Case studies / solstice-2019

The 2019 December Solstice Shadow Measurements

21 Dec 2019

Prediction

On the December solstice the Sun is over the Tropic of Capricorn (23.44° S), so at solar noon the Sun's altitude = 90° − latitude − 23.44°. For an observer at about 44° N that is 22.56°. The flat model has no consistent formula here: with its own numbers (the Sun tens of km up, positioned over the Tropic of Capricorn on the solstice, thousands of km from a 44° N observer) the Sun should sit within a degree or so of the horizon.

The test

MCToon and collaborators measured the Sun's noon altitude from shadow angles on the 2019 December solstice: a 50 1/8 inch pole (1.274445 m) cast a 120 7/8 inch shadow (3.070225 m). His page carries a spreadsheet of other people's measurements as well.

The result

angle = arctan(1.274445 / 3.070225) = 22.54325° - matching the globe prediction for about 44° N to within 0.02°, and about 60× the altitude the flat model's own geometry gives for that latitude on the solstice.

The reaction

The flat model has no consistent prediction for seasonal Sun angles to lose here - which is why the claim 'the flat model explains the seasons' never comes with a worked number. Every solstice measurement since has matched the same formula.

Why it matters

The seasons are the strongest everyday evidence for the 23.4° axial tilt: the Sun's noon altitude shifts by about 47° between the solstices, in exactly the way the tilt predicts. A $0 test (a stick and a tape measure) that has been run thousands of times.

Sources

  1. MCToon - '2019 December solstice' (the pole, the shadow, the angle, the spreadsheet) [1]