Derive every equation from scratch, starting at F = ma - #2

The README states the physics; it never derives it. This is the long
version, written for someone who has met "speed = distance / time" and not
much else, and it builds every formula the app evaluates from things you
can check on a playground.

Sixteen parts, each answering one question and ending at the equation the
code actually runs: orbits from balancing a pull against a corner, the
horizon from escape speed (with a warning that the easy derivation is a
fluke that happens to give the right number), light bending from the
equivalence principle, the photon sphere and the 2.6 r_s shadow from the
maximum of the photon potential, the ISCO and the Paczynski-Wiita shortcut,
the Shakura-Sunyaev profile, Doppler and beaming, tides and the M^(-2/3)
scaling that decides whether a star is shredded outside the horizon at all,
the tidal energy spread and why the debris splits in half, Peters and the
chirp, Flamm's paraboloid derived from Pythagoras on a stretched sheet, and
the Eddington limit behind the outflow.

Three of the eight diagrams are computed rather than drawn. The light rays
in the impact-parameter figure are real null geodesics integrated with the
same equation the shader uses, so the loop around the photon sphere is the
actual trajectory. The funnel is plotted from z(r) = 2 sqrt(rs (r - rs)),
which is why it flattens far out instead of being a cone. The wave figure
is a genuine two-armed spiral.

Also lists what the app cheats on, in a table, next to what would fix each
one.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>