What is the Distance to the Horizon?

I've been living on the oceanfront for the last quarter of a century.
During that time, I have often stood on some cliff near the beach,
and wondered how far it was to the horizon.
Many a friend I have asked, and many a friend simply shrugged their shoulders.
Now that I've moved to a new place (Mikie's Fun House #4) on the edge of the Pacific
I got to wondering again...
Only this time, I asked Walter, and he asked Google, and the answer comes easy...

Here's the short answer:
It's about 17 miles from Mikie's Fun House to the horizon.

The long answer is that it depends on a few factors:

1. The height above sea level of the eyeball of the viewer.
In the case of my webcam, it is approximately 160 feet above sea level.
If your eyeball were only 2 meters (about 6 feet) above sea level,
you would be able to see about 5 kilometers (about 3.6) miles to the horizon.
As you multiply the height by 4, you double the distance to the horizon.

2. The distance to the center of the earth.
It may seem strange that we need to know the distance to the center of the earth
in order to find the distance to something that is within the range of our vision,
but that's Geometry for you!

In any case, the distance to the center of the earth is computed as
one half of the diameter of the earth
which is the circumference of the earth (24,901.55 miles) divided by Pi (3.14etc).
The Greek Eratosthenes calculated the circumference of the earth thousands of years ago.
For more on this, link here.
It is now taught in high school geometry.

Put all that together and you get about 3,965 miles to the center of the earth.

3. There are some other factors
but they can be ignored for most purposes.
For example, there is a problem with the fact that
light rays bend (refract) as they pass through water vapor.
And, of course, there's more water vapor the closer you are to the sea surface.
Another factor would be weather.
For example a fog bank could obscure the true horizon.

The Formula To Calculate The Distance To The Horizon

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