Confirming the earth is spherical using reciprocal zenith angles

The Maine Surveyor measured the earth’s radius using reciprocal zenith angles.  See his videos for details:

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This method involves measuring the zenith angles between two points.  If the earth is flat the sum of the zenith angles will be 180°.  If the earth is convex the sum of the zenith angles will be more than 180°.  The amount over 180° and the distance between the two points can be used to calculate the radius of the earth.

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The difference in elevation does not affect the measurement as seen in this diagram.  The sum of the angles will still be over 180° regardless of the elevation.

Survey results

See Video Plumb Lines – Still Not Parallel for the procedure.  Below are data and images from the video.

Measurement #1

Date of Survey: 9 October, 2019

Coordinates (WGS 84):
401: 44-32-02.1338 N; 70-30-57.8225 W
402: 44-31-54.3033 N; 70-31-15.8431 W
Mean Slope Distance (point to point): 1529.878′ or 466.3068144 meters
Mean Slope Distance (Instrument to target): 1529.893′ or 466.3113864 meters
WGS84 Radius By Latitude: 20,891,285.7006 feet or 6,367,663.88154288 meters or 6,368 km.

Predicted Zenith Angle Divergence: 15.0″
Measured Zenith Angle Divergence: 17.1″

Measurement #2

Date of Survey: 10 October, 2019

Coordinates (WGS 84):
401: 44-32-02.1338 N; 70-30-57.8225 W; Ellipsoid Height: 128.6999m
402: 44-31-54.3033 N; 70-31-15.8431 W; Ellipsoid Height: 154.9975m

Mean Slope Distance (point to point): 1529.878′ or 466.3068144 meters
Mean Slope Distance (Instrument to target): 1529.849’or 466.2979752 meters
Radius By Latitude: 20,891,285.7006′
Predicted Zenith Angle Divergence: 15.0″
Measured Zenith Angle Divergence: 20.3″