Observations/Perspective: Difference between revisions
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====Derive the radius based on the angular resolution limit==== |
====Derive the radius based on the angular resolution limit==== |
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To derive the radius value of 3,959 miles based on the angular resolution limit of 0.0316° and the optic drop over a distance of 12 feet across 3 miles (using a drop rate of 8 inches per mile squared), we can calculate it as follows:<br> |
To derive the radius value of 3,959 miles based on the angular resolution limit of 0.0316° and the optic drop over a distance of 12 feet across 3 miles (using a drop rate of 8 inches per mile squared), we can calculate it as follows:<br> |
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Calculate the drop rate for the given drop over distance: For 12 feet over 3 miles, the drop rate is 8 inches per mile squared, or 8/12 feet per mile squared, which is approximately 0.666 feet per mile squared. |
Calculate the drop rate for the given drop over distance: For 12 feet over 3 miles, the drop rate is 8 inches per mile squared, or 8/12 feet per mile squared, which is approximately 0.666 feet per mile squared. <ref name=DecodingCurvature></ref> |
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Using the angular resolution limit of 0.0316° (or 0.000552 radians) for the Raleigh criterion, we can calculate the radius value by equating the angular resolution to the tangent of the arc angle: Arc angle = 0.0316° = 0.000552 radians tan(0.000552) = R / 3 miles, Solving for R, we get R ≈ 3,959 miles. |
Using the angular resolution limit of 0.0316° (or 0.000552 radians) for the Raleigh criterion, we can calculate the radius value by equating the angular resolution to the tangent of the arc angle: Arc angle = 0.0316° = 0.000552 radians tan(0.000552) = R / 3 miles, Solving for R, we get R ≈ 3,959 miles. |
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<references> |
<references> |
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<ref name="distancejudgment">[[:File:A distance judgment function based on space perception mechanisms revisiting gilinskys 1951 equation.pdf|PDF:A distance judgment function based on space perception mechanisms]]</ref> |
<ref name="distancejudgment">[[:File:A distance judgment function based on space perception mechanisms revisiting gilinskys 1951 equation.pdf|PDF:A distance judgment function based on space perception mechanisms]]</ref> |
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<ref name="DecodingCurvature">[https://youtu.be/VOwP_RPyV8A YouTube: Decoding Earth's Curvature / Mathematics]</ref> |
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</references> |
</references> |
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