that Apollo 10 did just this: used the descent stage to approach close to the surface, then jettisoned it and used the ascent stage to return to orbit. – jamesqf Feb 22 at 4:13
Yes, I believe if the descent stage had expended its fuel, he could have aborted. as long as he was to the left of the ascent engine curve in the figure. It does get questionable near zero altitude.... – Organic Marble Feb 22 at 14:58
In fact, Apollo 11 wasn't "running on fumes". The time being counted down during the final approach (something less than 30 seconds left when Eagle touched down) was the time until the mission rules called for a mandatory abort using the ascent stage, not time until the lander fell out of the sky. – Russell Borogove Feb 22 at 21:07
Correction: the time countdown was to the "bingo" call, at which point the rules were "land in the next 20 seconds or abort". If they were only 50 feet up at bingo they'd press on. They were about 15 seconds from bingo at touchdown, with over 700 pounds of fuel remaining in the descent tanks. See the annotation at 102:44:45 here: – Russell Borogove Feb 22 at 21:25

Yes. There is a lot of good information in this presentation from the June 1966 Apollo Lunar Landing Mission Symposium relative to landing flight design including abort planning. The crucial figure is this one:

enter image description here

which shows the capability of the ascent engine to abort all the way down to landing. It assumes a 4 second delay to separate the landing stage.

As far as returning to the orbit of the command module, the Apollo Experience Report - Abort Planning document explains on page 24 (33 of the pdf) that the Lunar Module would attempt to attain a safe orbit and the Command Module would rendezvous with it.

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