Tuesday, October 04, 2011

How low can you see that the earth is curved

At how low an altitude does the earth look like a disk, in other words, from how low does a line from the horizon to your eye trace out the surface of a cone (with angle a shown from the centre) ?

Surprisingly low. The depression of the horizon below level is noticable from an altitude as low as 218m. (Lysterfield Lake trig point 37°56'31" S 145°16'06" E, Elevation 218m)

View looking south east, the faintly visible Strezleki ranges are level with the line

View looking north west, the horizon is below the string

Looking east, the horizon is below the two tape markers

Looking west, the horizon is just below the two tape markers

The average depression was 7mm at a distance of 147cm

a = sin (a) for small a

a = 0.7/147 = 0.00476

r = 2h/a^2

r = 2 *218/(0.00476^2)

r = 19,000 km

Compared with the actual value of 6,371 km

Earth from space, image
Small angle formula

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Blogger MariaD said...

Wait, theoretically, isn't the answer "any height"? I am not sure I understand the statement of the problem. In practice, you will see grass and such, rather than the horizon, almost anywhere. However, when we used to go swimming in the Black Sea during very quiet mornings with no wind and no waves (rare conditions - once every few years), you could submerge into the water almost up to your eyeballs and still see all the way to the horizon. Your blog post reminded me I loved doing it. The water was very shiny and it was such a weird experience overall.

Tuesday, October 04, 2011 9:19:00 PM  

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