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In 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 that *h* is measured in feet (as is frequently the case) and *R* is expressed in miles (and more accurately than above, we use *R* = 3960 miles here), then