Tube Shadow Instrument Recovers Aristarchus Angle to 1.5° Precision

Researchers at Universidad Adolfo Ibáñez built a 1.2 m tube with a 5 cm aperture that casts a measurable shadow on the lunar disk during first and last quarter. Observations twice monthly over one year, timed to within 30 minutes of predicted quarter using lunar ephemerides, produced 12 usable data points. The measured angle averaged 89.85° ± 1.5°, directly convertible to the distance ratio via simple trigonometry without requiring absolute distances. The work exposes why Aristarchus underestimated the ratio by a factor of twenty: his naked-eye timing of quarter phase was off by roughly two hours, and he lacked any correction for the Moon's elliptical terminator. The modern device adds a single calibration step for atmospheric refraction and lunar libration, cutting systematic error from 20° to under 2°. Error propagation shows that timing uncertainty remains the dominant term; a 10-minute improvement in quarter-phase identification halves the final uncertainty. The experiment doubles as an undergraduate laboratory that links geometry, error analysis, and history of science. Students replicate the setup in under two hours and obtain ratios within 10 % of the modern value after four sessions. No comparable low-cost apparatus exists that lets non-specialists recover the same quantity Aristarchus attempted 2300 years ago. Next steps include automated timing via smartphone photometry of the terminator and crowdsourced observations to average out local weather. The authors predict that 50 independent tubes operated for one synodic year could reach 0.5° precision, sufficient to distinguish the true ratio from historical values at 3σ.