Trying to prove the earth is flat

Geometry Level 1

In 1838, Samuel Birley Rowbotham conducted observations leading him to conclude the earth was flat. His idea was the following: If light goes straight and I'm standing at AA with my friend, there must be a point BB where I can't see him.

Assuming light does not bend because of atmospheric refraction, which of these is closest to the minimum arc length of AB\stackrel\frown{AB} that would prevent Samuel from seeing his friend? Assume they are both 1.81.8 meters tall and the radius of the earth is 6,371,009 m.6,371,009\text{ m}.

Note: Though the earth is (of course) not flat, Samuel was able to see his friend at a farther distance than he was supposed to. This is due to atmospheric refraction, i.e. the non-homogeneous density of air creating a slight deviation of light. Without knowing this effect, a newspaper editor performed in 1896 the same experiment and concluded the earth was concavely curved.

×

Problem Loading...

Note Loading...

Set Loading...