Looked through the Jovian section of Rimward then followed up with some Wikipedia.
Now, I'm no math/physics expert but the numbers offered up by Wikipedia sounds like any spacecraft that would try to aerobrake in the Jovian atmosphere would be cooked by the radiation even before they touch the air.
So brings up even more questions:
1. How much shielding could a spacecraft practically carry to turn the aerobraking operation into something less risky.
1b. What would be ussed for shielding? Rock? Water? etc?
1c. Can a spacecraft generate its own magnetic field to deflect the radiation?
2. What is a minimum size/mass for such a spacecraft to carry all the above equipment? Assume it has meat crewmen.
3. Is there material that would be unaffected by the radiation? Inert materials?
3a. Like stay a container full of cortical stacks?
3b. Why did I ask question 3a? Players in my campaign please ignore it :-O