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We know Apollo could not have gotten anyone to Mars and returned them alive. My question is, using Apollo hardware, how far from earth could an astronaut have traveled and still return safely?

Notes:

  • You may either include or omit the lunar module (your choice)
  • If reducing the crew size helps, three astronauts do not have to have been sent (but one must have been sent)

EDIT Concerning the comments on how much wiggle room there is, I will restrict your choices to hardware that either flew or at least got far enough to have full-scale mock-up (So no Venus Flyby hardware). I will also limit you to a single Saturn V launch. (and I thought the question was simple)

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    $\begingroup$ Did you read about the Manned Venus Flyby? en.wikipedia.org/wiki/Manned_Venus_flyby $\endgroup$
    – Organic Marble
    Commented Mar 4 at 22:56
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    $\begingroup$ To generally expound on Organic Marble's point, how much wiggle room do we get on "Apollo hardware?" There were extraordinary plans based on the Apollo-Saturn stack, like the linked Manned Venus flyby; do those count? $\endgroup$
    – Erin Anne
    Commented Mar 4 at 23:31
  • $\begingroup$ "Using Apollo hardware": increased resources for the Fuel Cells and Oxygen generation system could be flown using some of the LM mass. The rest of the LM mass would be ignored, the fairings shortened, and a greater volume of MMH NTO. Some fuel for the SM would need to be reserved for deceleration on return to Earth. $\endgroup$
    – AnarchoEngineer
    Commented Mar 5 at 0:35
  • $\begingroup$ However I do not understand your specifics: Apollo Hardware could take you all the way to the outer solar system... It's just a matter of launching enough modules, fuel, atmosphere, and food... and having a lot of gravity assists... $\endgroup$
    – AnarchoEngineer
    Commented Mar 5 at 0:37
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    $\begingroup$ oh, if it has to have had a full-scale mockup and fit on one Saturn V, that'll get you to the moon and back $\endgroup$
    – Erin Anne
    Commented Mar 5 at 9:51

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Apollo 17 was the longest duration mission of the program, at 12 1/2 days. Let's assume that by flying a single crewperson, and taking aggressive power-conservation measures and extra snacks, we can extend the crew and spacecraft's endurance to 50 days.

An elliptical orbit around Earth, with an apogee of about 1,140,000 km and perigee of about 200 km, has a period of about 50 days. That orbit is comfortably within Earth's Hill Sphere, so from LEO, only a single apogee-raising burn needs to be done; if we save mass by not fueling the LM, the S-IVB should be able to provide the needed ~3170 m/s of delta-v easily -- it's only 140 m/s more than a normal TLI!. We'll keep the rest of the LM to give our crewperson a little more living space. Almost all the maneuvering capability of the CSM goes unused; we'd want to make a short burn on the return leg to slow our return velocity to match the usual atmospheric entry velocity for a lunar mission (but we're really not coming back much faster than usual, and I believe there was lots of margin on the heat shield).

That orbit takes the spacecraft to just about three times the distance from the Earth to the moon. As any experienced player of Kerbal Space Program knows, the rate at which apogee increases with increasing delta-v applied at perigee is very nonlinear -- it's much, much harder to get the apogee from 200 km to the moon's 384,400 km (~3030 m/s) than it is to raise the apogee from 384,400 km to 1,140,000 km (~140 m/s).

By burning some of the CSM's surplus ∆v on the injection to speed up, and the rest to brake at the 25-day mark, this could be increased a lot. Assuming we don't take the LM in this case, for simplicity, the CSM has about 2800 m/s of ∆v capability; reserving some for midcourse corrections, expending 1325 m/s times 25 days works out to another 2,862,000 km traveled, for just about 4,000,000 km apogee -- more than ten times the distance to the moon (and not even a tenth of the way to Mars).

If we retain the LM's fuel and burn that on the outbound leg, then discard the LM for the "boostback" burn at 25 days, we can probably increase the range still further, but I'm not up to doing the math.

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  • $\begingroup$ I had a feeling we'd be limited by life support rather than fuel. Do we have spare delta-v, and can we use it to accelerate and then brake on the way home, shaving time off the return trip and allowing a higher apogee? $\endgroup$
    – Nuclear Hoagie
    Commented Mar 6 at 19:01
  • $\begingroup$ Oh. Yeah. We have loads of delta-v, let me do some more math. $\endgroup$
    – Russell Borogove
    Commented Mar 6 at 19:04
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    $\begingroup$ Ehhh what's 2.8 million kilometers between friends? $\endgroup$
    – Russell Borogove
    Commented Mar 6 at 19:21
  • $\begingroup$ I read that Artemis flights to the Moon will take longer than for Apollo for two reasons. First, NASA did not trust the life support systems of Apollo to function reliably for much longer than 7-10 days (not sure exactly how many but it varied). This was a driver for the size and impulse of Saturn V (not the only driver but a primary one) to make the journey there in just three days instead of the currently planned five or more days. Second, Artemis's lighter and more reliable life support permits the use of slightly smaller boosters and a less energetic trip. How does this square with SLS? $\endgroup$
    – Chris Ison
    Commented Mar 15 at 0:46

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