Measure Earth with two or three shadows
Measure upright height and signed noon shadow angles at separated sites. Two sites estimate circumference; a third non-symmetric site tests competing angle curves.
What you need
- Vertical rods with plumb-line checks
- Level measuring surface, ruler and clock
- Site coordinates and northward meridian distances
Collect the readings
- Choose sites near one meridian and use the same date. Record each site’s local solar noon rather than assuming every clock reads 12:00. Avoid direct viewing of the Sun; measure the ground shadow.
- Measure the upright from the surface to its shadow-casting tip. Measure the shortest noon shadow repeatedly and retain its direction. Calculate angle magnitude atan(shadow length / upright height); use a positive zenith angle when the Sun is south of zenith.
- For two sites, enter the meridian baseline and angle difference in the circumference tool. Estimate distance uncertainty and the uncertainty of each angle separately.
- For three sites, keep one common distance origin and enter each signed angle. Fit both models to the same readings. A non-symmetric third location is more informative than a perfectly symmetric set.
Compare the predictions
Parallel-ray sphere: zenith angle changes linearly with meridian distance.
One nearby Sun over a plane: angles follow arctan((distance − source position)/source height).
Compare residuals with reading uncertainty; a shared alignment or timing bias must be corrected separately.
Open the related calculation →