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Interesting link. To be clear, I personally don't have a strong opinion on what may have actually occurred out there during the late 60s/early 70s. It can be any variation of A) Human moon landings occurred more or less exactly as publicly displayed, B) Human landings on the moon never actually occurred at all, or C) Human moon landings did occur, but not nearly as depicted to the populace, likely due to certain advanced technologies that couldn't be disclosed for undisclosed reasons, or prior 'moon landing programs' already in place which may include lunar bases and/or interactions with Alien races to discuss the latest intergalactic gossip, etc --- one's imagination can run wild with the possible speculations here.
I lean towards option B, though given limited intel on what's actually going on beyond our atmosphere, an iteration of Option C can't be ruled out either.
Re: acceptable levels of radiation, below is an excerpt from Chump's link that appears to directly contradict the blurb taken from the 'spacemath.gsfc.nasa' link:
Radiation beyond Low-Earth Orbit
Regarding the radiation limits for travelling beyond LEO, ‘NASA relies on external guidance from the National Academy of Sciences and the National Council on Radiation Protection and Measurements (NCRP) for establishing dose limits. Due to the lack of data and knowledge, the NAS and NCRP recommended that radiation limits for exploration missions could not be determined until new science data and knowledge [were] obtained.’ (Arch. Study, 2005 p.109)
The next year, in swift response to NASA's request, the NCRP produced a report with a title to puzzle an unprepared reader: Information Needed to Make Radiation Protection Recommendations for Space Missions Beyond Low-Earth Orbit (NCRP, 2006). By this, the NAS admits that there is no substantial information available on cosmic radiation beyond LEO, including data on lunar surface radiation, despite the alleged achievements of Apollo.
The Augustine Committee quotes another report, this time from the National Research Council (NRC, 2008), which largely confirms the problem: 'Lack of knowledge about the biological effects of and responses to space radiation is the single most important factor limiting the prediction of radiation risk associated with human space exploration.' (Augustine, 2009, p.100)
The National Academy of Sciences needed some raw information just to be able to start working on those recommendations. Of course, some data should have been readily available to the American scientific community over the 40 years since the Apollo program.
Common sense tells us that information regarding radiation effects on the Moon, if such information exists at all, should be available within NASA, but from the Committee’s report, it is clear that NASA does not have it either. This is an incredible omission because if the Apollo crews were indeed on the lunar surface, the agency definitely should have the relevant extra-vehicular radiation data. Where is this data? Especially significant would surely be those of the Apollo 15, 16 and 17 missions.
According to the mission reports, the six astronauts on these three missions spent from 18 to 20 hours each on the lunar surface during three exits (extravehicular activities, EVAs), under the direct radiation from the Sun and other sources, in their space suits – without any additional shielding. Moreover, some EVAs occurred at the time of elevated solar activity, potentially bringing excessive solar flares or particle events and resulting radiation to the crew. It is notable that more than 40 years later, there is no overt indication that the Apollo astronauts ever experienced any residual effects from radiation exposure.
In their late 70s and early 80s, the astronauts seemingly continue to lead normal lives. Neil Armstrong recently passed away at the respectable age of 82, due to causes apparently unrelated to radiation effects. This is a fantastic outcome of the Apollo program – provided it really was accomplished in 1969-72. Yet, strangely enough, there is little indication that NASA has ever paid any attention to this remarkable bio-medical fact which is a direct scientific outcome of the Apollo program. This is important self-evident information, and NASA should have started talking about this exciting finding: that no special medical and protective precautions against walking and working on the Moon are required.
On the contrary, NASA is silent on the matter and as shown above, has asked for help on a subject where the agency should be in full possession of the prime information and be the proud leader in this research. It is also noteworthy that in its mass media releases, NASA regularly reminds its audiences about Apollo 11, where astronauts were on the surface for only two hours, while it does not usually talk about circumstances of the Apollo 12 and 14 EVAs to such a degree, and is remarkably silent on Apollo missions 15 to 17 which would be crucial evidence in favour of harmless trips to the Moon.
Regarding radiation effects on humans, the Augustine Committee concludes: 'These radiation effects are insufficiently understood and remain a major physiological and engineering uncertainty in any human exploration program beyond low-Earth orbit.' (Augustine, 2009 p.100)
The Committee doesn't speak specifically about potential radiation problems on the lunar surface itself. Nor is the radiation danger during landing of crews on the Moon in the Apollo missions considered to any extent. Could it be that the decision not to mention Apollo was based not on the fact that the committee limited itself to studies carried out in LEO but precisely because there is no medical data on effects on human health beyond LEO? In fact, there is no connection or reference at all to the legendary Moon missions regarding the radiation problem in the quoted NASA reports (i.e. Arch. Study, 2005, and Augustine, 2009).