How a 2,100-Year-Old Shoebox of Bronze Gears Computed Keplerian Lunar Orbits
Retrieved by Greek sponge divers in $1900$ at a depth of $45\text{ meters}$ off the island of Antikythera, the Antikythera Mechanism ($\sim 150\text{–}60\text{ BCE}$) is the most complex scientific instrument surviving from antiquity. Micro-focus X-ray tomography revealed $30$ surviving bronze gears with triangular teeth and over $3,500$ microscopic Greek characters (some just $1.2\text{ mm}$ tall) engraved across its plates.
Most astonishing is the k1/k2 pin-and-slot differential mounted on the $127\text{-tooth}$ gear e3: by offsetting the rotational axes of two meshed gears by $1.1\text{ mm}$, ancient Rhodian or Syracusan engineers mechanically reproduced the Moon's variable orbital velocity (faster at perigee, slower at apogee)—sixteen centuries before Johannes Kepler formulated the laws of elliptical planetary motion.