B Energy needed to stop the Earth's inner core ---and its effects?

[xpell]

This is not for any kind of homework ---the last time that I went to school was 30+ years ago. However, I am a curious person, I've been asked by other people who know that I love science and I need to calculate this:

As you will most possibly know, a misreading of this paper by the media caused kind of a "panic" about how the Earth's inner core had stopped or even reversed its rotation and its "apocalyptic" effects, etc. When asked, I immediately knew that it wasn't possible ---by energetic reasons, to start with. I more-or-less thought that stopping the core relative to the mantle would need immense amounts of energy "appeared out of the blue" whose application would be truly apocalyptic ---basically, destroying the Earth. Which was and is obviously impossible.

Well, now I've been challenged to "prove it" by the usual you-know-whos and I'd like to calculate how much energy would be actually needed to stop the inner core rotation relative to the mantle, and its effects on the Earth. However, as I said, last time I went to school was 30+ years ago... and that was high school. I initially thought that a simple calculation of the rotational kinetic energy needed to deccelerate the inner core to 0 would be enough, but I'm now realizing that it's possibly more complex than that ---and I'd still wouldn't know how to translate the results into "Earth destruction units".

So... please, is anybody here kind enough to help me?

 

[Baluncore]

The Earth's surface crust rotates relative to the stars, once each sidereal day, which is about 23 hours 56 minutes and 4 seconds. Everything inside the Earth rotates at very close to the Earth's crust rotation rate.

Because the Earth's outer core is liquid, the solid inner core can rotate very slightly faster or slower than the crust. That can be measured by changes in the phase of earthquake waves that travel through the inner core, both ways around the Earth.

To calculate the energy needed to stop that relative rotation, we need to know how much faster or slower the inner core is now rotating relative to the crust. If the relative rate has changed recently, then the relative rate will now be very low.

Work out the angular kinetic energy of the inner core rotation, using the moment of inertia of a solid sphere, assuming it was rotating exactly once each sidereal day. Then work out the actual energy of the inner core at the rate it is now rotating. The difference between those, is the energy needed to slow down, or to speed up, the inner core to the same rate as the Earth's crust.

 

[A.T.]

I more-or-less thought that stopping the core relative to the mantle would need immense amounts of energy

This seems to be a misconception. Reducing the difference in rotation speed between inner core and mantle can release energy. The total kinetic energy of those two can be lowered by syncing their rotation. This released energy can go into heat or kinetic energy of the liquid outer core.

 

[Hornbein]

The trouble lies with this phrase.

inner-core rotation has recently paused

If it had really gone to zero relative to the Sun that would indeed be cataclysmic. But it's clear that they mean that the core and mantle have in the past decade been rotating at the same angular velocity. Usually there is some small difference. In the past decade, not.

You can get the average density of the core, the average radius of the core, and estimate the angular momentum. Then translate that into trillions of Megatons or something like that. But I would guess that nevertheless your friends will keep on believing whatever they feel like believing, which will be whatever most of their friends believe. If you persist in deviation maybe they will no longer consider you a friend. So in situations like this I usually nod sagely and keep my mouth shut.

 

[A.T.]

If it had really gone to zero relative to the Sun that would indeed be cataclysmic.

This might be the misconception of the people "panicking" about it. But @xpell seems to have the misconception that stopping the relative rotation between inner core and mantle would require external energy input.

 

[Baluncore]

Any differential velocity represents a potential source of energy.

The inner core rotation rate, relative to the crust, is of the order of 0.5 degree per year.
Therefore, the period of rotation is; T ≈ 720 years.