When you stand on the hill, the horizon you see
is farther away and so looks higher. What is
happening can be illustrated as follows: draw a
circle (or trace a drinking glass or whatever).
This is the earth. Now, put a little stick
standing on the circle (you). Use a ruler and find
the farthest point away from you that the straight
edge touches the circle. This is as far as you can
see. Mark it. Now, draw a hill, which is bigger
than you, and stand on top of it, and repeat the
process. You will notice that you can see
farther.When standing on the shore, you can
only see ground(or water) at the same altitude
as you are that is about six miles away due to the
curvature of the earth. If you're higher up (or
just taller), you see farther.
Don't have a really good answer for this other
than to say that I think it is difficult to tell
if we are really looking horizontally; we don't
have a good sensor in our head that tells us what
the angle is between where we are looking and some
reference such as the zenith or a the line
tangent to an Earth radius or something. Another
issue is that sometimes when looking out to the
horizon it is difficult to tell where the ocean
ends and the sky begins but it sounds like this
may not be a concern for you.
You should be able to make a simple instrument
to measure the angle between the horizon and a
line that points towards the Earth's center. You
can take a protractor, drill a hole in the
"center," tie a string through the hole,
and tie a weight on the other end of the string.
If you sight along the edge of the protractor
towards the horizon, someone else can see what the
angle is between the string and the horizon.
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