If I were freely floating in space within our solar system, and nothing could kill me but radiation from the Sun, what would be the safe distance? I know that Earth´s distance from the Sun would be lethal and I read somewhere that Mars isn´t very homey when it comes to radiation. I need to know what distance a body would have to be from the Sun as to harbor human life with no radiation problems. Thanks in advance.
tl;dr, It depends. On a lot of things. Mostly on how long you wanna be alive. But this is an area of modern research, and one we are looking for an answer to currently.
Like mentioned in one of the comments, GCR (galactic cosmic rays) are a high threat, but as you responded, you don’t want to incorporate these into this thought experiment. While I should mention not considering these is a significant loss of information if you want to really know what would physically happen, let’s consider some variables.
First, solar cycles.
Solar cycles play an interesting role in radiation in the interplanetary medium. On one hand solar wind carries charged particles that could potentially be life threatening. On the other hand, at solar maximum these charged ‘winds’ actually deflect (to a certain extent) galactic cosmic rays, making it (if considering GCR) cumulatively safer during solar maximum. But in this thought experiment, we are not considering these GCR, so you’re best bet would be timing your venture solar minimum (here is one instance where this thought experiment diverges from reality). A solar cycle lasts 11 years, so you would have to time things accordingly.
Next to consider is the fact that GCR come from distant, distant objects and carry the potential to kill you, so it would be reasonable to suggest that for an alien around another sun, our sun would contribute to the GCR and thus in theory, you would never be totally safe no matter how far away from the sun. There would always be a chance of receiving a certain amount of radiation, and with longer exposure in time, eventually it would be statistically improbable that you would survive indefinitely. If not if radiation poisoning, then at least of cancer.
Now, this is all assuming that it’s just you, with no other forms of protection. Some of the deadliest radiation form the sun is charged particles, and so magnetic fields do wonders for preventing some of the most high energy (and thus most deadly) particles from reaching you. So if you have a strong magnetic field in your local vicinity (say the Earth, or a gas giant with a dynamo effect producing some magnetic fields) it will do a lot to keep you alive. The magnetic influences of some of the bodies are very, very large in comparison to the size of these objects so you could potentially benefit from them from quite a distance away. Similarly, if you’re unlucky, they can be potentially harmful to you, as certain kinds of radiation get trapped in the magnetosphere of these objects (which again can be quite large).
So let’s assume you’re far away from these where their effects are negligible (again, may not be the best approximation). One thing that is unrelated to charged radiation from the sun is just the high-frequency light it emits. The sun is a G star so it peaks in the visible light, but a significant amount of light in its black body curve is produced in the UV and higher, which the Earths atmosphere blocks largely via water vapor. With no protection like this, the UV light and higher frequencies would eventually give you cancer or kill you from radiation poisoning.
So what then is the answer? It’s hard to say; the interplanetary medium is a harsh place. It’s these questions that modern space explorers are grappling with, and have yet to find satisfying answers to. Because of solar winds and electromagnetic radiation, you’re question really boils down to time scale. How long do you want to be free of radiation sickness and cancer. And even then it’s not a sure thing, it’s a matter of chance, and the probabilities of that are entirely situationally dependent, with the difficulty to give any kind of answer increasing exponentially with the time scales you’d like to be alive.
Moral of the story? Find a strong magnetic field to help you out and you’ll be off to a much better start.