Since it's not using radiation hardened ICs like they use in space probes, the Pi wouldn't be very resistant.
While I'm no expert, I think the biggest risk to the Pi would be that a bit in memory would be unexpectedly flipped by a stray particle, leading to anything from corrupted data to a program crash, or even the Pi freezing completely and requiring a power cycle.
The solution to this would depend on how reliable you want the Pi to be. If you'll be in the area then it might be enough to keep an eye on it, and switch it off and back on by hand if it has locked up.
If you want to leave it for long periods of time, you'll have to invent some kind of watchdog. A program that you run to monitor your data collecting program would be a good start. If it notices that the data collecting program has crashed, it can restart it. Then you just have to consider what happens if the monitoring program crashes.
Perhaps a second Pi, communicating via their serial ports. If one Pi stops responding (as it could if the monitoring program crashes), the other Pi would momentarily cut its power, forcing it to reboot and reload all the programs.
In this case, as long as one Pi is working, it can recover the other one. If you're unlucky enough to have both crash at the same time, you'll wish you had a third one in the loop, and so on.
All in all, it could be easier to just house the Pi in a very thick lead box. At least you (presumably) won't have to pay for all that weight to be launched into space!