If the Earth is flat, why is the shadow length I measured at a latitude of 40 degrees 23 arcminutes at 1:40 PM on 12/8/2018 53 inches instead of the 33 inches that the flat earth model predicts? I used a piece of plywood 22 11/16 inches long. By measuring the length of a shadow cast by a stick, we can take the arctangent of the length of the stick divided by the length of the shadow to determine the sun's angular elevation above the horizon. This formula can also be used to determine the predicted shadow length for each model by dividing the length of the stick by the tangent of the model's predicted angular elevation. By dividing the height of the sun by the horizontal distance to it, the arctangent of the result can be used to determine the flat earth model's predicted angular elevation of the sun. I have taken the value for the sun's height from the wiki (3000 mi/4800 km). The sun's angular altitude on a round earth can be found by finding the arcsine of the addition of the product of the sine of the observer's latitude and the sine of the sun's declination to the product of the cosine of the observer's latitude, the cosine of the declination of the sun, and the cosine of the hour angle. I have factored in the declination of the sun and the obliquity of the ecliptic to ensure the most accurate predictions for both models. The flat earth model predicts an angle of 37.578 degrees. The round earth model predicts an angle of 23.210 degrees. Why does the flat earth model have an error of 32.1% from reality? How does the flat earth model explain the deviation of the sun's angular elevation from its predictions? θ
sr is the round earth prediction and θ
sf is the flat earth prediction in the following desmos link.
https://www.desmos.com/calculator/sepoxbrqfz