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 the radius R = 6370 km

Correct result:

p =  2.6042 %

Solution:

h=350 km R=6370 km  α=arcsin(RR+h)=arcsin(63706370+350)1.2466 rad  (R+h)2=a2+R2  a=(R+h)2R2=(6370+350)263702=70 935 km2140.4439 km v=a cos(α)h=2140.4439 cos(1.2466)350=1592548331.7708 km S1=2π R v=2 3.1416 6370 331.770813278759.4734 km2 S2=4π R2=4 3.1416 63702509904363.782 km2 p=100 S1S2=100 13278759.4734509904363.782=12548=2.6042%



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