Big Earth

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.

Final 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)2−R2​=(6370+350)2−63702​=70 935​ km≐2140.4439 km  cos α = (v+h) : a  v=a⋅ cosα−h=2140.4439⋅ cos1.2466−350=4815925​≐331.7708 km  S1​=2π⋅ R⋅ v=2⋅ 3.1416⋅ 6370⋅ 331.7708≐13278759.4735 km2 S2​=4π⋅ R2=4⋅ 3.1416⋅ 63702≐509904363.7818 km2  p=100⋅ S2​S1​​=100⋅ 509904363.781813278759.4735​=2.6042%

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You need to know the following knowledge to solve this word math problem:

arithmeticsolid geometryplanimetricsbasic operations and conceptsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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