How fast would you have to spin Ceres to rip itself apart?

[Knaight]

You are converting energy (which come from an outside source, say chemical rockets or electricity) to angular momentum thus changing the angular momentum of the entire system.

You cannot convert energy to angular momentum. What you can do is convert energy of some sort to kinetic energy (in this case kinetic energy of rotation) while conserving momentum of the overall system.

What that system is varies - if you're converting the energy by pushing on the asteroid from the outside with a rocket that system is the asteroid, the rocket, and the rocket's reaction mass. The asteroid on its own can have momentum (including angular momentum) changes just fine, which are pulled from the change in momentum of whatever plume the rocket is throwing behind it.

In the context of a drum inside the asteroid, the drum+asteroid is a closed system. Rotating one one way will rotate the other the other, in such a way as to conserve angular momentum.

[monomer]

No, you cannot do that. Not by flying some kind of fuel or other energy storage to the asteroid and using it for some kind of motor. Angular momentum has to come from the outside in the form of other angular momentum, or be in someway removed from the asteroid to spin it up in the opposite direction. It's a fundamental conservation law (for this kind of system). There is no such thing as an energy to angular momentum conversion.

You could spin up the asteroid by flying a rocket into it at an angle, thus transferring that momentum to the asteroid. Or by building some kind of giant cannon on the asteroid and firing something off at an angle at escape velocity, thus gaining angular momentum by removing the momentum of the projectile.

Torque causes changes in angular momentum, and whether that torque is applied to something buried inside the system or on the surface, it is an external force, and the system is no longer closed so conservation of angular momentum doesn't apply until the external force acting on the system is removed.

[Knaight]

Torque causes changes in angular momentum, and whether that torque is applied to something buried inside the system or on the surface, it is an external force, and the system is no longer closed so conservation of angular momentum doesn't apply until the external force acting on the system is removed.

It's not just about what it's applied to though, but also what it's applied from. If the thing it's applied from is inside the system (e.g. it's from the asteroid because that's what's being pushed against) then it's still in the asteroid-drum system. Torque is no more an inherently external force than force is - and you can get pretty far with angular mechanics by thinking of it as equivalent to linear mechanics with substituted terms, where torque basically acts as force, moment of inertia acts as mass, etc.

[Fat Rooster]

This is beginning to feel like one of those arguments where almost everybody is arguing the same thing, but thinks everyone else is arguing something different. Sorry Monomer, but I am afraid you are sounding pretty wrong though. You cannot convert energy to angular momentum. They are almost entirely independent. You can store energy in a flywheel, but the angular momentum is a side effect rather than inherently connected to the energy.

You seem to be missing Newton's 3rd law, which applies to torques just as much as forces. For every torque there is an equal and opposite torque on something else.

The Ceres-Drum system is closed as far as angular momentum is concerned, but not in terms of energy. Can we agree on that? You are perfectly fine putting some solar panels and radiators on the outside of it without significantly opening up the angular momentum.
You are free to put any amount of angular momentum into your drum, as long as you put the opposite amount into the rest of the asteroid to conserve angular momentum. This will probably not conserve energy, so that has to come from somewhere or go somewhere.

Ceres is already spinning once every 9 hours, and it is big. Your drum would have to be gigantic for any sort of significant difference in angular velocity to appear. It is not unreasonable to regard it as an infinite mass angular momentum sink, and only consider the Drum as an open system. You need to understand that you are doing this though, so when your model breaks down you know why.


Also, if you were wanting to affect the angular momentum of Ceres, it is surprisingly easy to do. Un-supported structures are possible on Ceres out to several thousand kilometres, and torque is proportional to distance. By carefully moving masses closer and further from Ceres you can use the tiny tidal differences to slowly affect the angular momentum however you want. Note that this does not violate conservation of angular momentum, because it is no longer closed. You are applying forces to the Sun, so you also need to consider the angular momentum in the orbit of Ceres (and I guess the angular momentum of the sun itself, but the effect on that should be insignificant I think). You will slightly affect the orbit, but can be done without throwing any mass around.

It is like how the tides are gradually pushing the moon further away. The tides obviously dissipate a lot of energy, and that energy has to come from somewhere. It is drawn from the Earth's spin, which is gradually slowing down. Then you have to ask what happens to the angular momentum? The spin of the earth cannot slow without that angular momentum going somewhere, and it goes into the orbit of the moon (along with a lot of energy). This occurs naturally, because energy likes to dissipate, but there is no reason we can't artificially drive the process in reverse.

[Arcane_Secrets]

How much force would it take for the earth to be knocked out of orbit, and would that shatter the planet? (I know nobody survives either way, but I'm just curious about the physics calculations here)?

[factotum]

How much force would it take for the earth to be knocked out of orbit, and would that shatter the planet? (I know nobody survives either way, but I'm just curious about the physics calculations here)?

You'll have to define what you mean by "out of orbit" here. You could slow the Earth in its tracks by 0.1mph and it would put it into a different orbit than it currently has. Also, how much force it would take depends over what time period you're applying it--a small force applied over a million years could have the same effect as a large one for 1 second.

[Lvl 2 Expert]

It doesn't require a set amount of force at all, it requires an amount of energy set by which new orbit you want to move it into. How much force you need to use to apply that energy depends on what method you're using, specifically how efficient it is and over how long a period it can apply force.

Trying to move the Earth by ramming Mercury into it will be deadly, moving Earth by arranging a close slingshot pass with Mars could be better, even though the force used is still large. (Although an interesting question there is how you got Mars or Mercury for that matter to move in the first place, giant rocket engines?) If you can find a way to use a ridiculously huge cleverly designed solar sail to slowly pull Earth outwards and forwards, the force doesn't need to be large at all, relatively speaking at least. W=J/s, power is energy divided by the time over which it is applied.

[factotum]

(Although an interesting question there is how you got Mars or Mercury for that matter to move in the first place, giant rocket engines?)

In the Larry Niven novel "A World Out of Time" they actually do this, only they don't think small--they use Uranus, the idea being that the mostly hydrogen atmosphere is a great fuel source. They basically fire off the rocket, which sinks deeper into the atmosphere, fills up with fresh fuel and then bobs back up to a high level where it can be fired off again--an absolutely enormous pulsejet engine designed to move a planet. They end up using the mobile planet to move Earth further from the Sun, which has been tipped over the edge into an early red giant stage by an enemy having dropped a planet into it...no idea how robust the science in any of that is, but it's a cool read!

[Arcane_Secrets]

You'll have to define what you mean by "out of orbit" here. You could slow the Earth in its tracks by 0.1mph and it would put it into a different orbit than it currently has. Also, how much force it would take depends over what time period you're applying it--a small force applied over a million years could have the same effect as a large one for 1 second.

I'll try and be clearer (and maybe this would be a different question). What I meant by "out of orbit" was to send the planet on a more or less straight line trajectory out of the solar system by collision with a second astronomical body (perhaps reaching escape velocity from the solar system would be a good way of putting this?). I'm not sure how to define how quickly such a collision would take place.

[factotum]

Well, to actually achieve solar escape velocity (which is what you're talking about here) you'd need to accelerate the Earth to around 42km/s. If the impact occurred directly along the vector of the Earth's orbit then that would require an additional 12km/s (Earth's orbit is already around 30), if it was in the opposite direction then you'd need 72. However, even the minimum value there is a significant number--it's higher than the Earth's own escape velocity (a smidgeon over 11 km/sec). There's a very special meaning for an amount of energy which is capable of accelerating every particle of a planet's mass to escape velocity--it's the gravitational binding energy of the planet, or the amount of energy you'd have to dump into the planet to completely destroy it (e.g. fling its entire mass outward so fast it doesn't ever fall back in). So, since you're talking about adding this much energy via a single impact, I am 100% certain that this would obliterate the Earth and everything on it.

[Fat Rooster]

I'll try and be clearer (and maybe this would be a different question). What I meant by "out of orbit" was to send the planet on a more or less straight line trajectory out of the solar system by collision with a second astronomical body (perhaps reaching escape velocity from the solar system would be a good way of putting this?). I'm not sure how to define how quickly such a collision would take place.

The planet would not survive such a collision. To see this consider how much energy is required. You would need to change the velocity of the earth by something like 20 km/s (estimate, can't remember true value). That means energy in the region of 200 MJ/kg, or 50x the mass in TNT. In total that means something around 10³³J. The total gravitational binding energy of earth is about 1/5th of that.

Momentum considerations are maybe an easier way to see it. Imagine playing snooker in a bath tub. To get a coloured ball out of the bathtub you need to hit the white with enough force that it would leave the bathtub if you missed. If the white were less massive than the coloured ball you would need to hit it harder still. For a collision to send a planet out of the solar system the object it collides with needs to be going at solar escape velocity already if it was similar size or smaller. Getting hit by anything at solar escape velocity is messy.

A close approach by a rampaging gas giant could fling earth off into deep space, but a collision would shatter the earth completely before it changed it's trajectory enough to escape the sun.


Beaten by Factotum, but what he said. His delta V number sounds more reasonable now that I think again.