Details regarding the difference between exploding nuclear power stations and radiation in space is in the revised Moon Hoax book from 4th October 2018.
The first US satellite into space was called Explorer 1. It had a simple Geiger counter on board to detect radiation in space. As it was the very first of its kind, nobody knew how many counts of radiation hits would be recorded and so didn't know how to calibrate the equipment. The leading scientist of the time expected around 10-100 counts a minute. The Geiger counter was set for that. After achieving orbit, the hits were higher and went off scale. It could mean 101 hits per minute or 1,000,001.
The press took the high figure and announced 'Space is filled with deadly radiation.'
This misconception has lasted in the media ever since. But if one delved into this point in much more detail, then the truth is revealed. Even today announcements are still often made on deadly radiation, but figures and more detail is required to know what is meant by it rather than one sentence representing volumes of figures.
The new Orion spacecraft is designed for much longer and further missions than the moon, so its design had to include extra shielding against radiation. A few days to the moon and back was relatively short.
If a comparison is required between the Van Allen Belts and an exploding nuclear power station; a wine gum compared to a bottle of neat whisky.
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It would take an entire book to explain and give the full answer as to what real dangers there are in this field. Here is one example... Space Radiation and Astronaut Safety