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The LM had both ABORT and ABORT STAGE buttons. What was the difference and in which scenario would each be used?

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The abort switch is actuated to initiate an abort, using only the descent engine. Actuation of this switch causes the following events to occur: a command signal is sent to arm the descent engine; a signal is sent (via instrumentation) to telemetry to indicate that the LEM is preparing for an abort; and a signal is sent to the LGC and AGS to compute and execute the abort trajectory,using the abort program.

The abort stage switch is actuated to initiate an abort, using only the ascent engine. Actuation of this switch causes the following events to occur: a command signal is sent to electroexplosive devices to pressurize the ascent engine; a signal is sent to the LGC and AGS to compute and execute the abort trajectory, using the abort stage program; a signal is sent (via instrumentation) to telemetry to indicate that the LEM is preparing to stage for an abort; the descent engine is shut down; and an "engine on" command is enabled, which fires the appropriate electroexplosive device to initiate vehicle staging.The LGC simultaneously turns on the ascent engine, and signals telemetry, via serial down-link, that the ascent engine has been started.

(emphasis mine)

Source: LEM Familiarization Manual page 3-8

This chart shows the capability of each engine to abort versus altitude and descent rate.

enter image description here

Source: Apollo Lunar Landing Strategy

Acronymology:

  • AGS: Abort Guidance System
  • LEM / LM: Lunar Module
  • LGC: LM Guidance Computer

Here's an example of a page from the landing checklist from the Timeline Book with the abort callouts highlighted. (No acronymology will be supplied for this beast)

enter image description here

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    $\begingroup$ That graph is beautiful from an engineering standpoint, and from a graphic design standpoint. $\endgroup$ Commented Sep 27, 2022 at 18:51
  • $\begingroup$ Would it be accurate to summarize this as that the "abort stage" switch is an "abort + stage" switch? $\endgroup$ Commented Sep 28, 2022 at 13:21
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    $\begingroup$ I'm curious about the left end of the "descent engine" curve on that graph. Does that imply that using the descent engine below either 250 ft or 75 ft/s would be "unsuccessful", or would the curve continue all the way to the origin, as implied by the "nominal profile"? $\endgroup$
    – kgutwin
    Commented Sep 28, 2022 at 17:14
  • $\begingroup$ @kgutwin: That close to the surface you have to use a different abort protocol involving firing the descent stage at full power first and then switching to the ascent engine. $\endgroup$
    – Joshua
    Commented Sep 28, 2022 at 17:27

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