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I've always been curious how did the Apollo 11's Eagle ascent stage of the Apollo Lunar Module navigate back to the Apollo Command/Service Module (CSM) that was in lunar orbit?

Was it simply a case of being able to see it and thrust in the general direction, or was there something more sophisticated at work? Was the CSM itself in a selenostationary orbit, or was it moving with respect to the lunar surface, thus making it even more difficult?

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Please don't ask more than one question at a time. For a quick answer of your second question, there are no stable orbits that are stationary to a point on the luna surface, and even if there were, this would not make the rendezvous much simpler. – Rikki-Tikki-Tavi Feb 23 at 12:10
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It does not seem any different from any other orbital rendezvous - it starts with a proper launch timing - see en.wikipedia.org/wiki/Space_rendezvous – Suma Feb 23 at 13:24
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A selenostationery orbit would be right here on Earth, if I'm interpreting that correctly :). Anyway ground control knew exactly where the CSM was, but didn't know the lander's exact position! There is a mass of stuff on the Apollo lunar Surface Journal, try this page: hq.nasa.gov/alsj/a11/a11.launch.html – Andy Feb 23 at 15:13
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For reference the 'selenostationery orbit' bit was not my original words. I originally stated lunar stationary orbit - since I was looking for an equivalent to geostationary. I believe someone with more knowledge than me has changed that. – Chris Nevill Feb 23 at 15:24
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A "selenostationary" orbit would be 88465 km from the center of the Moon. Such an orbit would not be stable because it is outside the Moon's sphere of influence. – David Hammen Feb 23 at 17:16
up vote 24 down vote accepted

The process was a great deal more sophisticated than pointing and thrusting, and the CSM was cooking along at over 1600 m/s, circling the moon every 2 hours. Mission control, however, had fairly precise tracking of the positions of both the CSM and the landing site, and they computed the correct time of launch to begin the rendezvous.

The LM ascent stage launched initially into a 18km x 87km elliptical orbit somewhat behind the CSM, which was orbiting at 105km x 116km (a higher, slower orbit). The LM then circularized its orbit using its RCS thrusters.

I believe from this point on, Columbia could detect Eagle on rendezvous radar.

Two and a half hours later, with the LM about 72km from the CSM and approaching at 34 m/s, they did another RCS burn called "Terminal Phase Initiation" to intercept the CSM. 10 minutes after that, Armstrong was able to see the CSM. Until the ships were very close together, the maneuvering was all done under computer control using radar data; once they were close together and velocity-matched, they manually flew the approach.

All the maneuvering of the approach was done by the LM, but the CSM was at each point prepared to make the reciprocal maneuver, such that if the LM's crew, computers, or RCS failed, the CSM would have taken over as the active participant in the rendezvous.

This transcript and commentary covers the ascent and this one covers the rendezvous and docking. The mission timeline here summarizes the LM maneuvers from ascent starting at 124:22.

Since the rendezvous approach plan was fairly leisurely, and the RCS thrusters capable of quite precise small adjustments, any relatively small error in the initial ascent (such as the positions of the craft, the timing of the launch, or the performance of the ascent engine) would be easily taken care of in the following maneuvers. This incremental approach is the key to any orbital rendezvous, whether in Earth orbit or lunar.

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Incredible... especially when you consider the computers back then! Thanks :) – Chris Nevill Feb 23 at 16:57
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The key takeaway is that the computers back then, on the ground and in the two spacecraft, were, with the procedures in place, quite capable of handling the job. – John R. Strohm Feb 23 at 18:25
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"Mission control, however, had fairly precise tracking of the positions of both the CSM and the landing site" I wonder, do you have any information on how this was achieved? – Alex Feb 24 at 1:30
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The Unified S-Band system on the Apollo CSM provided range, range-rate, and direction information, with which the position of the ship could be determined pretty closely. en.wikipedia.org/wiki/Unified_S-band#Ranging I'm not sure if the LM position was determined in a similar way, or by the crew sighting landmarks, or dead reckoning, or what. – Russell Borogove Feb 24 at 1:34
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Well, the crew did use landmark sightings during the descent, at least. Compare hq.nasa.gov/alsj/a11/a11.landing.html at 102:36:11: "Armstrong (onboard): Okay, we went by the three-minute point early. We're (going to land) long." and then at 102:36:18 "Armstrong: (To Houston) Our position checks down range show us to be a little long." plus commentary at 102:36:21: "We picked a number of landmarks (to look at) while we were still in the face-down mode." – Michael Kjörling Mar 1 at 9:11

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