stupid physics questions

[zip accident]

On a slightly related note, how does a rotating body in hydrostatic eqilibrium go from an oblate sphereoid such as Earth to a binodal elipsoid such as Huamea? I mean, I suppose "in a collision" means chaotically, but if in a simulation you could increase the speed of rotatioin of a body smoothly and fairly slowly, how would it go from the one shape to the other, and why?

[pogo]

This is from here?

https://en.wikipedia.org/wiki/Haumea

Reading that it seems we know little about it, so a lot of what’s written there is speculative or at least extrapolations from limited observations.

But to answer if it‘s in hydrostatic equilibrium (it’s unclear that it is) then it will take a shape which minimises gravitational potential energy. For a stationary object that’s a sphere but for a rotating one (including the Earth) it’s an oblate spheroid, the greater the rate of rotation the greater the degree of oblateness.

How it gets there is going to be largely guesswork. It could be the collision not only gave it a large amount of rotational energy but also broke it into many pieces so it came apart and reformed in its new shape. Or the collision generated a lot of heat energy that melted it and flowed into its new shape. Or it occurred early enough in its history that it was still quite molten from its initial formation. Until we get are able to take a good look at it we will probably never know.

[pogo]

Ah, I think I misread your question. Briefly the whole point of hydrostatic equilibrium is the body is large enough that it takes a spherical/oblate spherical shape. It will do so through gravity flattening anything that gets too big. As on Earth we have tall mountains but only so tall, only so steep. Smaller bodies with less gravity can have bigger mountains – Mons Olympus on Mars is bigger than any Earth mountain – but they still can’t get too big and if built up due to e.g. volcanic activity will collapse under their own weight.

[zip accident]

Ah, I think I misread your question. Briefly the whole point of hydrostatic equilibrium is the body is large enough that it takes a spherical/oblate spherical shape. It will do so through gravity flattening anything that gets too big. As on Earth we have tall mountains but only so tall, only so steep. Smaller bodies with less gravity can have bigger mountains – Mons Olympus on Mars is bigger than any Earth mountain – but they still can’t get too big and if built up due to e.g. volcanic activity will collapse under their own weight.

You missed it the second time too.

How does speeding up an oblate spheroid get you to this?



It's not a spheriod. It's not a cylindrical elipsoid either, which I thought it was before skimming Wikipedia before first posting about this. Do oblate spheroids start out with near ifinitesimal nodes? if not, how do the nodes arise?

[pogo]

You mean it’s not rotationally symmetric about its axis ? Those are not photos but guesses based on light curve observations. They may be out by a little or a lot; it could e.g. have non-uniform albedo which distorts results. Or it may not be in hydrostatic equilibrium. As I wrote what we know is based on very limited information. Until we get actual photos they really are estimates, and the article has many of them in the last paragraph of this section:

https://en.wikipedia.org/wiki/Haumea#Si ... omposition

[zip accident]

You mean it’s not rotationally symmetric about its axis ? Those are not photos but guesses based on light curve observations. They may be out by a little or a lot; it could e.g. have non-uniform albedo which distorts results. Or it may not be in hydrostatic equilibrium. As I wrote what we know is based on very limited information. Until we get actual photos they really are estimates, and the article has many of them in the last paragraph of this section:

https://en.wikipedia.org/wiki/Haumea#Si ... omposition

The rotational physics of deformable bodies predicts that over as little as a hundred days,[9] a body rotating as rapidly as Haumea will have been distorted into the equilibrium form of a scalene ellipsoid.

This is an educated guess, not a random guess.

If you don't like it, that's you, not the guess being less likely. If speeding it up enough will break it, and we're almost certain that's the case, then it has to develop nodes at some point. I'm asking when, and how, becausse it struck me as randomly interesting.

[pogo]

Then read up on rotational physics of deformable bodies, which sounds like a branch of fluid dynamics. Something I should know more about but skipped over when doing a maths degree and haven’t had much reason to look at since.

(deformable ? very much so, even solid rock can be deformed. Think e.g. of how the mountains of Earth were formed. Some were volcanic but many of the biggest ranges, such as the Himalayas, were simply pushed up as plates moved together and compressed and warped the surface of the Earth)

[gumboot]

Assuming day length increases linearly,

That might be the opposite of what I was assuming. Tidal drag looks an awful lot like it would decrease exponentially. The slower you turn, the less 'out of phase' the lumps induced are, and the less back-pressure they exert.

At some point that effect isn't really doing much of anything anymore. It actually completely fails to describe something you could call 'lock' because in isolation it never actually reaches a stable zero point.

So I'm assuming another force overwhelms it. Like a heavy spot, or something like that, which eventually turns around and points at Earth.

For a while I was thinking that maybe it's a simple pendulum equation. The duration of the last rotation being the one where the lump swings to 90 degrees and does flip around, contrasted with the next one where it's 89.999 degrees and it turns back the other way, never to flip again.

Apparently for regular pendulums on earth you can cancel most terms and the period is determined by the radius of the swing, which would make it the radius of the moon (supposing all mass irregularity is on the surface, which is wrong, but I'm doing it anyway), and the equation would be trivial, but I don't think any of that works when the pendulum is attached to a whole lot of mass not at the same radius.

Then, of course, there are other forces. Magnetism, and all that. Solar wind pressure. Tidal drag (again). I really don't know.

[pogo]

Assuming day length increases linearly,

That might be the opposite of what I was assuming. Tidal drag looks an awful lot like it would decrease exponentially. The slower you turn, the less 'out of phase' the lumps induced are, and the less back-pressure they exert.

You might be right. My assumption was done to make the math easier, not from even considering the factors that would affect it. The article only has the 15µs figure, doesn’t say how long it would take except to say it will take longer than the lifetime of the Earth which is not helpful. It might even be different for different bodies, e.g. between a solid body like the moon and a mostly liquid one like the Earth.

edit: looking at the WP article again for guidance and it has formulae but says:

The above formulae for the timescale of locking may be off by orders of magnitude,

Which suggests it’s still a field with more questions than answers. For one apart from the Earth we are probably unable to measure the various factors that need to be considered at all.

[gumboot]

It's not a spheriod. It's not a cylindrical elipsoid either, which I thought it was before skimming Wikipedia before first posting about this. Do oblate spheroids start out with near ifinitesimal nodes? if not, how do the nodes arise?

If they start out only a few inches apart (just the inevitable variations from an imperfect surface) and are driven apart by centripetal force, is there a limiting factor or would they eventually split in two?

Hmm. I ask that like I'm unaware that by spreading your mass from the axis of rotation you slow the rotation. Is that the limiting factor already? I think it probably is as I remember experimenting as a child and pulling up tight felt more difficult the tighter I pulled.

[pogo]

The maths of that is I think pretty straightforward. As you add rotational energy and the thing spins faster then it should get more oblate, something like a Skittle/Paracetamol. Yes, it would lose some speed also as it got wider, as its moment of inertia increased, but it would still get faster if a little more slowly.

Eventually it would reach a speed at which it would lose structural integrity and fly apart. Its rotation would reduce apparent gravity, so you felt lighter at the equator. The faster it goes the lighter you feel until you simply float away, along with everything else not tied down which would be all the loose matter (rocks, dust, etc.), any mountains just resting on the ground, whole chunks of crust if they are only resting against each other and so on. The precise rotational speed at which this happens is the escape velocity

The only problem is there’s no natural mechanism for accelerating a body like that. You can imagine a geological processes such as vents providing some rotational effect if not pointing up but their effect is tiny. The only way for it to happen is in collisions, and if a collision imparts enough rotational energy for it to fly apart it probably also imparts enough other energy to blast it into pieces anyway.

[Absolute_Zero]

Any non-pecuniary bets on LHC x 2 ??

Previously, I've successfully relied on Hawking® to provide the wrong answers, but he hasn't committed this time around [that I'm aware of].

Dark matter - head on block... NO.

Supersymmetry superpartners - would be neat and tidy... perhaps too neat and tidy

Extra dimensions - *shrug*

Left field - hope so

[F-ZeroOne]

I think I'm contractually obliged to suggest "Minovsky Particles"...?

[pogo]

I don’t think there is anything concrete like the Higgs boson that LHC will be looking for after its downtime and upgrade. That was and is the only undiscovered particle they expected to find with it.

Supersymmetry is a possibility but the problem with that is unlike the Higgs boson no-one expects it to be true – it’s only a theory. If they found something it would be great for the theory but the theory is so vague that if they don’t find anything it won’t invalidate it. The energies could just be too high for the LHC.

Apart from that who knows what they will find. Maybe nothing, and they will just put a higher bound on the lowest energy for supersymmetry and other speculative theories. They should collect more information on the Higgs boson, to more accurately measure its mass and other properties.

[Absolute_Zero]

Seeing as this has become, by default, the physics thread.

If the following stands and is shown to be exploitably practical, then it could become revolutionary for electron-ics... or rather, Weyltronics.

Weyl Fermions Found, a Quasiparticle That Acts Like a Massless Electron

What is a Weyl fermion?