Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface.

Correct result:

h =  4252 km

Solution:

R=6378 km S1=4π⋅ R2=4⋅ 3.1416⋅ 63782≐511185932.5225 km2 S=1/5⋅ S1=1/5⋅ 511185932.5225≐102237186.5045 km2 S=2πRv v=S/(2π⋅ R)=102237186.5045/(2⋅ 3.1416⋅ 6378)=127565=2551.2 y=R−v=6378−2551.2=191345=3826.8 x=R2−y2=63782−3826.82=255125=5102.4 k=\cotanα=x/y=(h+v)/x x/y=(h+v)/x h+v=x2/y h=x2/y−v=5102.42/3826.8−2551.2=4252 km

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