Correct, Earth is not a globe. It is an oblate spheroid.
If you travel half the circumference of a cirlc,e you've traveled the entire radius Thus, 200 miles, or ~0.83% of the circumference would be ~1.66% of the radius 3836 Miles * 1.66% = ~63 Miles
What? The radius of the earth is about 3,900 miles. The circumference is about 25,000 miles. 200 miles is 0.8% of the circumference and about 5% of the radius. You fail grade school math.
Therefore, the mountain you're looking at that is 200 miles away is, allegedly, 63 Miles DOWN the curve of the earth.
You need to revise your maths.
https://sites.math.washington.edu/~conroy/m120-general/horizon.pdf
Hypotenuse: R+height of plane "h" = 3,900 + 6.8 = 3,906.8 miles Leg 1: R or 3,900 miles Leg 2: L (the variable we need to solve for, the visible distance to the horizon with a smooth globe shaped earth from a plane 6.8 miles up)
3,906.8 = √(L2 + 3,9002 ) Square both sides gives us... 15263086.24 = (L2 + 3,9002 ) We square 3,900 to get... 15263086.24 = (L2 + 15210000) Subtracting 15210000 from both sides gives us... 53086.24 = L2 Taking the square root of 53086.24 gives us... L = 230.404513844672757 miles
What? The radius of the earth is about 3,900 miles. The circumference is about 25,000 miles. 200 miles is 0.8% of the circumference and about 5% of the radius.
Re-read. Traveling 200 miles along the circumference means you've traveled 0.8% of the circumference which means youve' traveled ~1.6% of the distance of the radius, being about 60 miles.
You fail grade school math.
You are an idiot. Read the paper I linked. It shows in simple geometric terms how to calculate the visible distance using the Pythagorean theorem.
I then solved it for you and got 230 miles.
You edited your comment and added the paper after i made mine, so I didn't see it.
What exactly are you trying to solve here? Are you trying to solve for the distance down the curve, that the hypothetical mountain that is 200 miles away, would be?
My point is that you wouldn't be able to see said mountain because it would be too far down the curve of the earth. According to globe earth ttheory.
(post is archived)