If the Apollo 17 astronauts had gone for Mars, where would they have gotten?

Question

Suppose at the last minute, Houston and the Apollo 17 crew (let's assume that support extends all the way up to the White House) decided they should go for broke and attempt to reach Mars instead. The spacecraft has not been modified in any way; it's still entirely designed and loaded up for a moon mission. Where would they have wound up? (What systems would have failed first, and/or how long would they have stayed alive?)

Answer 1

The Saturn V + Apollo stack would have had just about enough performance to do a Mars flyby mission in the appropriate launch window, for example if the launch was delayed to summer of 1973.

The delta-v (change in velocity) provided by the Saturn V's third stage for Apollo's usual translunar injection is about 3200 m/s. The delta-v needed to reach Mars from LEO is about 4300 m/s. The Apollo CSM, fully fueled, can do about 2800 m/s. I think there'd be enough propellant left over for it to brake into a stable Mars orbit, though certainly not enough to return afterward.

The one-way transit time from Earth to Mars, however, would have been at least 8 or 9 months. The Apollo spacecraft's fuel cells, which were its only source of power, wouldn't have lasted more than a few weeks. Neither would the astronauts' other supplies. Assuming they packed extra snacks and CO₂ scrubbers, electricity would have been the limiting factor; once the fuel cells ran dry, they would have lost communication, air circulation, thermal management, and all control of the ship, dying in short order thereafter.

Answer 2

First, let's assume that this decision was made because there was a launch window to Mars at the time that Apollo 17 was about to launch. Perhaps credible intel was received that another country, such as the Soviet Union, was about to launch a manned mission to Mars and America's leaders felt that it was vital that Apollo 17 beat them there. If we don't make this kind of assumption, the hypothetical scenario is hard to accept.

According to this answer, Maximum speed reachable by Saturn V, the first three stages of the Apollo rocket would had a delta-v of 17911.9 m/s.

If we assume that the delta-v to a 200km LEO orbit is 9.3 km/s, the injection delta-v is 7.82 km/s, and the post-injection delta-v of 2.07 km/s is achieved through aero-breaking, then the mission requires the rocket to have 9.3+7.82 = 17.12 km/s of delta-v. So, it should be possible to reach Mars - barely. Of course, the guidance computer would have to be reprogrammed with the new trajectory while in LEO.

(ref)

The crew would need to survive for 240 days, which is 20 times longer than the actual Apollo 17 mission which was 12 days. Potentially this could be achieved by aggressively conserving power and rationing consumables.

As was done during Apollo 13, the crew could shut down the command module and live in the LEM until its power and supplies were used up, and then the LEM could be jettisoned and the astronauts could relocate to the command module for the rest of the journey.

Although, while perhaps not allowed by the framing of your question, potentially additional supplies could be tossed into the capsule right before launch. If an EVA was done to jettison everything non-essential to the last-minute Mars mission while still in orbit around Earth, then the delta-v lost due to the weight of the extra supplies could be made up during the Mars injection burn.

I think, however, that it is likely that the crew would do the math early in the mission and realize that they would need to draw straws. Two of them would have to sacrifice themselves so that there would be enough power, life support, and provisions for the third to survive to reach Mars - where they were likely to die anyway. There is a historical precedent for this...

The sinking of the Nantucket whaleship Essex on November 20, 1820 inspired Herman Melville to write Moby Dick. Melville’s story ends with Moby Dick sinking the Pequod, but for the Essex crew, their story began with the sinking. Far out in the Pacific Ocean, 2000 nautical miles west of South America, the sailors had just enough time to pack some provisions and load everyone into three whaleboats. They tried to sail east, but it took 95 days before they were rescued. Of the twenty crew members, only eight survived. And in order to survive, they had to resort to cannibalism. They also drew straws to decide which sailor would sacrifice his life to feed the others. (ref)

The next question is whether the Command Module would be capable of surviving reentry while aerobraking in Mars's atmosphere. Because the chutes are designed for Earth, they would not slow down the command module on Mars as much as they would on Earth. The remaining astronaut would experience a very hard - but conceivably survivable - landing.

From that point on it's hard to imagine a happy ending. Perhaps, if the intel was top-notch, our astronaut could have landed at the same landing site that the other country's mission was planning to land at. Then, there is a chance that arrangements could be made for the astronaut to join the crew of the better-planned mission and return to Earth with them.