this is the second attempt at this pointless hobby project. it seems
   rather harder than the first.
   I found it possible that most calculation ease could likely be found by
   modeling magnets as volumes of point magnet charges. the force between
   two charges is mu * q1 * q2 / (4 pi r^2).
   I recall it seemed to make the most sense to start with very tiny
   magnets, but to confirm that it would seem to be good to form a
   relation between the gravitational force on a magnet and the magnetic
   force. will a neodymium magnet accelerate more rapidly in a magnetic
   field if it is small, or large? why?
   last time this seemed obvious, which is slightly worrying.