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Outside of Earth, are there any objects (planets, moons, asteroids) in our solar system that are naturally shielded from the radiation of solar flares and coronal mass ejections (CMEs)?
Asked another way, is the radiation exposure discussed in Martian exploration a common concern for all other planets/objects?
There are two primary things that protect something from ionizing radiation with a source external to a planetary body: a magnetosphere for charged particles and an atmosphere for both charged particles and electromagnetic radiation. Both have limitations to the amount of protection they can provide and over what energies they can shield, which isn't a simple set of values one can just present. However, a generic statement can be made.
A magnetosphere is great for shielding against external, energetic particles, but only to a certain point. When the gyroradius of the incident particle starts to exceed the relevant scale size of the magnetosphere, then shielding becomes ineffective. So without an atmosphere, a magnetosphere only protects the surface of a planetary body up to the energies corresponding to gyroradii of the magnetospheric radius, give or take.
There is a catch, however. So the Jovian magnetosphere is great for protecting the surface from external sources of energetic, charged particles. However, it has incredibly energetic and intense radiation belts. So if we could transport to the surface of a planet with a huge magnetic moment like Jupiter's without going through the radiation belts, then great. If we have to fly through the radiation belts of such a planet, however, we will need a lot of shielding, which means a lot of mass.
For reference, there is a detailed review of space weather effects on humans in space by Townsend [2021].
Now an atmosphere is more indiscriminate as it can reduce ionizing radiation of both charged particles and electromagnetic radiation. The amount of attenuation depends upon the type of incident radiation and the composition and scale height of the atmosphere.
Below I list places with atmospheres, though the thickness/scale heights vary by a great amount so most aren't really viable for protecting someone on the surface (among other threats one would face on the "surface" of any given body).
Planetary bodies with atmospheres
Moons with atmospheres
Technically, Earth's moon has an atmosphere as well but I wouldn't rely on it for protection.
Planetary bodies with intrinsic magnetospheres
Planetary bodies with induced or small, localized magnetospheres
