# How tall would a tower at the South Pole have to be for the top to get year-around sunshine?

How tall would a tower at the South Pole have to be for the top to get year-around sunshine?

No doubt the height would vary each year since the Tropic of Cancer changes latitude slightly. Perhaps assume 23.5° N for calculation's sake.

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I have a flag suggesting that the question has zero physics content and that math.SE would be a better location for this question, and I tend to agree. The floor is open for discussion for a few hours. –  dmckee Aug 15 '11 at 14:49

## migrated from physics.stackexchange.comAug 16 '11 at 15:54

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assuming spherical earth with radius $R$ and axis tilt $\mu$, from geometry reasoning we get: $$\frac{R}{R+h}=\cos \mu \Rightarrow R\left( \frac{1}{\cos \mu} - 1 \right)=h$$
so your tower height should be $h=((1/\cos(23.5)-1)\cdot 6371 \text{ km} = 576.2 \text{ km}$; greetings to ISS