But I thought the Sun moved unpredictably in FE.
No no no, this is entirely false. The sun moves in a circle approximately over the equator (i.e. the circle centered at the north pole with radius half that of the earth), but whose radius varies seasonally, so during the summer it circles over the tropic of cancer and in winter over the tropic of capricorn. The motion is entirely predictable, but even if it weren't, it would be irrelevent to the experiment I described, as the whole point is that you are taking measurements at the same time at two different locations.