One of the most unexpectedly complicated things I have found during my research into determining the orbit of a meteor using Doppler measurements is the conversion between geographical coordinates and rectangular, or Cartesian coordinates, also called ECEF (Earth Centered Earth Fixed) coordinates:
At first sight it seems easy: The earth is a sphere, so it only need a few sines and cosines. But later, when you need more precision, you discover earth is not a sphere, it is an ellipsoid, so things start to become problematic.