For an observer at height h above the surface of the Earth,

i) What area, A, of the Earth's surface is visible?
ii) At what altitude, h, does the curvature of the Earth become apparent?

You may assume one can detect, with the human eye, an angle of one degree between the two ends of a line (i.e. two tangents at either end of the visible horizon, appear to intersect at an angle of one degree), that the average human field of view is 180°, also that the Earth is a sphere of radius 6378 km, or you may provide your own figures for the calculations.

(In reply to discussion by Charlie)

Charlie

Generally speaking, I liked your presentation.
However, there  are  two small points I would like to raise:

a)  You forgot to mention that r=rho.

b) Presenting so many digits implies accuracy, while the whole calculation is location dependant: rho is between 6356 km (at the poles) and 6378  km (equator), and since in the equation it appears squared the the error might be over 5%.

So why go over two decimal places after the decimal point?

Please comment.

Posted by Ady TZIDON on 2006-01-30 02:28:52