Re: circular earth...

Posted by Dale on Mar 28, 2002 at 13:58
(204.212.222.21)

Re: circular earth... (dogrock)

The Romans placed sticks in a canal all two feet above the water line and observed the curvature of the earth by looking along the sticks.

Ok, we go to a really calm lake and put a stick in the water cutting it off 2 feet above the water line. Now we row 1 mile out in the lake and float another stick with a mark 2 feet above the water line. Finally we row another mile and place a third stick. Now we sight from the third stick past the second stick to the first 2 miles away. How far off is the mark on the second stick?

5280*12=sqrt(R^2-(R-x)^2) where R is the radius of the earth in inches and x=the height of the mark on the center stick above a straight line in inches.

63360=sqrt(2.5e8^2-(2.5e8^2-5e8x+x^2))
63360=sqrt((6.25e16-(6.25e16-5e8x+x^2))
63360=sqrt(5e8x-x^2)
4e9=5e8x-x^2
x^2-5e8x+4e9=0
x=2*4e9/(5e8+sqrt(25e16-16e9))
x=8e9/(5e8+5e8)
x=8 inches

You really think your eyes are that good? Instead of having to sight across sticks 2 miles apart, let’s move them a little closer. How about a football field? The height change you have to see is less than Ľ inch. Somehow I don’t think you can see the curvature of the earth and not attribute it to a mismeasurement.