What percentage

What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km.

Correct answer:

p =  2.6042 %

Step-by-step explanation:

h=350 km R=6370 km   sin α = R : ( R+h)  α=arcsin(R+hR)=arcsin(6370+3506370)1.2466 rad β=α  °=α π180   °=1.2466 π180   °=71.42665  °  (R+h)2 = a2 + R2  a=(R+h)2R2=(6370+350)263702=70 935 km2140.4439 km  cos α = (v+h) : a  v=a cosαh=2140.4439 cos1.2466350=4815925331.7708 km  S1=2π R v=2 3.1416 6370 331.770813278759.4735 km2 S2=4π R2=4 3.1416 63702509904363.7818 km2  p=100 S2S1=100 4203961745519252296430=48125%=2.6042%

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