Science a GoGo's Home Page Forums General Discussion General Science Discussion Forum Did Earth coalesce from 2 medium sized planets?

Hi Mike Kremer.

"You are saying that the earths increase in size was the reason as to why pre-Pangea opened up"

Yes, indeed.

"and slowly split into the various Continents as we know them today?"

No, the splitting was not slow. The splitting took place in a day or two.

There is a rather old theory called the "expanding Earth theory," first proposed by the Australian S. Warren Carey in the 1950's.

Carey considered many possibilities for his "expanding Earth theory," but he never considered an impact as the reason for it,.. probably because he believed the splitting of Pangaea took place over millions of years.

"To my way of thinking that means that Heaven must have hit pre-Earth diametrically opposite Pangea, as the best position to expand Earth, to enable it to crack and break up into our recognisable continents."

True. Consider this animated GIF:



The impact area is that within the circle.

Pangea (considered as a land area on PreEarth) is outside the circle.

"Have I got that right? I mean Heaven could not have crashed onto Pangea, or even close to it, else it would have obliterated it rather than have it expand apart."

Yes, indeed.

Arrg, screwed up my original posts. Here is the corrected version:

I see quite a few issues with your hypothesis:

1) I think you need to re-consider he forces involved in even the slowest of two ~0.5 earth masses coming together. You wouldn't have pangea being forced apart; you'd have total fragmentation of both bodies, leading to complete destruction of the both planets. Its not a matter of heat, or anything like that, but rather is a simple issue that even if the relative velocity of the two bodies is zero upon their contact, you still have two massive object whose centers of mass are separated by an enormous distance. Ergo, the potential energy is huge, and since the earth is only marginally elastic, that energy is not going to be absorbed nicely.

For example, using your model (and using the over simplification that mass is linearly equal to radius):

[note: for simplicity the "subscript" p-e = pre-earth, h = heaven, e = earth; so Mp-e would be mass of the pre-earth)

Mass:
Mp-e = 0.52(5.9736 × 10^24 kg) = 3.11 x 10^27 g
Mh = 0.48(5.9736 × 10^24 kg) = 2.87 x 10^27 g

Gravitational Energy
U=[G(Mp-e + Mh)]/R, where:
U = potential energy (joules)
G = gravitational constant
R = dist. between centers of gravity

U=[6.67x10^-11(3.11 x 10^27 + 2.87 x 10^27)]/(5200+4800)
U = 5.94 X 10^40J

To put that into perspective, the meteor that wiped out the dino's was though to have had ~10^23 joules, thats ~100,000,000,000,000,000 LESS energy than you situation without the planets being in relative motion to each other. In fact, I believe we're on par here with the collision that is though to have created the moon (and also melted the earth).

Even a slow closing speed ups the ante significantly - kinetic energy is a real bitch.


2) The other problem you have is that in your model the flow of surface material during the collision is inwards, not towards or away from the site of impact. This is due to the fact that surface area does not increase linearly with volume.

For simplicity I'll assume both the pre-earth and heaven have the same volume, that being 50% that of earth. I'll also ignore compression and assume that this means that the volume of the final planet will be the sum of the two starting volumes. I'm using this calculator:

http://www.calculatorsoup.com/calculators/geometry-solids/sphere.php

Volume earth = 1.052 X 10^12 m^3
Volume (p-e & h) = 0.5(1.052 X 10^12) = 0.526 X 10^12 m^3
SA (each) = 3.15 X 10^8 m^2

In contrast, earth is:
SAe: 5.00 X 10^8 m^2

What this means is upon merger, earth is missing ~26% of the surface area of the old pre-earth and heaven.

This means is you have a net flow of the surface *inwards*, as surface must be subducted to maintain a spherical shape as the new earth forms. This inwards flow will occur at the site of contact (assuming fluid bodies), meaning you'll loose land area in the region of contact, while (in theory) having little effect in the areas outside of the contact sites.

You may argue that upwelling of new material from the interior would force the plates apart, but keep in mind that in this merger you are putting an equal volume into a region containing much less surface area, meaning that there will be tremendous force keeping the surface where it is. Your proposed expansion of the surface runs, in fact, in complete opposition to what physics dictates will happen when you merge two smaller objects into one.

Assuming a perfectly fluidic impact, you'd end up with the heavenly and earthly continents (assuming they both faced away from the impact) pretty much where they were, while the surface area of the contact itself would now be in the interior.

3) I didn't go through all your numbers, but I think a molten earth is a given in this situation. You have two tremendous sources of heat - the initial collision, and the heat as the new earth compresses down to a smaller size.

4) Ignoring the "stationary earths" for a moment, there is yet another source of heat and mass destruction in your system - any closely passing heavenly bodies of the size you envision will exert tremendous tidal forces on each other. Not "oooh, look at the big wave" tidal forces, but rather "holy s..t, who ripped north america in half" tidal forces. Assuming a close pass or two before collision (your model, I believe), the surface would be slice-and-diced into oblivion, long before the collision, which'll destroy whatever is left.

Bryan

EDIT:
Upon re-reading what I wrote, I realize point #2 is not totally clear.

That would only occur if the two planets made of a fluid were to come together, and only then, if they came together gently enough to allow a merger without significant "trauma". This could only occur if there was essentially zero velocity of collision, and something "held back" the planets so their gravity didn't accelerate them together at incredible speed.

The more "realistic" action should this pre-earth and heaven come together, even if they had a collision velocity of zero, would be rapid acceleration of the two bodies together (thanks to gravity), resulting in massive waves rushing around the two spheres, all kinds of distortions, leading to a quite traumatic merger. Since the surface of the earth isn't exactly flexible, those waves would pulverize the crust.

Bryan

I have had one geophysicist (professor from Monash University) state that the mathematics in the paper appeared to be correct.

Also, I am a Mathematician. PhD from UNSW, Australia.

When I get a chance, I will review your figures.

I would suggest that you actually read (and understand) the calculations in the paper. They were done to show you how these things are calculated and to save you the trouble of doing them yourself. But if you enjoy checking things, go for it.

The first thing to note is that your formula for the gravitational potential energy is wrong.

It should be U=[G(Mp-e * Mh)]/R

If you use the correct formula to obtain the potential energy and use it as an estimate for the kinetic energy, you are assuming that Heaven fell to PreEarth from infinitely far off.

So your estimate of the kinetic energy is the largest possible and thus not very realistic.

Also, you have mixed different systems of units. For example, you have R in kilometers and the masses in grams.

Also, G = 6.67428e-11 m^3/(kg s^2) has units meters, seconds and kilograms (not grams).

Note that G = 6.67428e-20 km^3/(kg s^2).

Also, any calculation after the collision begins (from when the planets touched) that uses point masses, will be completely wrong. So you can't do that.

Let me emphasize that no part of Pangaea was obliterated by the impact.

A circular cap region of crust on PreEarth was obliterated.

Heaven was completely submerged into PreEarth (causing the expansion).

Pangaea was the surviving region, that is, the region exterior to this circular cap.

Have another look at this animated GIF:



The impact area was that within the circle.

Pangaea (considered as a land area on PreEarth) was outside the circle.

When Pangaea (considered as a land area on PreEarth) is mapped from the sphere of PreEarth to a flat map, you get exactly the map of the first graphic way above. In fact, that is how this map was first produced.

The reason that standard maps of Pangaea are essentially circular is because they represents a sphere with a circular cap region cut from it.

Clearly, a sphere missing a circular cap explains why Pangaea was though to be concentrated on one side of Earth with ocean on the other (which is a very problematic unbalanced arrangement).

And, of course, splits in landmass (the Tethys Ocean and Bering Strait) had to be included in the standard maps of Pangaea to account for the map makers use of the wrong radius (Earth's instead of PreEarth's).

Here is a standard map of Pangaea



The expansion in size of PreEarth after swallowing Heaven, caused Pangaea to spilt apart and break up into what we now call continents.

The circular region where Heaven entered is now called the Pacific Ocean (not all the Pacific, but most of it).

A few thoughts.



If the moon was already there before heaven hit:

Why didn't the moon crash into Heaven? Heaven would have been rotating with the pre-Earth to have crashed so precisely, but the moon would presumably have had a different speed.

Why does the composition of the moon material match that of the current earth? Surely it should be either random, or match the pre-earth composition.




If the moon wasn't there:

If the giant impact hypothesis is correct, then that would have smashed up all the lovely continents.

Pangea was supposed to have existed a couple of hundred million years ago, much younger than the supposed 4.5 billion year old moon.

Let me more accurately state what I meant - I looked over your arguments, and while I did not check to make sure you math was correct, I do understand what you have calculated. More to the point, I agree that you've accurately taken into account some of the forces involved in a planetary merger, assuming of course:

1) That you did preform those calculations accurately, and
2) That you used the correct methods to come to your results

What I noticed though, while reading through your work, is you ignored/missed the single greatest source of energy in your system - the actual gravitational potential energy between the two masses (plus any kinetic energy in the system, which to be nice, I pretended was zero). You also missed/ignored the effect the SA:V ratio changes would have on your model.



I used the correct formula in my calcs, but I see that I used a plus sign in the formula I typed out. I'll own upto that mistake, but you do realize had I used the formula as I wrote it (rather than the correct one) that I would have come up with a gravitational potential energy many orders of magnitude less than the true value.

My typo does you no favours.

If you run the numbers, using the correct formula, you'll see that the 10^40J number I have is correct (ignoring my other mistake, which you identified; more on that later).



And since I did no such thing, your point is moot. Firstly, the value for potential energy I calculated was calculated assuming a separation equal to the sum of the planets radi, as in what the separation of the planets centers of mass would be if the planets surfaces were just barely touching - not infinite separation as you claim. I also assumed no initial movement (ergo, zero kinetic energy).

However, that potential gravitational energy has to go somewhere - the first law of thermodynamics dictates that. In the case of a collision that energy can go into three places - heat (due to friction during impact, largely from friction generated during the elastic movements of the planets crust and mantel), kinetic energy of ejecta, and "residual" potential energy due to the fact we cannot coalesce the matter into a point mass.



You need to go back, look at that formula, and use your mathematician skills to figure out what was actually calculated - it wasn't kinetic energy. Firstly, as I made eminently clear in my first post kinetic energy was zero in the situation I presented. I did not maximize it - to the contrary I did the polar opposite and created a situation where kinetic energy was ZERO at the starting point. A condition I would point out, that is a physical impossibility. There should be some kinetic energy in the system, on top of the gravitational potential energy.

What I did calculate was the gravitational potential energy; as in the amount of potential energy created between two objects, separated by a finite distance, by the gravitational attraction of their two masses. A portion of that potential energy will be converted into kinetic energy, some will be "consumed" in elastic interactions (i.e. the energy which distorts the actual masses), etc. But in the end, once everything settles down, most of that potential energy will be "consumed" by friction and converted into heat*

*with the exception of any ejecta; which will carry away some of that potential energy in the form of kinetic energy



100% my bad, and in this case I did not convert everything within the formulas when I ran the numbers. But once again, you're not doing your model any favours here. Using the correct units:

Mp-e = 3.11 × 10^24 kg
Mh = 2.87 x 10^24 kg
G = 6.67428e-11 m^3/(kg s^2)
R = [(5200km+4800km)*1000] = 10000000m

U=-[6.67428e-11(3.11 X 10^24 * 2.87 X 10^24)]/10000000
U=-[6.67428e-11(8.93 X 10^48)]/10000000
U=-5.95 X 10^31 joules

A lot lower than my first screwed up number, but it is still an energy ~100,000,000 - that is ONE HUNDRED MILLION - times greater than the asteroid that killed off the dino's.

EDIT: upon more reading, specifically of:
http://www.nature.com/nature/journal/v412/n6848/full/412708a0.html

and the references therein, it turns out I was also wrong about the impact that created the moon. It may have had an energy of "just" 10^26 J, well below the correct number for your system (and "only" a few thousand times that of Chicxulub). The higher estimates put the impact into the 10^29 joule range; still a few orders of magnitude lower than your hypothetical situation.

Quite interestingly, the impact that created the moon has some similarities to the one you envision - notably that the impact velocity is quite low (15m/s-ish). The similarities end there - the moon was a glancing blow, leading to most of the impact energy being "absorbed" in the form of the kinetic energy of the ejecta. Your system requires all of the energy to be absorbed by the earth, essentially as friction, ergo, absorbed as heat.



Nice try to weasel out; but without proof you do not have a counter-argument.

And to be blunt, you are 100% wrong with your claim vis-a-vis point masses. When talking about spherical objects of uniform density, the lower potential energy of the mass that falls between the two centers of mass is countered by the higher potential energy of the mass which is in opposition to the centers of mass. Ergo, when talking about uniform spherical objects, point masses do indeed accurately calculate the gravitational potential energy between the two objects, upto the point of contact.

Obviously, there are some assumptions in there - planets are rarely perfect spheres, nor of uniform density. But those facts don't help your model either. The obliqueness of planets is generally so low that they can be treated as spherical - at worst obliqueness would skew the potential energy a few tenths of a percent higher or lower (depending on the orientation of impact). The uneven density actually works against your model, as planets tend to have higher density in their centers. What this means is upon contact the potential energy is higher than in the point-mass assumption, due to the fact that a larger portion of the mass is located higher above the contact point then there would be if the mass was equally distributed.

Planets also tend to have angular momentum - i.e. they spin. I've completely ignored this energy to this point, but that also is a source of energy you have not accounted for.

Where my calculations do fall short - and I freely admit this - is that a portion of the potential energy that exists between the two objects will remain potential energy after the merger, since not all of the matter can coalesce to a single point. But even there you're talking about a few tens of percents of the total potential energy - a far cry from the magnitudes of order of excess energy you've failed to take into account. In plain English, something like 30-60% of the potential energy of the two masses will remain potential energy after impact. But to not completely melt the surface you need to "get rid" of 99.9999% (give or take a few points past the decimal) of the impact energy. And not melting the surface is the least of your problems; even if you get rid of 99.99999% of the total energy you're still going to pulverize the surface to the point where no continents will be left.

-----------------------------------
I'd also point out that you've not responded to the volume/surface area issue, which is an equally big thorn in the side of your model. You have not taken into account the fact that the surface area of the final planet will be less than the combined surface area of the two starting planets. Ergo, you are missing a huge contractile force in your calculations. 26% of the combined surface area will disappear upon the merger, without taking that into account your calculations are meaningless.

Bryan

all of this is unnecesarry , how could two orbiting planets
collide.

because if one planet gets closer for some reason the other would get further away.

there would have to be a third planet that strikes one of the orbiting planets and slows its orbit.

it cannot be just two planets that are already locked into a
central gravity system and orbiting each other because of the gravity between them.

Hopefully someone with a better understanding of astronomy will pipe in, but I believe even a collision with the moon wouldn't be end of the problems derived from having a moon.

I believe (this is where we need a real astronomer) that most cases where you have 3 bodies in close proximity like you would in this hypothetical case, that one body (usually the smaller one) is usually ejected from the system.

So there is another question to add to the ones I had before; if the moon was there before, why didn't it:

a) collide with heaven (or pre-earth), thus FUBARing the whole thing, or
b) get ejected from the system, as bodies tend to be during these kinds of close orbital interactions?

Bryan

Yeah, but it is fun. It's why I've come to this forum - I love science, love to debate science, and the people here seem to be above-par compared to other forums I checked out before deciding to come here.



Happened all the time while our solar system was forming. If in separate orbits gravitational tugs from the larger planets (or even a close pass or impact by a smaller one) could create a situation where there would be an impact.

Another possibility is what is thought to have happened in the case of the moon. The moon is thought to have accreated in the earths L4 or L5 point. This co-orbital position is stable until the smaller partner gets to be ~10% of the mass of the larger. At this point the orbit is no longer stable, the smaller mass slips out of the L-point and, according the the papers I read, a collision is now inevitable due to the closely spaced, but now separate, orbits.

Finally, if you had two planets in the same solar orbit, with the two planets orbiting a common center of mass, I think a collision would also be inevitable. Tidal forces would cause the two planets to spiral outwards from each other, until eventually one escaped into an independent orbit. Alternatively (or perhaps more likely) gravitational tugs from the sun and other large planets (Jupiter?) would eventually disrupt the system. Once disrupted its only a matter of time until the new solar orbit crosses the old - wham, bam, thankyou mam!




???how do you figure, that opposite of how gravity normally works???



As I said above, tidal forces and/or tugs from other masses in the solar system can break apart such systems. Once again, we need a real astronomer to comment, but I believe such co-orbits are fundamentally unstable; especially when the co-orbiting pairs are in orbit around a much larger mass (i.e. the sun).

Bryan

if the earth collided with another similar sized and massed object , the entire earths crust would melt.

depending on the velocity of each planet the mass would not just stop as they each reach what is the new center of gravity , the two masses would continue to move in the same direction and buldge outwards before they are pulled back in by the newly forming planets gravity.

etc.etc.etc.

this would occur for a few thousand years I would think as the new planet attains its new shape.

too much heat for what we call and know as life.

so the crust on the opposite side of the earth would first be pushed out a great distance then fall back or be pulled underneath the magma of the newly forming planet.

there would be no life on the earth or the other planet.

except any life that could survive inside magma !

after all the only reason the two orbit each other is the
center of gravity between them.

if that center changes then they change to adjust , if one moves closer to the other for some reason the center of gravity changes so the other will adjust --move further away.

and that is not opposite how gravity works it is exactly how gravity works.

the earth and its moon are orbiting around a mutual center of gravity.
even our moon causes our planet to increase and decrease its solar orbital path every time the moon orbits the earth.

if our moon leaves us , then the earths orbit would no longer wobble around our sun.

My bad, I mis-interpreted what you wrote as the gravity acting in some sort of repulsive fashion. You had not (at that point, anyhow) specified they were orbiting a common center of gravity.

But, as I stated in my last post, I do not believe that these types of orbits are stable with objects of similar mass. Even in the earth/moon situation tidal forces are causing the moon to recede from the earth. I do not believe this will ever reach the point where the moon can escape the earths gravity, but in the hypothetical situation the OP brings up, there probably is sufficient angular motion in the rotation of the two bodies (assuming 24 hour-ish days) to propel the bodies out of their co-orbit around their common center of mass, into two separate orbits around the sun.

As I said earlier, we really need a real astronomer to come by and clear the orbital stuff up...

Bryan

I totally agree. I think he calculated it for the objects being gently placed right next to each other, then let go. But even that sounds like a spectacular release of energy in what's effectively liquid blobs.

Sorry, but you do, do such a thing.

You are implicitly assuming that the loss of potential energy is countered by a gain in kinetic energy.

The potential energy you calculated is that lost in the planet coming from infinitely far off to where the planets surfaces were just touching. This is by the DEFINITION of potential energy.

This loss in potential energy gives the gain in kinetic energy, WHEN the planet has come from infinitely far off to where the planets surfaces were just barely touching.

By the way, are you a high school student or undergrad?



Nice try to weasel out; but you have simply restated what I said.

I said: any calculation after the collision begins (from when the planets touched) that uses point masses, will be completely wrong (and although unsaid, it is true that point masses do indeed accurately calculate the gravitational potential energy between the two spherical objects where their density depends only on the distance from the center).

You said: point masses do indeed accurately calculate the gravitational potential energy between the two objects, up to the point of contact.

Which is exactly the same thing.



I thought you would have figured this for yourself;

The entire surface of Heaven disappeared INTO PreEarth.

So, 100% of the surface area of Heaven is missing.

The surface area of PreEarth is dealt with as in the paper.

These are quick replies. Unfortunately, I do not have time for more at the moment.

Try re-reading what I wrote - I specifically stated that was not my assumption. I think you need to go back and read up on your basic forces, energies and how they relate to work. At the point of contact there is an enormous amount of potential energy due to the gravitational attraction between the two planets. A significant portion of that energy will be released as varying forms of work during the impact. Kinetic energy is but one source of that work; it is hardly the only one.

Your pretending that is not the case defies both basic physics, and basic logic.



Once again, you're 100% incorrect. The real definition of potential energy is:

"energy stored within a physical system as a result of the position or configuration of the different parts of that system."

As for gravitational potential energy:
"a stored energy determined by an object's position in a gravitational field"

Strange, how you come up with correct answers when you use the correct definitions.



Absolutely 100% wrong. The gravitational potential energy is simply the amount of energy available for work, due to the separation of mass. Work is not kinetic energy. Kinetic energy is but one form of energy through which potential energy can be "converted" inorder to preform work. However, it is not the only one. In the case of an impact you will generate elastic energy (largely in the form of waves and distortion of the impacting planets), pressure energy (in the fairly obvious form of having material squeezed between 2 masses of 0.5 earths), as well as kinetic energy (due to the acceleration of the masses themselves).

All of those, not just the kinetic energy, are forms of energy/work that gravitational potential energy will be converted into. The combination of those is not taken into account by your model.



LOL, insults I see. I guess we know just how strong your legitimate arguments are.

But since we're using insults now, lets just say I find your statement quite ironic, coming from someone who apparently missed the highschool physics class where they teach you that kinetic energy is not the only vehicle available for converting potential energy into work...



And this claim is still wrong. The amount of potential energy available at the time of contact between the two objects will be accurately calculated using point masses. That potential energy doesn't magically disappear once impact begins; instead it is converted into other forms of energy which conduct work on the system.

Whining that the events post-collision cannot be accurately predicted by point masses DOES NOT MAGICALLY MAKE THAT POTENTIAL ENERGY DISAPPEAR. It is still there, in all its glory - being absorbed in the form of elastic, pressure and kinetic energy; all of which will eventually be turned into heat.



I didn't figure that out by myself because, to be blunt, its an idea too stupid to have given thought to. How exactly do you propose that two objects comprised of incompressible viscous fluid (magma) would merge in such a fashion? Its defies the basic laws of fluid dynamics; especially the ones regarding surface tension.

Unless you're proposing that the planets are made of perfect fluids, or have indestructible crusts...both of which are laughable options at best.

========================================
I have a proposal for you, since you seem set on ignoring the well-though out counter arguments of those of us on this board - put your money where your mouth is. Every year I write up my work and send it to scientific journals, where it is reviewed by experts in my field, and (with luck) published.

Why don't you do the same? Write it up, send it into a geology or astronomy journal, and see what the experts in the field think. I'll bet you dollars to doughnuts that the exact same issues brought up here - especially the issue of where does all that potential energy go - will be brought up by them as well.

A bit of advice though, if you choose to do this - get rid of the religious terminology. Scientists tend to frown on the use of religious terminology in scientific works.

Bryan

No, it wasn't meant as an insult.

Your level of knowledge indicates a talented high school student or undergrad.

You certainly don't know/understand enough to be a grad.