| MadSci Network: Physics |
Donna - thank you for a very interesting question! I had an interesting time trying to answer it.
A couple of books I found helpful were:
The 'geometric horizon' is the horizon due to the curvature of the surface of the Earth. You can figure out what it is with some simple trigonometry (see either of the books above); an approximation which is pretty good is:
(distance from you to horizon) = 3.53 x (square root of your height in m)
The distance between horizons is twice the above number, so if you are 5'6" (168 cm) tall and at sea level, this means that the distance between geometric horizons is 9.2km. For a 6'6" tall person, the geometric horizon distance is 10.0km.
The optical horizon distance is larger than the geometric one, because the atmosphere bends light around the earth annd allows you to see further. The exact amount of bending depends on a lot of things, such as your altitude, the composition of the atmosphere (which varies with location, weather, etc.). There's no simple formula, but this page (about `over-the-horizon' radar - also has some good diagrams showing the different horizons) says that the optical horizon is about 8% greater than the geometric one. That would mean the 168-cm-tall person's horizon is really about 9.9km. So your estimate was pretty good.
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