Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.

Correct result:

p =  0.25 %


 α=arcsin(RR+32)=1.4708327444=841621" a=(6378+32)263782=639.7 km v=acos(α)32=31.84 km p=2πRv4πR2100=31.8426378100=0.25% \ \\ \alpha = \arcsin( \dfrac{R}{R+32} ) = 1.4708327444 = 84^\circ 16'21" \ \\ a = \sqrt{ (6378+32)^2-6378^2 } = 639.7 \ km \ \\ v = a \cos(\alpha) - 32 = 31.84 \ km \ \\ p = \dfrac{2 \pi R \cdot v}{4 \pi R^2 }\cdot 100 = \dfrac{ 31.84}{2 \cdot 6378 } \cdot 100 = 0.25 \%

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