When people talk of science and technical things, like the Van Allen belt or global warming or evolution or whatever, I leave plenty of space for doubt but often defer to experts who have studied and supposed worldwide concensus. "But that's appeal to authority, it's worthless you idiot!" they tell me

But I think we all have to live our lives depending on experts to a large extent, we can't study everything

I skimmed some moon landing hoax articles because conspirary theories are fun and the issue with the Van Allen belt is, I think, that the radiation is so stroong that you can't send humans through it and have them survive. I'm not a scientist or physicist so I couldn't hope to form an educated opinion on it. I can however conclude that the Chinese and Russians or any other country hasn't challenged the US moon landing and if I'm not mistaken the Chinese are planning to put a man on the moon soon, so...

One thing I always found curious is how NASA etc say they can't do it now because much of the research done back then has been lost

I know the project was extremely expensive and employed an insane amount of people.