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I'm wondering just how many burns the Apollo 11 mission required.

Did they first have to reach a circular orbit around Earth by a single burn at apogee or did they target the Moon immediately?

Then, when they've reached the Moon did they have to retroburn at perilune to circularize, or was the trajectory calculated so that it happened automatically?

On their way back was a single burn enough to leave the Moon or did they have to execute some corrections along the way?

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According to the plan, an Apollo mission to the moon uses eleven-ish burns. Here are the expected maneuvers:

Apollo mission profile

  1. Launch from earth. This you might count as three burns, since it requires all three stages of the Saturn V rocket. They're not only launching from earth at this point, but they're also burning to get into a circular orbit around the earth.
  2. Leave earth orbit for the moon (translunar injection). Here they relight the third stage of the Saturn V, using up the rest of its fuel. At this point, they should be on a free-return trajectory, meaning that if they do nothing else, they'll slingshot around the moon and come back to the vicinity of the earth.
  3. Make a midcourse correction. These corrections are made using the engine built onto the Service Module (SM).
  4. Make another midcourse correction, as needed.
  5. Get into an elongated orbit around the moon. This uses the SM engine.
  6. Circularize the orbit around the moon. This also uses the SM engine.
  7. Get into descent orbit. This uses the descent engine on the Lunar Module (LM).
  8. Descend to the moon. This also uses the descent engine on the LM.
  9. Ascend from the moon. This uses the ascent engine on the LM, leaving the descent portion behind.
  10. Leave lunar orbit for the earth (transearth injection). This uses the SM engine.
  11. Make a midcourse correction. This also uses the SM engine.
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    $\begingroup$ In practice, many of the midcourse corrections were either not needed at all or small enough that they were performed with the RCS rather than the SPS. There were also a few separate burns during the lunar ascent phase - one big one to get into lunar orbit, then a couple of smaller ones to set up the rendezvous with the CSM. $\endgroup$ – pericynthion Jun 13 '14 at 18:06
  • $\begingroup$ Stage 1 and stage 2 could count as burns, as could the initial burn of stage 3. I seem to recall Apollo making at least a couple of orbits around Earth, before the TLI burn -- did they do a circularization burn at apogee, or did they just accept a very elliptical orbit for the short time they'd be parked? $\endgroup$ – Phil Perry Jun 13 '14 at 22:22
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    $\begingroup$ The S-IVB injected directly into a parking orbit that was close to circular (albeit very low altitude); no need for a circularization burn. $\endgroup$ – pericynthion Jun 13 '14 at 23:49
  • $\begingroup$ Step 9 was composed of several individual burns, required to rendevous with the CM. $\endgroup$ – Innovine Jan 31 '17 at 14:28
  • $\begingroup$ Step 9 is a single burn of the ascent engine; the rest of the rendezvous maneuvers are conducted with the RCS thrusters. $\endgroup$ – Russell Borogove Feb 28 '17 at 16:46
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The accepted answer describes the general Apollo mission plan, but as the question references Apollo 11 specifically, we can check the mission timeline to see all the maneuvers done during the mission.

In later mission timelines the engine used for midcourse is consistently called out, but for Apollo 11 I had to check the transcripts to verify.

There was one SPS midcourse correction burn on the outbound leg of the trip. Four optional corrections were scheduled in the flight plan, but three were canceled as unnecessary. (Only one or two are ever needed, but by scheduling four they gain a lot of flexibility.) The sole midcourse correction on the return leg was done on RCS according to the transcripts.

  1. 0:00 S-IC ascent
  2. 0:02 S-II ascent
  3. 0:09 1st S-IVB Earth orbit insertion/circularization
  4. 2:44 2nd S-IVB trans-lunar injection
  5. 26:44 SPS midcourse correction
  6. 75:49 SPS lunar orbit insertion
  7. 80:11 SPS lunar orbit circularization
  8. 101:36 LM DPS descent orbit insertion
  9. 102:33 LM DPS descent
  10. 124:22 LM APS ascent
  11. 135:23 SPS trans-Earth injection

So that's 11 total burns if you count each stage of the ascent separately.

There is one more burn that's not strictly necessary to complete the mission; the S-IVB stage used its auxiliary propulsion system to fine-tune its trajectory for a lunar slingshot maneuver, or, on some later missions, to crash into the moon.

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