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?
$\begingroup$
$\endgroup$
1
-
$\begingroup$ The poles are points; the equator is a circle. You can rotate about 2 perpendicular axes to achieve two different final configurations. You'll also need to read up on "precession of a gyroscope". Further, there's a big difference between rotating the axis and changing the axis of rotation. Which do you want? $\endgroup$– Carl WitthoftFeb 9, 2021 at 15:05
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
3
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.
-
2$\begingroup$ Note that Earth's gravitational binding energy is $2.49 \times 10^{32}\,\mathrm J$, so you need to be careful how you twist it. ;) $\endgroup$– PM 2RingFeb 9, 2021 at 16:04
-
$\begingroup$ @PM2Ring Guess we're better off building Earth Engines to stop the rotation over a couple hundred years, then rotate the other axis, then start up rotation again $\endgroup$ Feb 9, 2021 at 18:28
-
$\begingroup$ precarious situation - more than expected , I am after buying some land in Antarctica from this fellow and trying to optimize my return on investment🙄🤔 $\endgroup$ Feb 10, 2021 at 3:36