Pilot

How high is the airplane's pilot to see 0.001 of Earth's surface?

Correct result:

h =  12.7816 km

Solution:

R=6378 km S1=4π⋅ R2=4⋅ 3.1416⋅ 63782≐511185932.522 km2 S=0.001⋅ S1=0.001⋅ 511185932.522≐511185.9325 km2  S=2πRv v=S/(2π⋅ R)=511185.9325/(2⋅ 3.1416⋅ 6378)=3189250=12.756 km y=R−v=6378−12.756=6365.244 km x=R2−y2=63782−6365.2442≐403.1784 km  x/y=(h+v)/x h+v=x2/y h=x2/y−v=403.17842/6365.244−12.756=6378499=12.7816 km

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