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If Earth were smaller than it is, but the Alexandria-to-Syene distance were the same, would the shadow of the vertical pillar in Alexandria be longer or shorter at noon during the summer solstice?

Stars and Galaxies

9th Edition

ISBN:9781305120785

Author:Michael A. Seeds, Dana Backman

Publisher:Michael A. Seeds, Dana Backman

Chapter4: Origins Of Modern Astronomy

Section: Chapter Questions

Problem 10RQ

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If Earth were smaller than it is, but the Alexandria-to-Syene distance were the same, would the shadow of the vertical pillar in Alexandria be longer or shorter at noon during the summer solstice?

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The shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 Earth’s radius. Is there a geometric connection between these two 1-to-8 ratios?
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