How did they know during Apollo how much radiation shielding was needed for their spacecrafts and their space suits?
Because they had been studying it continuously for nearly a decade beginning with Explorer I.
They are not even sure today how much shielding they will need on the return to the moon.
Of course they are. They just don't know yet how to reconcile it with other mission requirements and constraints. If I know how far it is to Las Vegas, but I don't know how exactly I'm going to get there, I can still tell everyone that "my getting to Las Vegas will be a problem," without intending that to mean I don't know what the goal is.
But on the moon which is radioactive...
That's news to astrophysicists.
...they were exposed to cosmic rays, solar radiation, x-rays, gamma rays, beta rays, protons, neutrons for days.
I hate to alarm you, but you're being exposed to those exact same hazards right now, as well as dozens of known carcinogens.
Why didn't any of the Apollo astranouts get sick from the radiation?
Because there wasn't as much radiation as conspiracy theorists say. A better question is why the world's astrophysicists don't seem surprised at the astronauts' general good health.
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