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$\begingroup$ I see, the trick is to ignore everything that happens before jettison time, then the problem then becomes trivial. It seems I'd overthunk it. $\endgroup$user12102– user121022018-11-11 07:30:36 +00:00Commented Nov 11, 2018 at 7:30
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1$\begingroup$ Well, that provides a lower bound on performance — if you keep the engine, you can use the engine, shortening time to orbit and reducing gravity losses, but (a) those losses are more significant early in the flight and (b) Atlas Original Flavor, at least, was already a brutal accelerator with an ascent time half that of most orbital launchers. $\endgroup$Russell Borogove– Russell Borogove2018-11-11 07:35:46 +00:00Commented Nov 11, 2018 at 7:35
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$\begingroup$ I see; in that case I'll hold off to see if someone would like to post an answer beyond by 6.8 - 4 = 2.8 that addresses part of the question. $\endgroup$user12102– user121022018-11-11 08:17:46 +00:00Commented Nov 11, 2018 at 8:17
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2$\begingroup$ Another factor is that a permanently attached set of engines can be lighter than a section that has to cleanly separate in flight, for the same performance. $\endgroup$Russell Borogove– Russell Borogove2018-11-11 14:57:18 +00:00Commented Nov 11, 2018 at 14:57
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$\begingroup$ That's true as well. For that though, I tried to work around it with careful wording of the question, asking only how the specific act of "engine-mass-dropping" increased payload mass to orbit, not the design. $\endgroup$user12102– user121022018-11-11 15:02:33 +00:00Commented Nov 11, 2018 at 15:02
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