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# Updated: I Need Math Help: How do I find the info needed and what formula do I use to figure this fluid physics and astronomy question with? Answered

### Finally, I have been given the source of the "info" the fellow talking to me, was drawing from:

It can be found here:   Hydroplate 'theory'

Ok, here is my problem.   I have been presented with, what at first sounds like a totally ludicrous concept, but in order to prove or disprove it, I need to have some math backing that I don't have in my head (nor in my experience).

I need the approximate mass of the asteroids in the belt.   And also I need the distance to the belt.
I will also need to figure how much pressure it would take to force a  column of water skyward at escape velocity, equal to that mass.

And if there is a way to give a simple explanation for the math, that would be apreciated also :-)

?

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## Comments

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Umm, did you need an answer real quick to save the world?

Um, no quite the opposite.   It has been posited that the asteroid belt is actually "spew" from a cracked earth, that slammed back together, and sent tremendous amounts of water skyward with such force that it created the asteroid belt.    Besides how far fetched this sounds, I wanted to see if there was a simple way to show this just can not be.

But the asteroids are not ice so you have to take into account something else being propelled into space besides water.

IIRC they are mostly ice, but I would have to look into that too later.

The asteroid belt is a mix of rock and iron - if there is any water, it is only as traces of frost in deep craters.

The closest orbital ice is found in the rings and moons of gas giants.

Other than that, you're looking at comets, which are mainly found in the Oort Cloud, wa-a-a-a-y too far away to be "splashed" water.

also, I would still like to understand whether or not it is possible for a volcanic / tectonic incident to actually project water to escape velocity....seems a bit over the top to me.

I don't know numbers, but large impacts (mass-extinction-sized) can certainly throw large ejecta (including masses of water if the impact is at sea) into sub-orbital trajectories, and we find small meteorites on Earth from Mars.

I also heard that super-volcanoes (like the one lurking under Yellowstone) can throw stuff to the top of the atmosphere.
So, I guess the answer would be...

Yes, terrestrial events could throw water into space, but...

No, any water that happened to would not end up as comets.  It would (quickly or slowly) end up back on Earth.

The comets aren't from any planet.  They're older than (most of?) the planets, debris from the original dust-cloud that spawned our Solar System.  If anything, the planets are from the comets...

Not sure, buuut, would it send up millions/billions of droplets of water that wouldn't be that big (comet sized) when they left our atmosphere? Or would the water stay together in places to make large lumps of ice when it reaches orbit?

The biggest problem I thought it had, was that the "tube effect" Kelsey mentions, is the "crust of the earth", and so once the water leaves the end of the "tube", it essentially has no "pressure" behind it.  Thus the needed force to propel it past orbit, would have to be supplied before it left the crust....and would need to be extremely large.....

The only thing that I could thing possibly big enough could be two planets colliding, so, it's possible to get enough speed up, but it would probably end up as spray.

Well, the postulation is that the entire crust of the earth is putting it's weight to bear on the water, when the fissure appears.   Like poking a hole in a balloon makes an "explosion" of sorts.

Where is this "balloon theory" coming from?!

L

Well, it isn't so much a "balloon" theory, as a water "postulation"  (called the hydroplate theory)

I am still hesitant to give out the site (the fellow finally revealed to me where he was getting his info from), for fear of a name calling session starting.

I have more then a few doubts about this whole thing myself, and so wanted to be able to present strictly information to the guy, without his feeling threatened (I am not in communication with the author of this, the fellow I am speaking of and to is in my meeting).

If I can be assured that only information will be forwarded here, so I can communicate to my acquaintance just facts, I will post the site's addy.

Here is one comment from someone that doesn't adhere to this theory, but likes the methods used:  "(The) theory is a rare example of a creationist actually trying to formulate a scientific theory." - Joyce Arthur

To put it differently, why does someone think this? What is the basis for the postulate?

L

Promise not to make prejudgement?    I mean, I see some problems with his overall theory. Tthose raised in the past for this agenda, have never gone to the lengths this fellow has gone to try to fit something into what he feels happened.  He is looking to explain a possible world wide flood situation.

It's usually the religiously convinced that try to collate evidence that such an event happened. I'm curious as to why the guy wants a theory other than God. Big flood, then the extra water gets blasted into outer space?!
Floods have explanations already, he'd need to explain why those aren't good enough first.

L

I don't think he is trying to say "other then God", but rather  trying to make this event, scientifically acknowledgeable (acceptable?).
He still has to find ways to demonstrate that there is evidence of a flood worldwide, but other then that, he makes a few good points. Still, there are a lot of things about it that bother me.  I don't have the ability to pinpoint them, but some things just don't feel right. And I am still not certain why, as a physicist, he'd use "inaccurate math" if this is what he's done.

As for "floods" having explanations already,  this one flood has this as it's main source of water:  "and the fountains of the great deep, burst forth".  This is what he is attempting to explain.

Oh right, so he's trying to counter something made-up with something else made-up?
A correct approach is to start with some evidence and try to explain that. He needs to establish that the event actually occurred, and work from what evidence supports that. Guessing, is not a good starting position.

L

Presumption that it is full of hot air or you can't hold a candle to it?

no,  not hot air,  hot water  :-)

Bam!
(Wit where it was needed, thanks)

L

A big lump with spray, I think.

That's what I thought.

Thanks.   I wanted to get all the unbiased facts about this scenareo presented to me before making any comments about the real reason the person thought that masses of water would reach escape velocity and become independant of our planet.   In fact, it is probably best if we don't go there :-)

I'm going to guess that a rainbow gets involved in the scenario...

Yes, sadly.   And I do thank you all for the unbiased help in making this clear to both myself and the person I will be forwarding this info to.   I hope he takes it well :-)

If your acquaintance fancies a more varied audience, he could try here, although it is only open UK office hours.

I have the feeling that, the person I am going to be talking to on Sunday, has two backgrounds only, one - medical as he is a male registered licensed nurse, and two - extensive experience in current day Sci-Fi movies showing fantastic things happening that defy physics (not to mention logic).

The originator of the idea, I will have no contact with however.  I am not sure where he even lives.
Yes, thanks...I think the fellow meant comets.

The asteroids are mostly rock -- the larger ones are differentiated iron-core bodies, the smaller ones are either solid silicate rocks (e.g., "basalt" or analogous material) or are loose collections of rubble barely held together by their gravity.

Comets are mostly ice.  Cometary bodies are mainly found in the Kuiper belt (around Pluto's distance) and in the inner and outer Oort clouds (much farther away).

There are a small number of so-called "Main Belt comets", cometary bodies in orbits near or partof the asteroid belt.  These are most likely Kuiper belt objects which were perturbed by the gas giants during passage through the inner solar system, and left in asteroidal orbits as a result.

Yes I think the fellow meant comets.   Since there is, as he put it, so much controversy around their formation, he was putting forth his own postulation.

I would like to show him whether or not it is even possible to project that amount of water skyward at such a speed as to even just escape our atmosphere.

There is essentially no actual controversy about the formation of the Solar System or its components.

The basic (arm-waving) mechanism has been known since Laplace -- condensation and fragmentatoin from a rotating cloud/disk of gas and dust.  Differentiation of that disk as a function of distance from the central star is a trivial consequence of temperature and angular momentum.

There is lots of lively debate about the details within that model, as is true of every field of scientific research.  None of that debate means that there is any controversy about the overall structure or the physics involved.

As always, crackpots and those with a politico-religious agenda will latch onto disagreement over details, and conflate them (stupidly or maliciously, take your pick) with uncertainty about the underlying science.  This is true of evolution; anthropogenic climate change; origins of life, the Universe and everything; relativity and quantum mechanics; take your pick.

None of that debate means that there is any controversy about the overall structure or the physics involved.

It wasn't the physics involved that he questioned, just some of the methods; trying to squeeze physical things to do things that were a little more than realistic.  But, yes I do agree that this was a doomed idea from the start, I just needed a sound way to explain that :-)

The math is pretty simple algebra; I outlined the procedure in another comment, but left out some steps.  Here's another go.  First, we'll ignore the 1g force holding the water down to the planet; that's going to be small compared to the force of the jet shooting upward at escape velocity :-).

Start with the basic equations.

• F = m a (assume constant acceleration)
• vfinal - vinitial = a dt (dt = time duration)

Using vinitial=0 and rearranging terms, a = vfinal/dt .

Let's treat the problem like a hose or a pipe pointed upward, with a height H and cross-sectional area A. As long as the water is in the pipe, it's under pressure and experiencing acceleration. Once it leaves the pipe the pressure is zero (effectively), so there's no force pushing it upward. You need enough pressure at the bottom of the pipe, where v=0, to reach escape velocity vesc (=11.2 km/s) at the top.

The average velocity is half the final, so the water spends a time

dt = H/(vesc/2) = 2H/vesc

inside the pipe. Plug this in for the acceleration, and you get

a = vesc / (2H/vesc)
= vesc2 / 2H

The mass of water in the pipe, m = d A H, where d is the density of water. Pressure p = F/A (or F = p A), so we can now re-write Newton's equation in terms of the quantities you care about:

F = m a
p A = d A H * vesc2 / 2H
p = d vesc2 / 2

This is an interesting, and non-trivial, result. The pressure you need depends only on the final (escape) velocity, provided the pressure stays constant! It doesn't matter how deep you push the water from, or how big the pipe is.

Now lets plug in numbers.

• d = 1000 kg/m3
• vesc = 11,200 m/s, so
• p = 1000 * 11200 * 11200 / 2
= 62.72E+09 kg m-1 s-2
or nearly 63 gigapascals (GPa).

For comparison the pressure at the mantle-core boundary is about 130 GPa. However, there's obviously not large cavities filled with water at the mantle-core boundary (seismic wave analysis, common sense).

If you want to find a (hypothetical) reservoir of water to shoot into space, you'll need to look in the crust, not the mantle.

The pressure in the crust can be computed simply from the overburden (mass of rock above where you're measuring). The crust-mantle boundary is about 50 km below the surface. The crust is mostly basalt with a density of 2.7 g/cm^3 (2.7 times the density of water). So the maximum density you'll find is 2700 kg/m^3 * 50000 m, or 135 MPa. That's a factor of 200 lower than you need to reach escape velocity.

Sorry, but this reminds me of the first day of Physics 101 in college.  Class was after lunch on a nice bright and warm autumn day, Professor walked in, turned his back to the class and started scribbling on the blackboard, did the same derivation, mumbled something along the way, and took two hours to do what you have summarized above without turning around, said that we will be quizzed next week, go read chapters 1-10 and left.  So without the advantage of other people in the class that had pre-calc, I think my brain went into overload and passed out somewhere mid-point in his ramblings.  I looked at my notes later and could actually see where I was trying to copy all the notes off the board and then my pen flatlined with a stroke of ink running off the edge of the page.

I don't think I was the same after that...

I don't think I was the same after that... Ah, so that explains the plushies....

No, that only explains a lot of failure of the educational system in many aspects and how an institution of higher learning can charge you an outrageous sum irregardless of their ability to teach something.

I had an algebra teacher like that in the 9th grade.....totally messed my math understanding until rather recently.   I can do "normal" math in my head, multiplication, division, fractions, percentages, etc. and that comes in useful since so many store clerks still can not operate a cash register correctly.

But, every time I pick up the Simple Algebra book I bought and try to work through the old problems,  I get stuck as soon as I get to Quadratic equations.... *sigh*  mental block I think

I guess we both went to the School of Hard Knocks.

Yeah, I know a lot of people that went there :-)

Over here they like to aim for overseas students (\$\$\$) - regardless of a student's ability to learn something. Them who care (domestic) usually check the course/institution before applying.

L

Yes, foreign students do have to pay in full with cash up front.  My class seemed to be filled with foreign nationals who were there to evade their home countries required military service.   I could not get in those established cliques that worked the system and seemed to throw the test curves off.   And in the days before the internet to help make a choice, it was harder to discern reviews of a school where it had an established reputation in name.  All I can say is I survived and will chalk it up to experience.

A friend of mine lived in a block with the son of someone rather big in Taiwan. He got a lot of gifts, but ended-up helping him out with a lot of the course (and sourcing pornography...).
Good for your experience anyway.

L

Ok,  I made a small mistake, and so I don't know if this makes a difference or not, but the fellow postulates that there was a layer of water just under the crust, and that the ensuing crack I described, allowed for the release of the tremendous pressure that would have been on that water out through the crack.   Assuming that there was such a layer of water, would this demand a different set of equations, or do they still apply, even under the new "circumstance"?

.  Since the asteroids are made primarily of rock and metal, it doesn't matter.
.  And it's still going to take X amount of power to move that much mass that far.

This was given me as the "reason" for water on the moon.

They still apply.  The "water" (uh, huh; this is pure Velikovsky) would be under exactly the pressure of the overlying rock of the crust, which I computed above; about 135 MPa.

Got cha......that is what I thought...but my algebra is really rusty, so my understanding was a bit limited...but that is what I THOUGHT you had said in that post.  Thanks again.

This is exactly what I was looking for.   Thank you SO much for all your effort in this.  I appreciate it more then you can know.

I didn't want to (and am still reticent about) reveal(ing)  the purpose the person had in creating this odd circumstance, although, you may have an inkling after reading all the posts here :-)    It appeared to me that the person was reaching to far (grasping for straws), in this case.

# THANKS AGAIN!

Smells like a YEC to me (but see above for an even crack-pottier crowd).