It could be stopped but it would require a majority fraction of the earths crust and shell to be thrown off into space.
The only source of such huge amounts of energy would probably require converting more mass to energy than is easily obtainable in a few millennia of continuous mining and filtering for nukes etc.
You could also do it by arranging for Earth to collide with other bodies whose angular momentum vector points opposite Earth's.
If would take a lot of time but this could actually be done without requiring a huge amount of energy. Find bodies in elongated orbits that bring them from the outer solar system to near Earth's orbit. Send something out to them when they are still far enough away that it only takes a nudge to alter their orbit into one that will hit Earth and give them an appropriate nudge.
To get to the targets without having to use a lot of energy use unstable orbits around Lagrange points [1].
Could you in theory counter the earths rotation by exerting force in the opposite direction? I always think about this every time I see one those videos of SpaceX where they test fire a rocket engine while it’s bolted down to the ground.
I don’t see why you can’t build scaled up versions of those engines, strategically place them around the globe so that when they’re fired up the force they create would counter the Earths rotation.
I’m really curious if the idea is feasible no matter how ridiculous it is.
Let's say you are less ambitious that stopping the rotation of the entire Earth. You cut a small ring out of the Earth, a very tiny one: 100 km wide and 100 km deep. The circumference of the Earth is 40000 km, so the volume of this ring is 0.4 billion km3. The Earth's crust density is about 2.5 tons/m3, so we got ourselves a ring of one billion billion tons, or one billion Gigatons. This ring does exactly one rotation in 24 hours so that's 40000 km in 24x3600 seconds, that's 462 m/s, let's call that 500 m/s.
Let's unroll this ring. It has become a gigantic spear that travels through space with 0.5 km/s and weighs 1 billion gigatons. Our task is to stop it. We put a gun at the tip of the spear, and fire shells. The recoil of the gun will slow the spear down. The heavier and the faster the shells, the greater the recoil. The product of the mass of the shells and their speed needs to be equal to the product of 0.5 km/s and 1 billion gigatons. If the shells you fire have relativistic speed, you need to multiply with an additional factor to account for that, but we can't fire relativistic shells, so we'll ignore that.
Now you have a problem: obviously even the US Air force can't find one billion billion tons of stuff to fire into space. So we need to use less mass and higher speed. But the energy goes up as the square of the speed, as every kid knows (m v-squared over two). But hey, we have nukes, we can afford, right? Let's go crazy.
We can use ion thrusters. They shoot ions at truly mind-bending speeds. Up to 100 km/s. Two hundred times higher than the speed of our cosmic spear. So, we'll need to only fire 5 million gigatons of ions into space.
How much energy do we need? m v-squared over 2, everything in the metric system: m is 5e18 kg, v is 2e5 m/s, we get 1e29 joules. One ton of TNT has about 4e9 joules, so our energy requirement is about 25e18 tons of TNT, or 25 billion gigatons of TNT. The largest nuclear bomb ever in possession of the US Air force had a yield of 15 megatons. So, we are talking about roughly speaking 15 trillion such bombs.
But that is to stop only a tiny, tiny bit of Earth. A tiny ring that has a volume of 0.4 billion km3. The whole Earth has a volume of 1000 billion km3. You would need many quadrillions of Castle Bravo bombs to do the job.
You were right that was really fun to read, you took my imagination on a wild ride! It really puts in perspective how big the Earth really is, thank you for dissecting my idea in such an informative way.
The problem is those engines exert force on their enclosure in one direction, and the same force on the air in the opposite direction. That air, i.e. wind, will eventually slow down through contact with the ground, returning the momentum to the Earth.
The only source of such huge amounts of energy would probably require converting more mass to energy than is easily obtainable in a few millennia of continuous mining and filtering for nukes etc.