Artemis mission launching tomorrow- Back to the moon and beyond...

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It works basically the same, since they are still depending on heavy power for a short time then coast, coast, coast, just as Apollo did, and as pretty much all current spacecraft must do. It would take a different propulsion mechanism, probably one with nearly continuous power use, to change that "equation."
I think they'd also have to be at about the same speed at the gravity EQ point, so in case of a retro rocket failure they'd go into lunar orbit or even into an earth return path instead of continuing into steep space. So a faster acceleration rate won't make a large difference in transit time.
 
That's where the "continuous power" comes in Lou, using a different mechanism, not rocket power. Just greater acceleration alone won't, as you indicate, be a large help, though it could shorten the time a little.
 

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