Gravity Math
Notes: (1) Gravitational_Constant is 6.6695 if we measure masses in kilos,
distances in kilometers and time slices in seconds. (2) the algorithm is an
approximate solution to the n body problem, which has no exact solution.
We cheat by first netting accelerations, then finding out how far objects
move ***while assuming that the accelerations don't change!!!*** This is a
false assumption, because the moment objects move even a little bit, all of
the netted accelerations are changed a little bit — accelerations follow
from proximities and proximities are changed by accelerations: an orbital
mechanical Catch-22). We get away with this (approximately) as long as
objects don't move significantly during the time slice we pick — we get
caught when objects get close together: small distances –> big
accelerations –> significant movement during the given time slice. (3)
Don't ask me why there is no exact solution in (2). That answer would
entail the practice of math I'm not licensed for, and I don't want to have
the CompuServ Thought Police catch me. (4) I have this coded somewhere —
an early Amiga effort developed under Workbench 1.0 using Manx 3.2. If I
find it, I'll dust it off and post it, though I wouldn't be suprised if a
spiffy version of this toy aready lurks in the libraries somewhere.