Energy required to change a sphere's axis of rotation OR pole location

[Jonathan212]

There is a disaster movie about a global cataclysm that results in Kilimantzaro becoming the north pole or something. Maybe this is plausible in terms of plate tectonics. Or maybe not. But I've got another question, a purely mathematical one: if the Earth were a solid sphere, no plates and such, no magma, no liquid core, no density variation, just a mathematical uniform solid sphere, then how much energy would it require to shift its geographical north pole to another point on its surface 90 degrees away from its previous location OR change the place in the sky where the axis points without changing the pole location? So it's two questions. Make the sphere as big as the Earth and just as massive, and give it the same moment of inertia and period of rotation too.

 

[jbriggs444]

An Earth rotating on one axis has the same energy as an Earth rotating on another axis. It takes zero energy to change the axis.

You could do it the simple way: Spin down the Earth so that is stationary. Save the energy in a big battery somewhere. Spin up the Earth on a new axis. Use the energy you saved.

Or the somewhat clever way: Apply a torque at right angles to both the current and desired rotation axes. Keep applying the torque until precession changes the axis as desired. Since the torque is always at right angles to angular momentum, no energy is required.

But angular momentum has changed. And angular momentum is a conserved quantity. You'll have to dump it somewhere. That is harder to do. And cannot be done by muttering "plate tectonics".

 

[Jonathan212]

So you're suggesting changing the direction of the axis and changing the pole location is the same thing energywise?

 

[DrStupid]

But angular momentum has changed.

That applies to the second option but not to the first one. Changing the geographical north pole to another point of the surface without changing the orientation of the rotational axis requires neither energy nor angular momentum.

 

[Jonathan212]

How would you actually do it, with a spherical meteor and rockets attached to it, how would you keep the axis in the same direction and move the pole location, or vice versa?

 

[jbriggs444]

That applies to the second option but not to the first one. Changing the geographical north pole to another point of the surface without changing the orientation of the rotational axis requires neither energy nor angular momentum.

I think that is a third option -- move the crust around relative to the rotating spheroid so that the lump labelled Kilomanjaro is located at the pole.

Edit: Oh, I'm with you now. You want to leave the axis of rotation unchanged but re-orient the entire rigid assembly without changing its angular momentum while so doing. A torque-free precession.

 

[Jonathan212]

It's a solid sphere we said. A meteor.