Very interesting science this.
New system could predict solar flares, give advance warning
Nuclear decay of any particular radioactive nuclei is supposed to be random and independent of everything else in the universe. The rate of nuclear decay is based on probability, and supposedly constant and universal for a particular material. There is a lot of science built on these assumptions.
Some scientists in the US have found a correlation between the rate of nuclear decay and the time of year, and solar activity. Their theory is that the flow of neutrinos from the sun arriving to earth (which varies depending no how close we are to the sun - we are closest during the northern hemisphere's winter) influences when radioactive atoms decay. Basically, neutrinos sometimes hit an unstable nucleus and make it pop - more neutrinos means more decay.
There are quite a few implication of this. If you had a spacecraft powered by nuclear decay, the power output would decline the farther it went from the sun. I believe Voyager has seen a decline in power output - some of which is expected for other reasons.
More solar activity would cause an increase in volcanic activity on earth - as the heat in the mantle is due to nuclear decay. Active solar periods might explain some of the more volcanic periods in earth history.
Carbon dating also becomes suspect. In normal times, this effect would cause 1% per year uncertainty in carbon dating. But we don't know if the sun was more or less active in the past. So its hard to put a number on that one.