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A Mathematical Nature Walk by John Adam

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imagesIn the sky

 

Q.39: How far away is the horizon (neglecting refraction)?

This is, of course, question 14, “reloaded,” and it leads naturally to question 40.

From figure 39.1, we can approximate the distance x from an observer at O, a height h above sea level to the horizon at T. This neglects the effect of atmospheric refraction, of course, but since that increases the effective “distance” by about 9% (see the article by French) this result represents a lower bound. Also ignored is the limiting effect of haze. By Pythagoras' theorem, if the distance OT= x, then

since h << R. A useful rule of thumb version is easily established if we suppose ...

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