66 Chapter 1 Is Earth the Center ofthe Universe?
What Is the Approximate Distance to the Horizon?
If Earth was flat and the air was perfectly clear, you could see for an unlimited distance.
Therefore, the fact that there is a horizon—that is, an apparent line that separates Earth
from the sky—is evidence that Earth is round.
So approximately how far is it to the horizon?
If we let r represent the radius of Earth and let h represent the height of the observers
viewpoint, then the relationship to the desired distance L will be as follows, according to the
Pythagorean theorem:
rh
rL
+
()
=+
2
22
Therefore,
Lr
hr
rh h
=+
()
=+
2
2
2
2
Since the radius of Earth (r) is approximately 6,378 km (which is 3,963 miles), if we
assume that the height of a normal persons eye (h) is 0.0015 km (equal to 5 feet), then
we can calculate L as approximately 4.4 km (2.75 miles). In other words, if we gaze at the
ocean from the beach, we will only be able to see the oceans surface out to a little more
than 4.4 km (2.75 miles).
Incidentally, even when looking out of the window of a plane flying at an altitude of
approximately 10 km (33,000 feet), the distance to the horizon is approximately 360 km
(224 miles). Since this is no more than the distance from New York City to Washington, DC,
we can’t see very far even at that great height.
L
h
r
This is the horizon.
Earth
Distance to the horizon

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