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Looking at the Apollo 13 mission timeline within three hours after the explosion of O2 tank two all oxygen in the SPS was completely depleted. Fuel cells #1 and #3 were off line. CM had even started to cannibalize its reentry batteries, before it was shut down. The damage to the SPS was unknown and deemed unreliable (you couldn't fire it with the LEM attached anyway) [see comment]. It seems to me that, at that point, the Service Module had no resources that were of any use anymore.

What were the reasons NASA opted to keep the SM attached for the rest of mission? I would expect that attitude and trajectory control would have been much easier without hauling the dead SM around.

The only explanation I could think of was to protect the CM's heat shield from direct exposure to space?

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    $\begingroup$ The SM SPS was very much usable with the LM attached; it's how the trip between TLI and CSM/LM separation was normally done. What couldn't be done with the SM SPS was to initiate a direct abort trajectory while keeping the LM; besides the unknown state of the SPS, a SPS midcourse abort required LM jettison, which was deemed unacceptable (would have left the crew without their lifeboat). And while I don't have any references handy (I might look around later if nobody beats me to it), protecting the CM heat shield was probably a major reason behind the decision to keep the SM attached. $\endgroup$ – a CVn May 17 '16 at 13:57
  • $\begingroup$ @MichaelKjörling Thanks for the clarification. I thought that was a little wacky :) It seems I misunderstood the mission report. On page III-17 it says "It was obvious that we were committed to going around the moon rather than performing a direct abort because the large delta V could have been supplied by the SPS only if the LEM were jettisoned, but that was out of the question." So they would have been forced to lose mass in order to pull of a direct abort. That make much more sense. $\endgroup$ – djf May 17 '16 at 14:17
  • $\begingroup$ There was a question here where someone calculated (in a comment, unfortunately, so not searchable) that it should in theory have been possible to get the delta-v required for a midcourse direct abort without LM jettison. However, I'm sure NASA at the time had people double-check all possibilities including that one, so there's probably some non-obvious reason why that still wouldn't be sufficient, and I don't remember if that scheme would have required SM jettison. About all we know with full certainty is that in the end they decided on a circumlunar free return trajectory abort using the LM. $\endgroup$ – a CVn May 17 '16 at 14:25
  • $\begingroup$ There also was the uncertain state of the engine because they didn't know exactly what had gone wrong. If the engine is damaged and they try a direct abort the mission is lost. $\endgroup$ – Loren Pechtel Jul 10 '17 at 2:42
  • $\begingroup$ There was another safety concern as well. If the SPS did a partial direct abort burn by failing before completing that burn, the spacecraft could end up on a collision course with the Moon. Maybe the burn could be completed with the descent engine on the LM, but it would have been touch-and-go to say the least not to mention extremely time-critical and incredibly risky. $\endgroup$ – Ken Clement Aug 23 '18 at 23:23
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It appears that your speculation is correct. From the Lunar and Planetary Institute's Apollo 13 Mission Overview (emphasis mine):

On the Apollo spacecraft, the Service Module (SM) was intended to provide most of the consumables such as oxygen, water, and power for the mission. It was also designed to serve as the primary propulsion and maneuvering system of the spacecraft. The explosion of the oxygen tank however, led to the loss of the consumables and rendered the service module nonfunctional. The SM was retained until just before reentry to protect the command module heat shield from the possible degrading effects of long exposure to the cold of space.

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    $\begingroup$ I found more along those lines in the mission operations report . On pages 20 and 23 it mentions "[a] concern was the cold environment to which the heat shield and CMRCS would be exposed [to]" and "uncovering the heat shield of the CM for many hours and thereby reaching the hazy area of thermal limits" $\endgroup$ – djf May 18 '16 at 6:16
  • $\begingroup$ @djf: Why oh why didn't they test the heatshield in space before sending it on a munar mission? $\endgroup$ – Sean Apr 24 at 23:58
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    $\begingroup$ When you are schedule and budget limited, why would you test a scenario that was never supposed to happen? $\endgroup$ – Organic Marble Apr 25 at 0:02

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