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In the NPR podcast On Apollo 11 Anniversary, A Former Crew Member Reflects On The Lunar Trip Scott Simon interviews Michael Collins. Near the beginning is this exchange:

SIMON: We asked the man who helped get there what people of a certain age are asked all the time: “Where were you when man landed on the Moon?

COLLINS: You know I really don’t know. I was in an orbit that went around the Moon at 50 miles, so sometimes I was over… I could see the dinky little Earth, sometimes I was over behind the Moon. I don’t know where I was when they landed to tell you the truth!

Question: Where in orbit was Michael Collins when the LM landed? Can this be estimated from available data about and understanding of the CM orbit and historical timestamps?

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    $\begingroup$ How much accuracy are you looking for? The back of my envelope says he was about 400 miles west of the LM at touchdown. $\endgroup$
    – Russell Borogove
    Jul 21, 2019 at 23:43
  • $\begingroup$ @RussellBorogove I removed "exactly" from the title a few minutes ago, that's fine! $\endgroup$
    – uhoh
    Jul 21, 2019 at 23:49
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    $\begingroup$ The back of my envelope is terrible. $\endgroup$
    – Russell Borogove
    Jul 22, 2019 at 0:37
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    $\begingroup$ Definitely not behind the moon (Collins was in contact with Houston) and within a few hundred miles of the LM. I'm working on an estimate based on LOS/AOS times and orbital period right now. $\endgroup$
    – Russell Borogove
    Jul 22, 2019 at 0:45
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    $\begingroup$ @RussellBorogove the trick is to use a really big envelope. $\endgroup$
    – Hobbes
    Jul 22, 2019 at 10:16

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I estimate that Collins, in the CSM, was over about 16.7º E longitude when Eagle touched down, about 200 km ground-track West of the LM.

I got approximate loss-of-signal and acquisition-of-signal times for the last couple of revs before landing from the Apollo 11 annotated journals. The CSM was in an orbit that took about 119 minutes per revolution; for about 46 minutes of each rev it was behind the moon and out of contact, leaving 73 minutes to pass the front of the moon. 0 longitude is the point directly facing Earth, so it's about 36.5 minutes from AOS to 0º.

Touchdown at 102:45:57 was 31 minutes after AOS at 102:15, so 5.5 minutes short of 0º longitude. With the CSM covering one degree every 19.83 seconds, it would be about 16.7º E longitude. Tranquility Base was at 23º26' E, so that's about 200 km ground-track distance away (and 100km up).

The AOS and LOS times are mostly round-minute estimates, and I am implicitly assuming a perfectly circular orbit and a ground station at the closest Earthside point to the moon, and ignoring the 1.25º orbital inclination, so I'm sure I'm off by a few degrees one way or the other (at 30km of lunar circumference per degree), but almost certainly Columbia was somewhere in Eagle's visible sky at touchdown. Let's say, somewhere within the red dot in this image:

enter image description here

My initial estimation technique was very crude: I assumed that the horizontal speed of the LM went linearly down from 1600 m/s to zero over the 13 minutes of powered descent, which would make it cover 624 km less distance than the CSM over that period. (The horizontal deceleration obviously isn't linear, because the engine throttles up and down, and the thrust angle changes, but the area under the curve has to be somewhere between 0 and 1248 km, and closer to the middle of the road than not.) However, when PDI starts, the LM is already ahead of the CSM, having gone into a lower, faster orbit during the blackout period, so some of that ~624km loss is canceled by the LM's head start.

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  • $\begingroup$ Wow, very ice! Does the 73 vs 46 minutes reflect line-of-sight to Earth? $\endgroup$
    – uhoh
    Jul 22, 2019 at 1:40
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    $\begingroup$ Yeah, the orbital height means the CSM is in lunar shadow for less than half the rev. $\endgroup$
    – Russell Borogove
    Jul 22, 2019 at 1:43
  • $\begingroup$ Huh. From his own "Carrying the Fire" we know he was listening to the LM radio via the Earth relay rather than direct. The result of this is the official transcript has his lines of the moon landing out of order. $\endgroup$
    – Joshua
    Jan 6, 2022 at 17:29

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