Energy required to tilt Earth’s axis by 90 degrees? How much energy would be required to tilt Earth’s rotation axis in such a way that what is now poles would be where to equators are relative to Sun and vice versa?
 A: Very rough calculation ignoring the orbital angular momentum of the Earth around the sun:
Assuming you are preserving the magnitude $L$ of the spin angular momentum, a $\pi/2$ flip of the earth will result in an angular momentum change of $\sqrt{2} L$. The magnitude of the torque necessary to achieve this is time $\Delta t$ is $$\Delta \tau = \frac{\sqrt{2} L}{\Delta t}.$$ The work necessary is $$\Delta W = \Delta \tau \Delta \theta = \frac{\sqrt{2} L}{\Delta t} \cdot \frac{\pi}{2} = \frac{L\pi}{\sqrt{2}\Delta t}. $$ Further assuming the earth is a perfect sphere rotating around an axis connecting its poles, $L \approx 7 \times 10^{33} \, \mathrm{kg m/s}$ (see this). This means the work done as a function of the total time taken to flip the earth is
$$\Delta W = \frac{1.55 \times 10^{34}}{\Delta t}.$$ You can put whatever value of $\Delta t$ in there; in particular assume you can rotate the earth in $1$ second. In that case,
$$\Delta W = 1.55 \times 10^{34} \, \mathrm{J},$$ which is a lot of energy.
