How tall would a tower at the South Pole have to be for the top to get year-around sunshine?
Solution 1:
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
for ellipsoid-Earth the height is bit different, but the above is a fine estimate