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Apollo 8 to Apollo 11 flew on a free return trajectory (later missions left the free return trajectory during a mid course correction after TLI).

If those spacecraft had just stayed on that trajectory, would they have reentered in Earth's atmosphere or would they just have been flung around Earth and back towards the Moon's orbit again?

So would they have returned to Earth without any propulsion at all after TLI?

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    $\begingroup$ This paper may have the answer, but it's behind a paywall... NTRS doesn't have it either. $\endgroup$
    – Ludo
    Feb 10, 2022 at 13:31
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    $\begingroup$ Thank you! I found it. Will have some reading to do now... $\endgroup$
    – TrySCE2AUX
    Feb 10, 2022 at 13:49
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    $\begingroup$ Can you share where you found it? It's 50+ years old... I can't believe it's still being paywalled... $\endgroup$
    – Ludo
    Feb 10, 2022 at 17:22
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    $\begingroup$ @ludo there are places on the internet that you can find when searching for "free access to scientific papers" and than put the doi number in the search field... Not, that I would ever recommend doing something like that! ;/ $\endgroup$
    – TrySCE2AUX
    Feb 11, 2022 at 10:22

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Yes. From the Apollo 8 press kit (direct link to PDF):

The translunar injection burn of the third state will place the spacecraft on a free-return trajectory, so that if for some reason no further maneuvers are made, Apollo 8 would sweep around the Moon and make a direct entry into the Earth's atmosphere at about 136 hours after liftoff and land in the Atlantic off the west coast of Africa.

(page 4, emphasis mine)

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    $\begingroup$ In theory. My understanding is the burn tolerance wasn't that good and NASA expected to need a course correction. The idea was to get close enough that the course correction could be done with RCS only in case the SM engine didn't work. $\endgroup$
    – Joshua
    Feb 10, 2022 at 21:59
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    $\begingroup$ @Joshua Agreed, but it was designed to have the spacecraft reenter. The ability of the spacecraft to make small corrections with the RCS is in fact also mentioned in the referenced document. $\endgroup$
    – Ludo
    Feb 11, 2022 at 8:06
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    $\begingroup$ I found mentions of "RCS is enough" in a document talking about orbits as well. It was not clear to me if this was just for course corrections or if it was needed for a deorbit burn. Seems, it's only for corrections. Thank you! $\endgroup$
    – TrySCE2AUX
    Feb 11, 2022 at 10:24
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    $\begingroup$ @kruemi There wouldn't have needed a deorbit burn, since their trajectory is one that would have intersected the atmosphere anyway. So all they needed was course corrections on the way back. However, it is possible to use RCS alone to deorbit a spacecraft in a stable orbit, depending of course on how high the orbit is vs. how much fuel the RCS system has. $\endgroup$
    – HiddenWindshield
    Feb 11, 2022 at 16:06

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